View source for Maximum triangle path sum

{{task}}

Starting from the top of a pyramid of numbers like this, you can walk down going one step on the right or on the left, until you reach the bottom row:
<pre>
                          55
                        94 48
                       95 30 96
                     77 71 26 67
</pre>

One of such walks is 55 - 94 - 30 - 26. 
You can compute the total of the numbers you have seen in such walk, 
in this case it's 205.

Your problem is to find the maximum total among all possible paths from the top to the bottom row of the triangle. In the little example above it's 321.


;Task:
Find the maximum total in the triangle below:
<pre>
                          55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
</pre>

Such numbers can be included in the solution code, or read from a "triangle.txt" file.

This task is derived from the [http://projecteuler.net/problem=18 Euler Problem #18].
<br><br>

=={{header|11l}}==
{{trans|Python}}

<syntaxhighlight lang="11l">F solve(&tri)
   L tri.len > 1
      V t0 = tri.pop()
      V t1 = tri.pop()
      tri.append(enumerate(t1).map((i, t) -> max(@t0[i], @t0[i + 1]) + t))
   R tri[0][0]

V data = ‘                55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93’

print(solve(&data.split("\n").map(row -> row.split(‘ ’, group_delimiters' 1B).map(Int))))</syntaxhighlight>

{{out}}
<pre>
1320
</pre>

=={{header|360 Assembly}}==
<syntaxhighlight lang="360asm">*        Maximum triangle path sum - 28/04/2023
MAXTRIA  CSECT
         USING  MAXTRIA,R13        base register
         B      72(R15)            skip savearea
         DC     17F'0'             savearea
         SAVE   (14,12)            save previous context
         ST     R13,4(R15)         link backward
         ST     R15,8(R13)         link forward
         LR     R13,R15            set addressability         
         LA     R9,1               k=1
         LA     R6,1               i=1 
       DO WHILE=(CH,R6,LE,=AL2(N)) do i=1 to hbound(t)
         LR     R1,R6                i
         BCTR   R1,0                 -1
         MH     R1,=AL2(X)           *x
         LA     R14,T(R1)            @t(i)
         MVC    C,0(R14)             c=t(i)
         LA     R7,1                 j=1 
       DO WHILE=(CR,R7,LE,R9)        do j=1 to k
         MVC    CC,C                   cc=substr(c,1,2)
         MVC    XDEC,=CL12' '          clear
         MVC    XDEC(L'CC),CC          cc
         XDECI  R2,XDEC                r2=int(cc)
         LR     R1,R9                  k
         BCTR   R1,0                   -1
         MH     R1,=AL2(N)             *n
         LR     R0,R7                  j
         BCTR   R0,0                   -1
         AR     R1,R0                  (k-1)*n+(j-1) 
         SLA    R1,1                   *2 (H)
         STH    R2,MM(R1)              m(k,j)=xdeci(substr(c,1,2),2)
         LA     R10,X                  l=length(c)
       DO WHILE=(CH,R10,GE,=AL2(1))    do l=length(c) to 1 by -1
         LA     R14,C-1                  @c-1
         AR     R14,R10                  +l
         MVC    CL,0(R14)                cl=substr(c,l,1)
       IF   CLI,CL,NE,C' ' THEN            if substr(c,l,1)^=' ' then
         B      LEAVEL                     leave l
       ENDIF    ,                        endif
         BCTR   R10,0                    l--
       ENDDO    ,                      enddo l
LEAVEL   EQU    *
       IF    CH,R10,GT,=AL2(4) THEN    if l>4 then
         LR     R5,R10                   l
         SH     R5,=H'3'                 l-3   (mvcl source length)
         LA     R3,L'C64                 x     (mvcl target length)
         LA     R4,C+3                   @c+3  (mvcl source)
         LA     R2,C64                   @c64  (mvcl target)
         ICM    R3,B'1000',=C' '         padding char
         MVCL   R2,R4                    mvcl @c64[64] <- @c+3[l-3]
         MVC    C,C64                    c=substr(c,4,l-3)
       ENDIF    ,                      endif
         LA     R7,1(R7)               j++
       ENDDO    ,                    enddo j
         LA     R9,1(R9)             k=k+1
         LA     R6,1(R6)             i++ 
       ENDDO    ,                  enddo i
         LR     R6,R9              k
         SH     R6,=H'2'           k-2
       DO WHILE=(CH,R6,GE,=AL2(1)) do i=k-2 to 1 by -1
         LA     R7,1                 j=1 
       DO WHILE=(CR,R7,LE,R6)        do j=1 to i
         LR     R1,R6                  i
         MH     R1,=AL2(N)             *n
         LR     R0,R7                  j
         BCTR   R0,0                   j-1
         AR     R1,R0                  i*n+(j-1)
         SLA    R1,1                   *2 (H)
         LH     R2,MM(R1)              m(i+1,j)
         STH    R2,S1                  s1=m(i+1,j)
         LR     R1,R6                  i
         MH     R1,=AL2(N)             *n
         AR     R1,R7                  i*n+j
         SLA    R1,1                   *2 (H)
         LH     R2,MM(R1)              m(i+1,j+1)
         STH    R2,S2                  s2=m(i+1,j+1)
         LH     R4,S1                  s1
       IF    CH,R4,GT,S2 THEN          if s1>s2 then 
         LH     R8,S1                    sm=s1
       ELSE     ,                      else
         LH     R8,S2                    sm=s2
       ENDIF    ,                      endif
         LR     R1,R6                  i
         BCTR   R1,0                   i-1
         MH     R1,=AL2(N)             *n
         LR     R0,R7                  j
         BCTR   R0,0                   j-1
         AR     R1,R0                  (i-1)*n+(j-1)
         SLA    R1,1                   *2 (H)
         LH     R2,MM(R1)              m(i,j)
         LR     R10,R1                 index m(i,j)
         AR     R2,R8                  m(i,j)+sm
         STH    R2,MM(R10)             m(i,j)=m(i,j)+sm
         LA     R7,1(R7)               j++
       ENDDO    ,                    enddo j
         BCTR   R6,0                 i--
       ENDDO    ,                  enddo i
         LH     R1,MM              m(1,1)
         XDECO  R1,PG              edit m(1,1)
         XPRNT  PG,L'PG            output m(1,1)
         L      R13,4(0,R13)       restore previous savearea pointer
         RETURN (14,12),RC=0       restore registers from calling save
N        EQU    18                 n
X        EQU    64                 x
MM       DS     (N*N)H             m(n,n)
S1       DS     H                  s1
S2       DS     H                  s2
C        DS     CL(X)              c
CC       DS     CL2                cc
CL       DS     CL1                cl
C64      DS     CL(X)              c64 
PG       DC     CL80' '            buffer
XDEC     DS     CL12               temp for xdeci xdeco
T     DC CL(X)'55'                 t(18) char(64) 
      DC CL(X)'94 48'
      DC CL(X)'95 30 96'
      DC CL(X)'77 71 26 67'
      DC CL(X)'97 13 76 38 45'
      DC CL(X)'07 36 79 16 37 68'
      DC CL(X)'48 07 09 18 70 26 06'
      DC CL(X)'18 72 79 46 59 79 29 90'
      DC CL(X)'20 76 87 11 32 07 07 49 18'
      DC CL(X)'27 83 58 35 71 11 25 57 29 85'
      DC CL(X)'14 64 36 96 27 11 58 56 92 18 55'
      DC CL(X)'02 90 03 60 48 49 41 46 33 36 47 23'
      DC CL(X)'92 50 48 02 36 59 42 79 72 20 82 77 42'
      DC CL(X)'56 78 38 80 39 75 02 71 66 66 01 03 55 72'
      DC CL(X)'44 25 67 84 71 67 11 61 40 57 58 89 40 56 36'
      DC CL(X)'85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52'
      DC CL(X)'06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15'
      DC CL(X)'27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93'
         REGEQU
         END    MAXTRIA</syntaxhighlight>
{{out}}
<pre>
        1320
</pre>

=={{header|Action!}}==
<syntaxhighlight lang="action!">INT FUNC Max(INT a,b)
  IF a>b THEN RETURN (a) FI
RETURN (b)

PROC Main()
  DEFINE ROWCOUNT="18"
  INT i,row,len,a,b
  INT ARRAY rows(ROWCOUNT)
  INT ARRAY data=[
                            55
                          94 48
                         95 30 96
                       77 71 26 67
                      97 13 76 38 45
                    07 36 79 16 37 68
                   48 07 09 18 70 26 06
                 18 72 79 46 59 79 29 90
                20 76 87 11 32 07 07 49 18
              27 83 58 35 71 11 25 57 29 85
             14 64 36 96 27 11 58 56 92 18 55
           02 90 03 60 48 49 41 46 33 36 47 23
          92 50 48 02 36 59 42 79 72 20 82 77 42
        56 78 38 80 39 75 02 71 66 66 01 03 55 72
       44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
     85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
    06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
  27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93]

  row=0 len=1
  FOR i=0 TO ROWCOUNT-1
  DO
    rows(i)=row
    row==+len len==+1
  OD

  row=ROWCOUNT-2
  WHILE row>=0
  DO
    len=row+1
    FOR i=0 TO len-1
    DO
      a=data(rows(row+1)+i)
      b=data(rows(row+1)+i+1)
      data(rows(row)+i)==+Max(a,b)
    OD
    row==-1
  OD

  PrintI(data(0))
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Maximum_triangle_path_sum.png Screenshot from Atari 8-bit computer]
<pre>
1320
</pre>

=={{header|Ada}}==
<syntaxhighlight lang="ada">with Ada.Text_Io; use Ada.Text_Io;
 
procedure Max_Sum is

   Triangle : array (Positive range <>) of integer :=
                                     (55,
                                    94, 48,
                                  95, 30, 96,
                                77, 71, 26, 67,
                              97, 13, 76, 38, 45,
                            07, 36, 79, 16, 37, 68,
                          48, 07, 09, 18, 70, 26, 06,
                        18, 72, 79, 46, 59, 79, 29, 90,
                      20, 76, 87, 11, 32, 07, 07, 49, 18,
                    27, 83, 58, 35, 71, 11, 25, 57, 29, 85,
                  14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55,
                02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23,
              92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42,
            56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72,
          44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36,
        85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52,
      06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15,
    27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93);

   Last  : Integer := Triangle'Length;
   Tn    : Integer := 1;

begin
   while (Tn * (Tn + 1) / 2) < Last  loop
      Tn := Tn + 1;
   end loop;
   for N in reverse 2 .. Tn loop
      for I in 2 .. N loop
	 Triangle (Last - N) := Triangle (Last - N) +
	   Integer'Max(Triangle (Last - 1), Triangle (Last));
	 Last := Last - 1;
      end loop;
      Last := Last - 1;
   end loop;
   Put_Line(Integer'Image(Triangle(1)));
end Max_Sum;</syntaxhighlight>
{{out}}
<pre> 1320
</pre>

=={{header|ALGOL 68}}==
{{works with|ALGOL 68G|Any - tested with release 2.6.win32}}
Basically the same algorithm as Ada and C++ but using a triangular matrix.
<syntaxhighlight lang="algol68"># create a triangular array of the required values #

    [ 1]INT row  1 :=                           ( 55 );
    [ 2]INT row  2 :=                         ( 94, 48 );
    [ 3]INT row  3 :=                        ( 95, 30, 96 );
    [ 4]INT row  4 :=                      ( 77, 71, 26, 67 );
    [ 5]INT row  5 :=                     ( 97, 13, 76, 38, 45 );
    [ 6]INT row  6 :=                   ( 07, 36, 79, 16, 37, 68 );
    [ 7]INT row  7 :=                  ( 48, 07, 09, 18, 70, 26, 06 );
    [ 8]INT row  8 :=                ( 18, 72, 79, 46, 59, 79, 29, 90 );
    [ 9]INT row  9 :=               ( 20, 76, 87, 11, 32, 07, 07, 49, 18 );
    [10]INT row 10 :=             ( 27, 83, 58, 35, 71, 11, 25, 57, 29, 85 );
    [11]INT row 11 :=            ( 14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55 );
    [12]INT row 12 :=          ( 02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23 );
    [13]INT row 13 :=         ( 92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42 );
    [14]INT row 14 :=       ( 56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72 );
    [15]INT row 15 :=      ( 44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36 );
    [16]INT row 16 :=    ( 85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52 );
    [17]INT row 17 :=   ( 06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15 );
    [18]INT row 18 := ( 27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93 );

[18]REF[]INT triangle := ( row  1, row  2, row  3, row  4, row  5, row  6
                         , row  7, row  8, row  9, row 10, row 11, row 12
                         , row 13, row 14, row 15, row 16, row 17, row 18
                         );

PROC max = ( INT a, INT b )INT: IF a > b THEN a ELSE b FI;

# working backwards, we replace the elements of each row with the sum of that #
# element and the maximum of the two elements below it.                       #
# That destroys the triangle but leaves element [1][1] equal to the required  #
# maximum                                                                     #


FOR row FROM UPB triangle - 1 BY -1 TO 1
DO
    FOR element FROM 1 TO UPB triangle[row]
    DO
        # the elements "under" triangle[row][element] are                     #
        # triangle[row+1][element] and triangle[row+1][element+1]             #
        triangle[row][element]
            +:= max( triangle[row+1][element], triangle[row+1][element+1] )
    OD
OD;

print( ( triangle[1][1], newline ) )
</syntaxhighlight>
{{out}}
<pre>
      +1320
</pre>

=={{header|APL}}==
{{works with|Dyalog APL}}
<syntaxhighlight lang="apl">parse ← ⍎¨(~∊)∘⎕TC⊆⊢
maxpath ← ⊃(⊣+2⌈/⊢)/
⎕ ← maxpath parse ⊃⎕NGET'G:\triangle.txt'</syntaxhighlight>
{{out}}
<pre>1320</pre>

=={{header|AppleScript}}==
{{Trans|JavaScript}}
<syntaxhighlight lang="applescript">---------------- MAXIMUM TRIANGLE PATH SUM ---------------

-- Working from the bottom of the triangle upwards,
-- summing each number with the larger of the two below
-- until the maximum emerges at the top.

-- maxPathSum :: [[Int]] -> Int
on maxPathSum(xss)
    
    -- With the last row as the initial accumulator,
    -- folding from the penultimate line,
    -- towards the top of the triangle:
    
    -- sumWithRowBelow :: [Int] -> [Int] -> [Int]
    script sumWithRowBelow
        on |λ|(row, accum)
            
            -- plusGreaterOfTwoBelow :: Int -> Int -> Int -> Int
            script plusGreaterOfTwoBelow
                on |λ|(x, intLeft, intRight)
                    x + max(intLeft, intRight)
                end |λ|
            end script
            
            -- The accumulator, zipped with the tail of the
            -- accumulator, yields pairs of adjacent sums so far.
            
            zipWith3(plusGreaterOfTwoBelow, row, accum, tail(accum))
        end |λ|
    end script
    
    -- A list of lists folded down to a list of just one remaining integer.
    -- Head returns that integer from the list.
    
    head(foldr1(sumWithRowBelow, xss))
end maxPathSum


--------------------------- TEST -------------------------
on run
    
    maxPathSum({¬
        {55}, ¬
        {94, 48}, ¬
        {95, 30, 96}, ¬
        {77, 71, 26, 67}, ¬
        {97, 13, 76, 38, 45}, ¬
        {7, 36, 79, 16, 37, 68}, ¬
        {48, 7, 9, 18, 70, 26, 6}, ¬
        {18, 72, 79, 46, 59, 79, 29, 90}, ¬
        {20, 76, 87, 11, 32, 7, 7, 49, 18}, ¬
        {27, 83, 58, 35, 71, 11, 25, 57, 29, 85}, ¬
        {14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55}, ¬
        {2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23}, ¬
        {92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42}, ¬
        {56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72}, ¬
        {44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36}, ¬
        {85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52}, ¬
        {6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15}, ¬
        {27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93} ¬
            })
    
    --> 1320    
end run


-------------------- GENERIC FUNCTIONS -------------------

-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        repeat with i from 1 to lng
            set v to |λ|(v, item i of xs, i, xs)
        end repeat
        return v
    end tell
end foldl


-- foldr1 :: (a -> a -> a) -> [a] -> a
on foldr1(f, xs)
    if length of xs > 1 then
        tell mReturn(f)
            set v to item -1 of xs
            set lng to length of xs
            repeat with i from lng - 1 to 1 by -1
                set v to |λ|(item i of xs, v, i, xs)
            end repeat
            return v
        end tell
    else
        xs
    end if
end foldr1


-- head :: [a] -> a
on head(xs)
    if length of xs > 0 then
        item 1 of xs
    else
        missing value
    end if
end head


-- max :: Ord a => a -> a -> a
on max(x, y)
    if x > y then
        x
    else
        y
    end if
end max


-- min :: Ord a => a -> a -> a
on min(x, y)
    if y < x then
        y
    else
        x
    end if
end min


-- minimum :: [a] -> a 
on minimum(xs)
    script min
        on |λ|(a, x)
            if x < a or a is missing value then
                x
            else
                a
            end if
        end |λ|
    end script
    
    foldl(min, missing value, xs)
end minimum


-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn


-- tail :: [a] -> [a]
on tail(xs)
    if length of xs > 1 then
        items 2 thru -1 of xs
    else
        {}
    end if
end tail


-- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
on zipWith3(f, xs, ys, zs)
    set lng to minimum({length of xs, length of ys, length of zs})
    set lst to {}
    tell mReturn(f)
        repeat with i from 1 to lng
            set end of lst to |λ|(item i of xs, item i of ys, item i of zs)
        end repeat
        return lst
    end tell
end zipWith3</syntaxhighlight>
{{Out}}
<pre>1320</pre>

=={{header|Arturo}}==
<syntaxhighlight lang="arturo">data: {:
                          55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
:}

solve: function [triangle][
    tri: triangle
    while [1 < size tri][
        t0: last tri
        chop 'tri
        loop.with:'i tri\[dec size tri] 't ->
            tri\[dec size tri]\[i]: t + max @[t0\[i] t0\[inc i]]
    ]
    tri\0\0
]

print solve map split.lines strip data 'x ->
    map split.by:" " strip x 'y ->
        to :integer y
</syntaxhighlight>

{{out}}

<pre>1320</pre>

=={{header|Astro}}==
<syntaxhighlight lang="python">fun maxpathsum(t): #: Array{Array{I}}
    let a = val t
    for i in a.length-1..-1..1, c in linearindices a[r]:
        a[r, c] += max(a[r+1, c], a[r=1, c+1])
    return a[1, 1]

let test = [
    [55],
    [94, 48],
    [95, 30, 96],
    [77, 71, 26, 67],
    [97, 13, 76, 38, 45],
    [07, 36, 79, 16, 37, 68],
    [48, 07, 09, 18, 70, 26, 06],
    [18, 72, 79, 46, 59, 79, 29, 90],
    [20, 76, 87, 11, 32, 07, 07, 49, 18],
    [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
    [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
    [02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23],
    [92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42],
    [56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72],
    [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
    [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52],
    [06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15],
    [27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
]

@print maxpathsum test
</syntaxhighlight>

=={{header|AutoHotkey}}==
Examples:<syntaxhighlight lang="autohotkey">data :=[
(join ltrim 
                 55,
                94,48,
               95,30,96,
              77,71,26,67,
             97,13,76,38,45,
            07,36,79,16,37,68,
           48,07,09,18,70,26,06,
          18,72,79,46,59,79,29,90,
         20,76,87,11,32,07,07,49,18,
        27,83,58,35,71,11,25,57,29,85,
       14,64,36,96,27,11,58,56,92,18,55,
      02,90,03,60,48,49,41,46,33,36,47,23,
     92,50,48,02,36,59,42,79,72,20,82,77,42,
    56,78,38,80,39,75,02,71,66,66,01,03,55,72,
   44,25,67,84,71,67,11,61,40,57,58,89,40,56,36,
  85,32,25,85,57,48,84,35,47,62,17,01,01,99,89,52,
 06,71,28,75,94,48,37,10,23,51,06,48,53,18,74,98,15,
27,02,92,23,08,71,76,84,15,52,92,63,81,10,44,10,69,93
)]

i	:= data.MaxIndex()
row	:= Ceil((Sqrt(8*i+1) - 1) / 2)
path:=[]

loop % row {
	path[i] := data[i]
	i--
}

while i {
	row := Ceil((Sqrt(8*i+1) - 1) / 2)
	path[i] := data[i] "+" (data[i+row] > data[i+row+1] ? path[i+row] : path[i+row+1])
	data[i] += data[i+row] > data[i+row+1] ? data[i+row] : data[i+row+1]
	i --
}

MsgBox % data[1] "`n" path[1]</syntaxhighlight>
Outputs:<pre>1320
55+94+95+77+97+7+48+72+76+83+64+90+48+80+84+85+94+71</pre>

=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f MAXIMUM_TRIANGLE_PATH_SUM.AWK filename(s)
{   printf("%s\n",$0)
    cols[FNR] = NF
    for (i=1; i<=NF; i++) {
      arr[FNR][i] = $i
    }
}
ENDFILE {
    for (row=FNR-1; row>0; row--) {
      for (col=1; col<=cols[row]; col++) {
        arr[row][col] += max(arr[row+1][col],arr[row+1][col+1])
      }
    }
    printf("%d using %s\n\n",arr[1][1],FILENAME)
    delete arr
    delete cols
}
END {
    exit(0)
}
function max(x,y) { return((x > y) ? x : y) }
</syntaxhighlight>
{{out}}
<pre>
55
94 48
95 30 96
77 71 26 67
321 using MAXIMUM_TRIANGLE_PATH_SUM_4.TXT

55
94 48
95 30 96
77 71 26 67
97 13 76 38 45
7 36 79 16 37 68
48 7 9 18 70 26 6
18 72 79 46 59 79 29 90
20 76 87 11 32 7 7 49 18
27 83 58 35 71 11 25 57 29 85
14 64 36 96 27 11 58 56 92 18 55
2 90 3 60 48 49 41 46 33 36 47 23
92 50 48 2 36 59 42 79 72 20 82 77 42
56 78 38 80 39 75 2 71 66 66 1 3 55 72
44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
85 32 25 85 57 48 84 35 47 62 17 1 1 99 89 52
6 71 28 75 94 48 37 10 23 51 6 48 53 18 74 98 15
27 2 92 23 8 71 76 84 15 52 92 63 81 10 44 10 69 93
1320 using MAXIMUM_TRIANGLE_PATH_SUM_18.TXT
</pre>

=={{header|Bracmat}}==
<syntaxhighlight lang="bracmat">(   "
                          55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
"
  : ?triangle
& ( max
  =   a b
    . !arg:(?a.?b)&(!a:>!b|!b)
  )
& 0:?accumulator
&   whl
  ' ( @(!triangle:?row (\n|\r) ?triangle)
    & :?newaccumulator
    & 0:?first
    &   whl
      ' ( @(!row:? #%?n (" " ?row|:?row))
        & !accumulator:#%?second ?accumulator
        & !newaccumulator max$(!first.!second)+!n:?newaccumulator
        & !second:?first
        )
    & !newaccumulator 0:?accumulator
    )
& (   -1:?Max
    &   !accumulator
      : ? (%@:>!Max:?Max&~) ?
  | out$!Max
  )
)</syntaxhighlight>
{{out}}
<pre>1320</pre>

=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
The [[#Chipmunk Basic|Chipmunk Basic]] solution works without any changes.

==={{header|BASIC256}}===
<syntaxhighlight lang="freebasic">arraybase 1
dim ln(19)
ln[1] = "                   55"
ln[2] = "                  94 48"
ln[3] = "                95 30 96"
ln[4] = "               77 71 26 67"
ln[5] = "              97 13 76 38 45"
ln[6] = "             07 36 79 16 37 68"
ln[7] = "            48 07 09 18 70 26 06"
ln[8] = "           18 72 79 46 59 79 29 90"
ln[9] = "          20 76 87 11 32 07 07 49 18"
ln[10] = "         27 83 58 35 71 11 25 57 29 85"
ln[11] = "        14 64 36 96 27 11 58 56 92 18 55"
ln[12] = "       02 90 03 60 48 49 41 46 33 36 47 23"
ln[13] = "      92 50 48 02 36 59 42 79 72 20 82 77 42"
ln[14] = "     56 78 38 80 39 75 02 71 66 66 01 03 55 72"
ln[15] = "    44 25 67 84 71 67 11 61 40 57 58 89 40 56 36"
ln[16] = "   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52"
ln[17] = "  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15"
ln[18] = " 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
ln[19] = "end"

dim matrix(20,20)
x = 1
tam = 0

for n = 1 to length(ln) - 1
	ln2 = trim(ln[n])
	for y = 1 to x
		matrix[x, y] = fromradix((left(ln2, 2)), 10)
		if length(ln2) > 4 then ln2 = mid(ln2, 4, length(ln2)-4)
	next y
	x += 1
	tam += 1
next n

for x = tam - 1 to 1 step - 1
	for y = 1 to x
		s1 = matrix[x+1, y]
		s2 = matrix[x+1, y+1]
		if s1 > s2 then
			matrix[x, y] = matrix[x, y] + s1
		else
			matrix[x, y] = matrix[x, y] + s2
		end if
	next y
next x

print "  maximum triangle path sum = " + matrix[1, 1]</syntaxhighlight>
{{out}}
<pre>  maximum triangle path sum = 1320</pre>

==={{header|Chipmunk Basic}}===
{{works with|Chipmunk Basic|3.6.4}}
{{works with|Applesoft BASIC}}
{{works with|GW-BASIC}}
{{works with|Just BASIC}}
{{works with|PC-BASIC|any}}
{{works with|QBasic}}
<syntaxhighlight lang="qbasic">100 DIM LN$(19)
110 LN$(1) = "55"
120 LN$(2) = "94 48"
130 LN$(3) = "95 30 96"
140 LN$(4) = "77 71 26 67"
150 LN$(5) = "97 13 76 38 45"
160 LN$(6) = "07 36 79 16 37 68"
170 LN$(7) = "48 07 09 18 70 26 06"
180 LN$(8) = "18 72 79 46 59 79 29 90"
190 LN$(9) = "20 76 87 11 32 07 07 49 18"
200 LN$(10) = "27 83 58 35 71 11 25 57 29 85"
210 LN$(11) = "14 64 36 96 27 11 58 56 92 18 55"
220 LN$(12) = "02 90 03 60 48 49 41 46 33 36 47 23"
230 LN$(13) = "92 50 48 02 36 59 42 79 72 20 82 77 42"
240 LN$(14) = "56 78 38 80 39 75 02 71 66 66 01 03 55 72"
250 LN$(15) = "44 25 67 84 71 67 11 61 40 57 58 89 40 56 36"
260 LN$(16) = "85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52"
270 LN$(17) = "06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15"
280 LN$(18) = "27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
290 LN$(19) = "end"
300 DIM MATRIX(20,20)
310 X = 1
320 TAM = 0
330 FOR N = 1 TO 19
340   LN2$ = LN$(N)
350   FOR Y = 1 TO X
360     MATRIX(X,Y) = VAL(LEFT$(LN2$,2))
370     IF LEN(LN2$) > 4 THEN LN2$ = MID$(LN2$,4,LEN(LN2$)-4)
380   NEXT Y
390   X = X+1
400   TAM = TAM+1
410 NEXT N
420 FOR Z = TAM-1 TO 1 STEP -1
430   FOR Y = 1 TO Z
440     S1 = MATRIX(Z+1,Y)
450     S2 = MATRIX(Z+1,Y+1)
460     IF S1 > S2 THEN MATRIX(Z,Y) = MATRIX(Z,Y)+S1
470     IF S1 <= S2 THEN MATRIX(Z,Y) = MATRIX(Z,Y)+S2
480   NEXT Y
490 NEXT Z
500 PRINT "  maximum triangle path sum = ";MATRIX(1,1)</syntaxhighlight>
{{out}}
<pre>  maximum triangle path sum = 1320</pre>

==={{header|GW-BASIC}}===
The [[#Chipmunk Basic|Chipmunk Basic]] solution works without any changes.

==={{header|MSX Basic}}===
The [[#Chipmunk Basic|Chipmunk Basic]] solution works without any changes.

==={{header|PureBasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="PureBasic">OpenConsole()
Dim ln.s(19)
ln(1) = "                   55"
ln(2) = "                  94 48"
ln(3) = "                95 30 96"
ln(4) = "               77 71 26 67"
ln(5) = "              97 13 76 38 45"
ln(6) = "             07 36 79 16 37 68"
ln(7) = "            48 07 09 18 70 26 06"
ln(8) = "           18 72 79 46 59 79 29 90"
ln(9) = "          20 76 87 11 32 07 07 49 18"
ln(10) = "         27 83 58 35 71 11 25 57 29 85"
ln(11) = "        14 64 36 96 27 11 58 56 92 18 55"
ln(12) = "       02 90 03 60 48 49 41 46 33 36 47 23"
ln(13) = "      92 50 48 02 36 59 42 79 72 20 82 77 42"
ln(14) = "     56 78 38 80 39 75 02 71 66 66 01 03 55 72"
ln(15) = "    44 25 67 84 71 67 11 61 40 57 58 89 40 56 36"
ln(16) = "   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52"
ln(17) = "  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15"
ln(18) = " 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
ln(19) = "end"

Dim matrix.i(20,20)
Define.i x = 1, tam = 0
Define.i i, y, s1, s2, n

For n = 1 To ArraySize(ln(),1) - 1
  ln2.s = LTrim(ln(n))
  For y = 1 To x
    matrix(x, y) = Val(Left(ln2, 2))
    If Len(ln2) > 4:
      ln2 = Mid(ln2, 4, Len(ln2)-4)
    EndIf
  Next y
  x + 1
  tam + 1
Next n

For x = tam - 1 To 1 Step - 1
  For y = 1 To x
    s1 = matrix(x+1, y)
    s2 = matrix(x+1, y+1)
    If s1 > s2:
      matrix(x, y) = matrix(x, y) + s1
    Else
      matrix(x, y) = matrix(x, y) + s2
    EndIf
  Next y
Next x

PrintN(#CRLF$ + "  maximum triangle path sum = " + Str(matrix(1, 1)))

Input()
CloseConsole()</syntaxhighlight>
{{out}}
<pre>  maximum triangle path sum = 1320</pre>

==={{header|QBasic}}===
{{works with|QBasic|1.1}}
The [[#Chipmunk Basic|Chipmunk Basic]] solution works without any changes.

==={{header|Run BASIC}}===
{{works with|Just BASIC}}
{{works with|Liberty BASIC}}
<syntaxhighlight lang="freebasic">dim ln$(19)
ln$(1) = "                   55"
ln$(2) = "                  94 48"
ln$(3) = "                95 30 96"
ln$(4) = "               77 71 26 67"
ln$(5) = "              97 13 76 38 45"
ln$(6) = "             07 36 79 16 37 68"
ln$(7) = "            48 07 09 18 70 26 06"
ln$(8) = "           18 72 79 46 59 79 29 90"
ln$(9) = "          20 76 87 11 32 07 07 49 18"
ln$(10) = "         27 83 58 35 71 11 25 57 29 85"
ln$(11) = "        14 64 36 96 27 11 58 56 92 18 55"
ln$(12) = "       02 90 03 60 48 49 41 46 33 36 47 23"
ln$(13) = "      92 50 48 02 36 59 42 79 72 20 82 77 42"
ln$(14) = "     56 78 38 80 39 75 02 71 66 66 01 03 55 72"
ln$(15) = "    44 25 67 84 71 67 11 61 40 57 58 89 40 56 36"
ln$(16) = "   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52"
ln$(17) = "  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15"
ln$(18) = " 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
ln$(19) = "end"

dim matrix(20,20)
x = 1
tam = 0

for n = 1 to 19 'ubound(ln$) - 1
    ln2$ = trim$(ln$(n))
    for y = 1 to x
        matrix(x, y) = val(left$(ln2$, 2))
        if len(ln2$) > 4 then ln2$ = mid$(ln2$, 4, len(ln2$)-4)
    next y
    x = x +1
    tam = tam +1
next n

for z = tam-1 to 1 step -1
    for y = 1 to z
        s1 = matrix(z+1, y)
        s2 = matrix(z+1, y+1)
        if s1 > s2 then
            matrix(z, y) = matrix(z, y) +s1
        else
            matrix(z, y) = matrix(z, y) +s2
        end if
    next y
next z

print "  maximum triangle path sum = "; matrix(1, 1)</syntaxhighlight>
{{out}}
<pre>  maximum triangle path sum = 1320</pre>

==={{header|True BASIC}}===
<syntaxhighlight lang="qbasic">DATA "                  55"
DATA "                 94 48"
DATA "                95 30 96"
DATA "               77 71 26 67"
DATA "              97 13 76 38 45"
DATA "             07 36 79 16 37 68"
DATA "            48 07 09 18 70 26 06"
DATA "           18 72 79 46 59 79 29 90"
DATA "          20 76 87 11 32 07 07 49 18"
DATA "         27 83 58 35 71 11 25 57 29 85"
DATA "        14 64 36 96 27 11 58 56 92 18 55"
DATA "       02 90 03 60 48 49 41 46 33 36 47 23"
DATA "      92 50 48 02 36 59 42 79 72 20 82 77 42"
DATA "     56 78 38 80 39 75 02 71 66 66 01 03 55 72"
DATA "    44 25 67 84 71 67 11 61 40 57 58 89 40 56 36"
DATA "   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52"
DATA "  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15"
DATA " 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
DATA "END"                        ! no more DATA

DIM matrix(1 TO 20, 1 TO 20)
LET x = 1
DO
   READ ln$
   LET ln$ = LTRIM$(RTRIM$(ln$))
   IF ln$ = "END" THEN EXIT DO
   FOR y = 1 TO x
       LET matrix(x, y) = VAL((ln$)[1:2])
       LET ln$ = (ln$)[4:maxnum]
   NEXT y
   LET x = x+1
   LET tam = tam+1
LOOP
FOR x = tam-1 TO 1 STEP -1
    FOR y = 1 TO x
        LET s1 = matrix(x+1, y)
        LET s2 = matrix(x+1, y+1)
        IF s1 > s2 THEN LET matrix(x, y) = matrix(x, y)+s1 ELSE LET matrix(x, y) = matrix(x, y)+s2
    NEXT y
NEXT x

PRINT "  maximum triangle path sum ="; matrix(1, 1)
END</syntaxhighlight>
{{out}}
<pre>  maximum triangle path sum = 1320</pre>

==={{header|Yabasic}}===
<syntaxhighlight lang="freebasic">dim ln$(19)
ln$(1) = "                   55"
ln$(2) = "                  94 48"
ln$(3) = "                95 30 96"
ln$(4) = "               77 71 26 67"
ln$(5) = "              97 13 76 38 45"
ln$(6) = "             07 36 79 16 37 68"
ln$(7) = "            48 07 09 18 70 26 06"
ln$(8) = "           18 72 79 46 59 79 29 90"
ln$(9) = "          20 76 87 11 32 07 07 49 18"
ln$(10) = "         27 83 58 35 71 11 25 57 29 85"
ln$(11) = "        14 64 36 96 27 11 58 56 92 18 55"
ln$(12) = "       02 90 03 60 48 49 41 46 33 36 47 23"
ln$(13) = "      92 50 48 02 36 59 42 79 72 20 82 77 42"
ln$(14) = "     56 78 38 80 39 75 02 71 66 66 01 03 55 72"
ln$(15) = "    44 25 67 84 71 67 11 61 40 57 58 89 40 56 36"
ln$(16) = "   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52"
ln$(17) = "  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15"
ln$(18) = " 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
ln$(19) = "end"

dim matrix(20,20)
x = 1
tam = 0

for n = 1 to arraysize(ln$(),1) - 1
	ln2$ = trim$(ln$(n))
	for y = 1 to x
		matrix(x, y) = val(left$(ln2$, 2))
		if len(ln2$) > 4  ln2$ = mid$(ln2$, 4, len(ln2$)-4)
	next y
	x = x + 1
	tam = tam + 1
next n

for x = tam - 1 to 1 step - 1
	for y = 1 to x
		s1 = matrix(x+1, y)
		s2 = matrix(x+1, y+1)
		if s1 > s2 then
			matrix(x, y) = matrix(x, y) + s1
		else
			matrix(x, y) = matrix(x, y) + s2
		end if
	next y
next x

print "\n  maximum triangle path sum = ", matrix(1, 1)</syntaxhighlight>
{{out}}
<pre>  maximum triangle path sum = 1320</pre>

=={{header|C}}==
<syntaxhighlight lang="c">
#include <stdio.h>
#include <math.h>

#define max(x,y)  ((x) > (y) ? (x) : (y))

int tri[] = {
        55,
	94, 48,
	95, 30, 96,
	77, 71, 26, 67,
	97, 13, 76, 38, 45,
	7, 36, 79, 16, 37, 68,
	48, 7, 9, 18, 70, 26, 6,
	18, 72, 79, 46, 59, 79, 29, 90,
	20, 76, 87, 11, 32, 7, 7, 49, 18,
	27, 83, 58, 35, 71, 11, 25, 57, 29, 85,
	14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55,
	2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23,
	92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42,
	56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72,
	44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36,
	85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52,
	6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15,
	27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93
};

int main(void)
{
    const int len  = sizeof(tri) / sizeof(tri[0]);
    const int base = (sqrt(8*len + 1) - 1) / 2;
    int step       = base - 1;
    int stepc      = 0;

    int i;
    for (i = len - base - 1; i >= 0; --i) {
        tri[i] += max(tri[i + step], tri[i + step + 1]);
        if (++stepc == step) {
            step--;
            stepc = 0;
        }
    }

    printf("%d\n", tri[0]);
    return 0;
}
</syntaxhighlight>
{{out}}
<pre>
1320
</pre>

=={{header|C sharp|C#}}==

<syntaxhighlight lang="csharp">
using System;

namespace RosetaCode
{
	class MainClass
	{
		public static void Main (string[] args)
		{
			int[,] list = new int[18,19];
			string input = @"55
	                        94 48
	                       95 30 96
	                     77 71 26 67
	                    97 13 76 38 45
	                  07 36 79 16 37 68
	                 48 07 09 18 70 26 06
	               18 72 79 46 59 79 29 90
	              20 76 87 11 32 07 07 49 18
	            27 83 58 35 71 11 25 57 29 85
	           14 64 36 96 27 11 58 56 92 18 55
	         02 90 03 60 48 49 41 46 33 36 47 23
	        92 50 48 02 36 59 42 79 72 20 82 77 42
	      56 78 38 80 39 75 02 71 66 66 01 03 55 72
	     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
	   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
	  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
	27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93";
			var charArray = input.Split ('\n');

			for (int i=0; i < charArray.Length; i++) {
				var numArr = charArray[i].Trim().Split(' ');

				for (int j = 0; j<numArr.Length; j++)
				{
					int number = Convert.ToInt32 (numArr[j]);
					list [i, j] = number;
				}
			}

			for (int i = 16; i >= 0; i--) {
				for (int j = 0; j < 18; j++) {
					list[i,j] = Math.Max(list[i, j] + list[i+1, j], list[i,j] + list[i+1, j+1]);
				}
			}
			Console.WriteLine (string.Format("Maximum total: {0}", list [0, 0]));
		}
	}
}

</syntaxhighlight>
{{out}}
<pre>Maximum total: 1320</pre>

=={{header|C++}}==
{{trans|Ada}}
<syntaxhighlight lang="cpp">
/* Algorithm complexity: n*log(n) */
#include <iostream>

int main( int argc, char* argv[] )
{
    int triangle[] = 
    {
	55,
	94, 48,
	95, 30, 96,
	77, 71, 26, 67,
	97, 13, 76, 38, 45,
	7, 36, 79, 16, 37, 68,
	48, 7, 9, 18, 70, 26, 6,
	18, 72, 79, 46, 59, 79, 29, 90,
	20, 76, 87, 11, 32, 7, 7, 49, 18,
	27, 83, 58, 35, 71, 11, 25, 57, 29, 85,
	14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55,
	2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23,
	92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42,
	56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72,
	44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36,
	85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52,
	6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15,
	27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93
    };

    const int size = sizeof( triangle ) / sizeof( int );
    const int tn = static_cast<int>(sqrt(2.0 * size));
    assert(tn * (tn + 1) == 2 * size);    // size should be a triangular number

    // walk backward by rows, replacing each element with max attainable therefrom
    for (int n = tn - 1; n > 0; --n)   // n is size of row, note we do not process last row
        for (int k = (n * (n-1)) / 2; k < (n * (n+1)) / 2; ++k) // from the start to the end of row
            triangle[k] += std::max(triangle[k + n], triangle[k + n + 1]);

    std::cout << "Maximum total: " << triangle[0] << "\n\n";
}
</syntaxhighlight>
{{out}}
<pre>Maximum total: 1320</pre>

=={{header|Clojure|ClojureScript}}==

<syntaxhighlight lang="clojure">
(ns clojure.examples.rosetta
	(:gen-class)
        (:require [clojure.string :as string]))

(def rosetta                     "55
	                        94 48
	                       95 30 96
	                     77 71 26 67
	                    97 13 76 38 45
	                  07 36 79 16 37 68
	                 48 07 09 18 70 26 06
	               18 72 79 46 59 79 29 90
	              20 76 87 11 32 07 07 49 18
	            27 83 58 35 71 11 25 57 29 85
	           14 64 36 96 27 11 58 56 92 18 55
	         02 90 03 60 48 49 41 46 33 36 47 23
	        92 50 48 02 36 59 42 79 72 20 82 77 42
	      56 78 38 80 39 75 02 71 66 66 01 03 55 72
	     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
	   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
	  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
	27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93")

;; The technique is described here in more detail http://mishadoff.com/blog/clojure-euler-problem-018/
;; Most of the code converts the string data to a nested array of integers.
;; The code to calculate the max sum is then only a  single line

;; First convert string data to nested list
;;  with each inner list containing one row of the triangle
;;   [[55] [94 48] [95 30 96] ... [...10 69 93]
(defn parse-int [s]
    " Convert digits to a number (finds digits when could be surrounded by non-digits"
  (Integer. (re-find #"\d+" s)))

(defn data-int-array [s]
  " Convert string to integer array"
  (map parse-int (string/split (string/trim s) #"\s+")))

(defn nested-triangle [s]
  " Convert triangle to nested vector, with each inner vector containing one triangle row"
  (loop [lst s n 1 newlist nil]
    (if (empty? lst) (reverse newlist)
                     (recur (drop n lst) (inc n) (cons (take n lst) newlist)))))
; Create nested list
(def nested-list (nested-triangle (data-int-array rosetta)))

;; Function to compute maximum path sum
(defn max-sum [s]
  " Compute maximum path sum using a technique described here: http://mishadoff.com/blog/clojure-euler-problem-018/"
  (reduce (fn [a b] (map + b (map max a (rest a)))) (reverse s)))

; Print result
(println (max-sum nested-list))

</syntaxhighlight>
{{out}}
<pre>1320</pre>

=={{header|Common Lisp}}==
<syntaxhighlight lang="lisp">(defun find-max-path-sum (s)
  (let ((triangle (loop for line = (read-line s NIL NIL) 
                        while line 
                        collect (with-input-from-string (str line) 
                                  (loop for n = (read str NIL NIL) 
                                        while n 
                                        collect n)))))
    (flet ((get-max-of-pairs (xs)
             (maplist (lambda (ys) 
                        (and (cdr ys) (max (car ys) (cadr ys))))
                      xs)))
      (car (reduce (lambda (xs ys) 
                     (mapcar #'+ (get-max-of-pairs xs) ys))
                   (reverse triangle))))))

(defparameter *small-triangle* 
  "    55
     94 48
    95 30 96
  77 71 26 67")
(format T "~a~%" (with-input-from-string (s *small-triangle*)
                   (find-max-path-sum s)))
(format T "~a~%" (with-open-file (f "triangle.txt")
                   (find-max-path-sum f)))</syntaxhighlight>

{{Out}}
<pre>321
1320</pre>

=={{header|D}}==
<syntaxhighlight lang="d">void main() {
    import std.stdio, std.algorithm, std.range, std.file, std.conv;

    "triangle.txt".File.byLine.map!split.map!(to!(int[])).array.retro
    .reduce!((x, y) => zip(y, x, x.dropOne)
                       .map!(t => t[0] + t[1 .. $].max)
                       .array)[0]
    .writeln;
}</syntaxhighlight>
{{out}}
<pre>1320</pre>

=={{header|EasyLang}}==
<syntaxhighlight>
a[] = [ 0 0 ]
repeat
   s$ = input
   until s$ = ""
   i = 1
   while substr s$ i 1 = " "
      i += 1
   .
   s$ = "0 " & substr s$ i 999 & " 0"
   b[] = number strsplit s$ " "
   for i = 2 to len b[] - 1
      b[i] = higher (b[i] + a[i - 1]) (b[i] + a[i])
   .
   swap a[] b[]
.
for v in a[]
   max = higher max v
.
print max
# 
input_data
                          55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
</syntaxhighlight>

=={{header|Elena}}==
{{trans|C#}}
ELENA 6.x :
<syntaxhighlight lang="elena">import system'routines;
import extensions;
import extensions'math;
 
string input =               "55
                            94 48
                          95 30 96
                        77 71 26 67
                       97 13 76 38 45
                     07 36 79 16 37 68
                    48 07 09 18 70 26 06
                  18 72 79 46 59 79 29 90
                 20 76 87 11 32 07 07 49 18
               27 83 58 35 71 11 25 57 29 85
              14 64 36 96 27 11 58 56 92 18 55
            02 90 03 60 48 49 41 46 33 36 47 23
           92 50 48 02 36 59 42 79 72 20 82 77 42
         56 78 38 80 39 75 02 71 66 66 01 03 55 72
        44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
      85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
     06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
   27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93";
 
public program()
{
    var list := IntMatrix.allocate(18,19);
 
    int i := 0;
    int j := 0;
    input.splitBy(newLineConstant).forEach::(string line)
    {
        j := 0;
        line.trim().splitBy(" ").forEach::(string num)
        {
            list[i][j] := num.toInt();
 
            j += 1
        };
 
        i += 1
    };
 
    for(int i := 16; i >= 0; i-=1)
    {
        for(int j := 0; j < 18; j += 1)
        {
            list[i][j] := max(list[i][j] + list[i+1][j], list[i][j] + list[i+1][j+1])
        }
    };
 
    console.printLine("Maximum total: ", list[0][0])
}</syntaxhighlight>
{{out}}
<pre>
Maximum total: 1320
</pre>

=={{header|Elixir}}==
<syntaxhighlight lang="elixir">defmodule Maximum do
  def triangle_path(text) do
    text
    |> String.split("\n", trim: true)
    |> Enum.map(fn line ->
      line
      |> String.split()
      |> Enum.map(&String.to_integer(&1))
    end)
    |> Enum.reduce([], fn x,total ->
         [0]++total++[0]
         |> Enum.chunk_every( 2, 1)
         |> Enum.map(&Enum.max(&1))
         |> Enum.zip(x)
         |> Enum.map(fn{a,b} -> a+b end)
       end)
    |> Enum.max()
  end
end

text = """
                          55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
"""

IO.puts Maximum.triangle_path(text)
</syntaxhighlight>

{{out}}
<pre>
1320
</pre>

=={{header|Erlang}}==
Reads the data from the file "triangle.txt"
<syntaxhighlight lang="erlang">
-mode(compile).
-import(lists, [foldl/3]).

main(_) ->
   {ok, Tmat} = file:open("triangle.txt", [read, raw, {read_ahead, 16384}]),
   Max = max_sum(Tmat, []),
   io:format("The maximum total is ~b~n", [Max]).

max_sum(FD, Last) ->
    case file:read_line(FD) of
        eof -> foldl(fun erlang:max/2, 0, Last);
        {ok, Line} ->
            Current = [binary_to_integer(B) || B <- re:split(Line, "[ \n]"), byte_size(B) > 0],
            max_sum(FD, fold_row(Last, Current))
    end.

% The first argument has one more element than the second, so compute
% the initial sum so that both lists have identical length for fold_rest().
fold_row([], L) -> L;
fold_row([A|_] = Last, [B|Bs]) ->
    [A+B | fold_rest(Last, Bs)].

% Both lists must have same length
fold_rest([A], [B]) -> [A+B];
fold_rest([A1 | [A2|_] = As], [B|Bs]) -> [B + max(A1,A2) | fold_rest(As, Bs)].
</syntaxhighlight>
{{Out}}
<pre>
The maximum total is 1320
</pre>

=={{header|ERRE}}==
<syntaxhighlight lang="erre">
PROGRAM TRIANGLE_PATH

CONST ROW=18

DIM TRI[200]

!
! for rosettacode,org
!

FUNCTION MAX(X,Y)
   MAX=-X*(X>=Y)-Y*(X<Y)
END FUNCTION

BEGIN

     DATA(55)
     DATA(94,48)
     DATA(95,30,96)
     DATA(77,71,26,67)
     DATA(97,13,76,38,45)
     DATA(7,36,79,16,37,68)
     DATA(48,7,9,18,70,26,6)
     DATA(18,72,79,46,59,79,29,90)
     DATA(20,76,87,11,32,7,7,49,18)
     DATA(27,83,58,35,71,11,25,57,29,85)
     DATA(14,64,36,96,27,11,58,56,92,18,55)
     DATA(2,90,3,60,48,49,41,46,33,36,47,23)
     DATA(92,50,48,2,36,59,42,79,72,20,82,77,42)
     DATA(56,78,38,80,39,75,2,71,66,66,1,3,55,72)
     DATA(44,25,67,84,71,67,11,61,40,57,58,89,40,56,36)
     DATA(85,32,25,85,57,48,84,35,47,62,17,1,1,99,89,52)
     DATA(6,71,28,75,94,48,37,10,23,51,6,48,53,18,74,98,15)
     DATA(27,2,92,23,8,71,76,84,15,52,92,63,81,10,44,10,69,93)

     PRINT(CHR$(12);) !CLS
     LUNG=ROW*(ROW+1)/2
     FOR I%=0 TO LUNG-1 DO
        READ(TRI[I%])
     END FOR

     BSE=(SQR(8*LUNG+1)-1)/2
     STP=BSE-1
     STEPC=0

     FOR I%=LUNG-BSE-1 TO 0 STEP -1 DO
        TRI[I%]=TRI[I%]+MAX(TRI[I%+STP],TRI[I%+STP+1])
        STEPC=STEPC+1
        IF STEPC=STP THEN
             STP=STP-1
             STEPC=0
        END IF
     END FOR

     PRINT(TRI[0])
END PROGRAM
</syntaxhighlight>

=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
// Maximum triangle path sum. Nigel Galloway: October 23rd., 2023
let g=[[27;02;92;23;08;71;76;84;15;52;92;63;81;10;44;10;69;93];[06;71;28;75;94;48;37;10;23;51;06;48;53;18;74;98;15];[85;32;25;85;57;48;84;35;47;62;17;01;01;99;89;52];[44;25;67;84;71;67;11;61;40;57;58;89;40;56;36];[56;78;38;80;39;75;02;71;66;66;01;03;55;72];[92;50;48;02;36;59;42;79;72;20;82;77;42];[02;90;03;60;48;49;41;46;33;36;47;23];[14;64;36;96;27;11;58;56;92;18;55];[27;83;58;35;71;11;25;57;29;85];[20;76;87;11;32;07;07;49;18];[18;72;79;46;59;79;29;90];[48;07;09;18;70;26;06];[07;36;79;16;37;68];[97;13;76;38;45];[77;71;26;67];[95;30;96];[94;48];[55]]
let fG n g=List.map2(fun (n1,n2) g->(max n1 n2)+g) (n|>List.pairwise) g
let rec fN=function n::g::t->fN ((fG n g)::t) |n::_->List.head n
printfn "%d" (fN g)
</syntaxhighlight>
{{out}}
<pre>
1320
</pre>

=={{header|Factor}}==
<syntaxhighlight lang="factor">USING: grouping.extras io.encodings.utf8 io.files kernel
math.order math.parser math.vectors prettyprint sequences
splitting ;
IN: rosetta-code.maximum-triangle-path-sum

: parse-triangle ( path -- seq )
    utf8 file-lines [ " " split harvest ] map
    [ [ string>number ] map ] map ;

: max-triangle-path-sum ( seq -- n )
    <reversed> unclip-slice [ swap [ max ] 2clump-map v+ ]
    reduce first ;

"triangle.txt" parse-triangle max-triangle-path-sum .</syntaxhighlight>
{{out}}
<pre>
1320
</pre>

=={{header|Forth}}==
<syntaxhighlight lang="forth">
\ Triangle representation; words created by this defining word return the address of element
\ specified by its row number and position within that row, both indexed from 0.
: TRIANGLE ( "name" -- |DOES: row pos -- addr )
   CREATE DOES> ROT DUP 1+ * 2/ CELLS +  SWAP CELLS +
;

18 CONSTANT #ROWS   \ total number of rows in triangle
TRIANGLE triang
                                             55 ,
                                           94 , 48 ,
                                        95 , 30 , 96 ,
                                      77 , 71 , 26 , 67 ,
                                   97 , 13 , 76 , 38 , 45 ,
                                  7 , 36 , 79 , 16 , 37 , 68 ,
                              48 ,  7 ,  9 , 18 , 70 , 26 ,  6 ,
                            18 , 72 , 79 , 46 , 59 , 79 , 29 , 90 ,
                         20 , 76 , 87 , 11 , 32 ,  7 ,  7 , 49 , 18 ,
                       27 , 83 , 58 , 35 , 71 , 11 , 25 , 57 , 29 , 85 ,
                    14 , 64 , 36 , 96 , 27 , 11 , 58 , 56 , 92 , 18 , 55 ,
                   2 , 90 ,  3 , 60 , 48 , 49 , 41 , 46 , 33 , 36 , 47 , 23 ,
               92 , 50 , 48 ,  2 , 36 , 59 , 42 , 79 , 72 , 20 , 82 , 77 , 42 ,
             56 , 78 , 38 , 80 , 39 , 75 ,  2 , 71 , 66 , 66 ,  1 ,  3 , 55 , 72 ,
          44 , 25 , 67 , 84 , 71 , 67 , 11 , 61 , 40 , 57 , 58 , 89 , 40 , 56 , 36 ,
        85 , 32 , 25 , 85 , 57 , 48 , 84 , 35 , 47 , 62 , 17 ,  1 ,  1 , 99 , 89 , 52 ,
      6 , 71 , 28 , 75 , 94 , 48 , 37 , 10 , 23 , 51 ,  6 , 48 , 53 , 18 , 74 , 98 , 15 ,
   27 ,  2 , 92 , 23 ,  8 , 71 , 76 , 84 , 15 , 52 , 92 , 63 , 81 , 10 , 44 , 10 , 69 , 93 ,

\ Starting from the row above the bottom row and ending on the top, for every item in row
\ find the bigger number from the two neighbours underneath and add it to this item. At
\ the end, the result will be returned from the top element of the triangle.
: MAX-SUM ( -- n )
   0 #ROWS 2 - DO
      I 1+ 0 DO
         J 1+ I triang @  J 1+ I 1+ triang @
         MAX  J I triang  +!
      LOOP
   -1 +LOOP
   0 0 triang @
;

MAX-SUM .</syntaxhighlight>
{{out}}
<pre>
1320
</pre>

=={{header|Fortran}}==
This being Fortran, why not a brute-force scan of all possible paths? This is eased by noting that from a given position, only two numbers are accessible, and always two numbers. Just like binary digits. So, for three levels, the choices would be 000, 001, 010, 011, 100, 101, 110, 111 or somesuch. Since however the pinnacle of the pyramid is always chosen, there is no choice there so the digits would be 100, 101, 110, 111.

A triangular array can be defined in some languages, and in some circumstances a square array is used with a lower triangle and upper triangle partition, but here, a simple linear array is in order, with some attention to subscript usage. The first layer has one number, the second has two, the third has three, ... easy enough. The more refined method that determines the maximum sum without ascertaining the path through working upwards from the base employs a FOR ALL statement in adding the maximum of the two possible descendants to each brick in the current layer, employing array BEST that starts off with all the values of the bottom layer. As each layer is one value shorter than the one below and the expression computes <code>BEST(i) = ... + MAX(BEST(i),BEST(i + 1))</code> the special feature of the FORALL statement, that ''all'' rhs expressions are evaluated before ''any'' results are placed on the lhs is not needed if a DO-loop were to be used instead.

For input, free-format is convenient. Bad input still is a problem, and can lead to puzzles. If say when N values are to be read but an input line is short of numbers, then additional lines will be read and confusion is likely. So, read the file's record into a text variable and then extract the expected N values from that. Should a problem arise, then the troublesome record can be shown.

<syntaxhighlight lang="fortran">
      MODULE PYRAMIDS	!Produces a pyramid of numbers in 1-D array.
       INTEGER MANY		!The usual storage issues.
       PARAMETER (MANY = 666)	!This should suffice.
       INTEGER BRICK(MANY),IN,LAYERS	!Defines a pyramid.
       CONTAINS
        SUBROUTINE IMHOTEP(PLAN)!The architect.
Counting is from the apex down, the Erich von Daniken construction.
         CHARACTER*(*) PLAN	!The instruction file.
         INTEGER I,IT		!Steppers.
         CHARACTER*666 ALINE	!A scratchpad for input.
          IN = 0		!No bricks.
          LAYERS = 0		!In no courses.
          WRITE (6,*) "Reading from ",PLAN	!Here we go.
          OPEN(10,FILE=PLAN,FORM="FORMATTED",ACTION="READ",ERR=6)	!I hope.
          GO TO 10		!Why can't OPEN be a function?@*&%#^%!
    6     STOP "Can't grab the file!"
Chew into the plan.
   10     READ (10,11,END = 20) ALINE	!Get the whole line in one piece.
   11     FORMAT (A)			!As plain text.
          IF (ALINE .EQ. "") GO TO 10	!Ignoring any blank lines.
          IF (ALINE(1:1).EQ."%") GO TO 10	!A comment opportunity.
          LAYERS = LAYERS + 1		!Righto, this should be the next layer.
          IF (IN + LAYERS.GT.MANY) STOP "Too many bricks!"	!Perhaps not.
          READ (ALINE,*,END = 15,ERR = 15) BRICK(IN + 1:IN + LAYERS)	!Free format.
          IN = IN + LAYERS		!Insufficient numbers will provoke trouble.
          GO TO 10			!Extra numbers/stuff will be ignored.
Caught a crab? A bad number, or too few numbers on a line? No read-next-record antics, thanks.
   15     WRITE (6,16) LAYERS,ALINE	!Just complain.
   16     FORMAT ("Bad layer ",I0,": ",A)
Completed the plan.
   20     WRITE (6,21) IN,LAYERS	!Announce some details.
   21     FORMAT (I0," bricks in ",I0," layers.")
          CLOSE(10)			!Finished with input.
Cast forth the numbers in a nice pyramid.
   30     IT = 0		!For traversing the pyramid.
          DO I = 1,LAYERS	!Each course has one more number than the one before.
            WRITE (6,31) BRICK(IT + 1:IT + I)	!Sweep along the layer.
   31       FORMAT (<LAYERS*2 - 2*I>X,666I4)	!Leading spaces may be zero in number.
            IT = IT + I				!Thus finger the last of a layer.
          END DO		!On to the start of the next layer.
        END SUBROUTINE IMHOTEP	!The pyramid's plan is ready.

        SUBROUTINE TRAVERSE	!Clamber around the pyramid. Thoroughly.
C   The idea is that a pyramid of numbers is provided, and then, starting at the peak,
c work down to the base summing the numbers at each step to find the maximum value path.
c The constraint is that from a particular brick, only the two numbers below left and below right
c may be reached in stepping to that lower layer.
c   Since that is a 0/1 choice, recorded in MOVE, a base-two scan searches the possibilities.
         INTEGER MOVE(LAYERS)		!Choices are made at the various positions.
         INTEGER STEP(LAYERS),WALK(LAYERS)	!Thus determining the path.
         INTEGER I,L,IT		!Steppers.
         INTEGER PS,WS		!Scores.
          WRITE (6,1) LAYERS		!Announce the intention.
    1     FORMAT (//,"Find the highest score path across a pyramid of ",
     1     I0," layers."/)	!I'm not worrying over singular/plural.
          MOVE = 0	!All 0/1 values to zero.
          MOVE(1) = 1	!Except the first.
          STEP(1) = 1	!Every path starts here, without option.
          WS = -666	!The best score so far.
Commence a multi-level loop, using the values of MOVE as the digits, one digit per level.
   10       IT = 1		!All paths start with the first step.
            PS = BRICK(1)	!The starting score,.
c            write (6,8) "Move",MOVE,WS
            DO L = 2,LAYERS	!Deal with the subsequent layers.
              IT = IT + L - 1 + MOVE(L)	!Choose a brick.
              STEP(L) = IT		!Remember this step.
              PS = PS + BRICK(IT)	!Count its score.
c              WRITE (6,6) L,IT,BRICK(IT),PS
    6         FORMAT ("Layer ",I0,",Brick(",I0,")=",I0,",Sum=",I0)
            END DO		!Thus is the path determined.
            IF (PS .GT. WS) THEN	!An improvement?
              IF (WS.GT.0) WRITE (6,7) WS,PS	!Yes! Announce.
    7         FORMAT ("Improved path score: ",I0," to ",I0)
              WRITE (6,8) "Moves",MOVE		!Show the choices at each layer..
              WRITE (6,8) "Steps",STEP		!That resulted in this path.
              WRITE (6,8) "Score",BRICK(STEP)	!Whose steps were scored thus.
    8         FORMAT (A8,666I4)			!This should suffice.
              WS = PS				!Record the new best value.
              WALK = STEP			!And the path thereby.
            END IF			!So much for an improvement.
            DO L = LAYERS,1,-1		!Now add one to the number in MOVE.
              IF (MOVE(L).EQ.0) THEN	!By finding the lowest order zero.
                MOVE(L) = 1		!Making it one,
                MOVE(L + 1:LAYERS) = 0	!And setting still lower orders back to zero.
                GO TO 10		!And if we did, there's more to do!
              END IF		!But if that bit wasn't zero,
            END DO		!Perhaps the next one up will be.
          WRITE (6,*) WS," is the highest score."	!So much for that.
        END SUBROUTINE TRAVERSE	!All paths considered...

        SUBROUTINE REFINE	!Ascertain the highest score without searching.
         INTEGER BEST(LAYERS)	!A scratchpad.
         INTEGER I,L		!Steppers.
          L = LAYERS*(LAYERS - 1)/2 + 1	!Finger the first brick of the lowest layer.
          BEST = BRICK(L:L + LAYERS - 1)!Syncopation. Copy the lowest layer.
          DO L = LAYERS - 1,1,-1	!Work towards the peak.
            FORALL (I = 1:L) BEST(I) = BRICK(L*(L - 1)/2 + I)	!Add to each brick's value
     1                               + MAXVAL(BEST(I:I + 1))	!The better of its two possibles.
          END DO			!On to the next layer.
          WRITE (6,*) BEST(1)," is the highest score. By some path."
        END SUBROUTINE REFINE	!Who knows how we get there.
      END MODULE PYRAMIDS

      PROGRAM TRICKLE
      USE PYRAMIDS
c      CALL IMHOTEP("Sakkara.txt")
      CALL IMHOTEP("Cheops.txt")
      CALL TRAVERSE			!Do this the definite way.
      CALL REFINE			!Only the result by more cunning.
      END
</syntaxhighlight>

Output:
<pre>
 Reading from Cheops.txt
171 bricks in 18 layers.
                                    55
                                  94  48
                                95  30  96
                              77  71  26  67
                            97  13  76  38  45
                           7  36  79  16  37  68
                        48   7   9  18  70  26   6
                      18  72  79  46  59  79  29  90
                    20  76  87  11  32   7   7  49  18
                  27  83  58  35  71  11  25  57  29  85
                14  64  36  96  27  11  58  56  92  18  55
               2  90   3  60  48  49  41  46  33  36  47  23
            92  50  48   2  36  59  42  79  72  20  82  77  42
          56  78  38  80  39  75   2  71  66  66   1   3  55  72
        44  25  67  84  71  67  11  61  40  57  58  89  40  56  36
      85  32  25  85  57  48  84  35  47  62  17   1   1  99  89  52
     6  71  28  75  94  48  37  10  23  51   6  48  53  18  74  98  15
  27   2  92  23   8  71  76  84  15  52  92  63  81  10  44  10  69  93


Find the highest score path across a pyramid of 18 layers.

   Moves   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
   Steps   1   2   4   7  11  16  22  29  37  46  56  67  79  92 106 121 137 154
   Score  55  94  95  77  97   7  48  18  20  27  14   2  92  56  44  85   6  27
Improved path score: 864 to 904
   Moves   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0
   Steps   1   2   4   7  11  16  22  29  37  46  56  67  79  92 106 121 138 155
   Score  55  94  95  77  97   7  48  18  20  27  14   2  92  56  44  85  71   2
Improved path score: 904 to 994
   Moves   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1
   Steps   1   2   4   7  11  16  22  29  37  46  56  67  79  92 106 121 138 156
   Score  55  94  95  77  97   7  48  18  20  27  14   2  92  56  44  85  71  92
Improved path score: 994 to 1041
   Moves   1   0   0   0   0   0   0   0   0   0   0   0   0   1   1   1   1   1
   Steps   1   2   4   7  11  16  22  29  37  46  56  67  79  93 108 124 141 159
   Score  55  94  95  77  97   7  48  18  20  27  14   2  92  78  67  85  94  71
Improved path score: 1041 to 1087
   Moves   1   0   0   0   0   0   0   0   0   0   0   1   0   0   1   1   1   1
   Steps   1   2   4   7  11  16  22  29  37  46  56  68  80  93 108 124 141 159
   Score  55  94  95  77  97   7  48  18  20  27  14  90  50  78  67  85  94  71
Improved path score: 1087 to 1104
   Moves   1   0   0   0   0   0   0   0   0   0   0   1   1   1   0   0   1   1
   Steps   1   2   4   7  11  16  22  29  37  46  56  68  81  95 109 124 141 159
   Score  55  94  95  77  97   7  48  18  20  27  14  90  48  80  84  85  94  71
Improved path score: 1104 to 1137
   Moves   1   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   1   1
   Steps   1   2   4   7  11  16  22  29  37  46  57  68  80  93 108 124 141 159
   Score  55  94  95  77  97   7  48  18  20  27  64  90  50  78  67  85  94  71
Improved path score: 1137 to 1154
   Moves   1   0   0   0   0   0   0   0   0   0   1   0   1   1   0   0   1   1
   Steps   1   2   4   7  11  16  22  29  37  46  57  68  81  95 109 124 141 159
   Score  55  94  95  77  97   7  48  18  20  27  64  90  48  80  84  85  94  71
Improved path score: 1154 to 1193
   Moves   1   0   0   0   0   0   0   0   0   1   0   0   0   0   1   1   1   1
   Steps   1   2   4   7  11  16  22  29  37  47  57  68  80  93 108 124 141 159
   Score  55  94  95  77  97   7  48  18  20  83  64  90  50  78  67  85  94  71
Improved path score: 1193 to 1210
   Moves   1   0   0   0   0   0   0   0   0   1   0   0   1   1   0   0   1   1
   Steps   1   2   4   7  11  16  22  29  37  47  57  68  81  95 109 124 141 159
   Score  55  94  95  77  97   7  48  18  20  83  64  90  48  80  84  85  94  71
Improved path score: 1210 to 1249
   Moves   1   0   0   0   0   0   0   0   1   0   0   0   0   0   1   1   1   1
   Steps   1   2   4   7  11  16  22  29  38  47  57  68  80  93 108 124 141 159
   Score  55  94  95  77  97   7  48  18  76  83  64  90  50  78  67  85  94  71
Improved path score: 1249 to 1266
   Moves   1   0   0   0   0   0   0   0   1   0   0   0   1   1   0   0   1   1
   Steps   1   2   4   7  11  16  22  29  38  47  57  68  81  95 109 124 141 159
   Score  55  94  95  77  97   7  48  18  76  83  64  90  48  80  84  85  94  71
Improved path score: 1266 to 1303
   Moves   1   0   0   0   0   0   0   1   0   0   0   0   0   0   1   1   1   1
   Steps   1   2   4   7  11  16  22  30  38  47  57  68  80  93 108 124 141 159
   Score  55  94  95  77  97   7  48  72  76  83  64  90  50  78  67  85  94  71
Improved path score: 1303 to 1320
   Moves   1   0   0   0   0   0   0   1   0   0   0   0   1   1   0   0   1   1
   Steps   1   2   4   7  11  16  22  30  38  47  57  68  81  95 109 124 141 159
   Score  55  94  95  77  97   7  48  72  76  83  64  90  48  80  84  85  94  71
        1320  is the highest score.
        1320  is the highest score. By some path.
</pre>

=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">' version 21-06-2015
' compile with: fbc -s console

Data "                  55"
Data "                 94 48"
Data "                95 30 96"
Data "               77 71 26 67"
Data "              97 13 76 38 45"
Data "             07 36 79 16 37 68"
Data "            48 07 09 18 70 26 06"
Data "           18 72 79 46 59 79 29 90"
Data "          20 76 87 11 32 07 07 49 18"
Data "         27 83 58 35 71 11 25 57 29 85"
Data "        14 64 36 96 27 11 58 56 92 18 55"
Data "       02 90 03 60 48 49 41 46 33 36 47 23"
Data "      92 50 48 02 36 59 42 79 72 20 82 77 42"
Data "     56 78 38 80 39 75 02 71 66 66 01 03 55 72"
Data "    44 25 67 84 71 67 11 61 40 57 58 89 40 56 36"
Data "   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52"
Data "  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15"
Data " 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
Data "END"   ' no more data

' ------=< MAIN >=------

Dim As String ln
Dim As Integer matrix(1 To 20, 1 To 20)
Dim As Integer x = 1, y, s1, s2, size

Do
    Read ln
    ln = Trim(ln)
    If ln = "END" Then Exit Do
    For y = 1 To x
        matrix(x, y) = Val(Left(ln, 2))
        ln = Mid(ln, 4)
    Next
    x += 1
    size += 1
Loop

For x = size - 1 To 1 Step - 1
    For y = 1 To x
        s1 = matrix(x + 1, y)
        s2 = matrix(x + 1, y + 1)
        If s1 > s2 Then
            matrix(x, y) += s1
        Else
            matrix(x, y) += s2
        End If
    Next
Next

Print 
Print "  maximum triangle path sum ="; matrix(1, 1)

' empty keyboard buffer 
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</syntaxhighlight>
{{out}}<pre>  maximum triangle path sum = 1320</pre>

=={{header|Go}}==
<syntaxhighlight lang="go">package main

import (
    "fmt"
    "strconv"
    "strings"
)

const t = `               55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93`

func main() {
    lines := strings.Split(t, "\n")
    f := strings.Fields(lines[len(lines)-1])
    d := make([]int, len(f))
    var err error
    for i, s := range f {
        if d[i], err = strconv.Atoi(s); err != nil {
            panic(err)
        }
    }
    d1 := d[1:]
    var l, r, u int
    for row := len(lines) - 2; row >= 0; row-- {
        l = d[0]
        for i, s := range strings.Fields(lines[row]) {
            if u, err = strconv.Atoi(s); err != nil {
                panic(err)
            }
            if r = d1[i]; l > r {
                d[i] = u + l
            } else {
                d[i] = u + r
            }
            l = r
        }
    }
    fmt.Println(d[0])
}</syntaxhighlight>
{{Out}}
<pre>
1320
</pre>

=={{header|Haskell}}==
<syntaxhighlight lang="haskell">parse = map (map read . words) . lines
f x y z = x + max y z
g xs ys = zipWith3 f xs ys $ tail ys
solve = head . foldr1 g
main = readFile "triangle.txt" >>= print . solve . parse</syntaxhighlight>
{{out}}
<pre>1320</pre>

Or, inlining the data for quick testing, and using an applicative expression:

<syntaxhighlight lang="haskell">---------------- MAXIMUM TRIANGLE PATH SUM ---------------

maxPathSum :: [[Int]] -> Int
maxPathSum =
  head
    . foldr1
      ((<*> tail) . zipWith3 (\x y z -> x + max y z))

--------------------------- TEST -------------------------
main :: IO ()
main =
  print $
    maxPathSum
      [ [55],
        [94, 48],
        [95, 30, 96],
        [77, 71, 26, 67],
        [97, 13, 76, 38, 45],
        [07, 36, 79, 16, 37, 68],
        [48, 07, 09, 18, 70, 26, 06],
        [18, 72, 79, 46, 59, 79, 29, 90],
        [20, 76, 87, 11, 32, 07, 07, 49, 18],
        [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
        [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
        [02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23],
        [92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42],
        [56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72],
        [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
        [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52],
        [06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15],
        [27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
      ]</syntaxhighlight>
{{Out}}
<pre>1320</pre>


ZipList variant:

<syntaxhighlight lang="haskell">import Control.Applicative (ZipList (ZipList, getZipList))


---------------- MAXIMUM TRIANGLE PATH SUM ---------------

maxPathSum :: [[Int]] -> Int
maxPathSum [] = 0
maxPathSum triangleRows =
 head
    ( foldr1
        ( \xs ->
            ( \ys zs ->
                getZipList
                  ( ( ( (\x y z -> x + max y z)
                          <$> ZipList xs
                      )
                        <*> ZipList ys
                    )
                      <*> ZipList zs
                  )
            )
              <*> tail
        )
        triangleRows
    )
 

--------------------------- TEST -------------------------
main :: IO ()
main =
  print $
    maxPathSum
      [ [55],
        [94, 48],
        [95, 30, 96],
        [77, 71, 26, 67],
        [97, 13, 76, 38, 45],
        [07, 36, 79, 16, 37, 68],
        [48, 07, 09, 18, 70, 26, 06],
        [18, 72, 79, 46, 59, 79, 29, 90],
        [20, 76, 87, 11, 32, 07, 07, 49, 18],
        [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
        [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
        [02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23],
        [92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42],
        [56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72],
        [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
        [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52],
        [06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15],
        [27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
      ]</syntaxhighlight>
{{Out}}
<pre>1320</pre>

=={{header|J}}==
<syntaxhighlight lang="j">padTri=: 0 ". ];._2                  NB. parse triangle and (implicitly) pad with zeros
maxSum=: [: {. (+ (0 ,~ 2 >./\ ]))/  NB. find max triangle path sum</syntaxhighlight>

'''Example Usage'''
<syntaxhighlight lang="j">   maxSum padTri freads 'triangle.txt'
1320</syntaxhighlight>

Explanation:

First, we pad all short rows with trailing zeros so that all rows are the same length. This eliminates some ambiguity and simplifies the expression of both the data and the code.

Second, starting with the last row, for each pair of numbers we find the largest of the two (resulting in a list slightly shorter than before, so of course we pad it with a trailing zero) and add that row to the previous row. After repeating this through all the rows, the first value of the resulting row is the maximum we were looking for.

Instead of padding, we could instead trim the other argument to match the current reduced row length.

<syntaxhighlight lang="j">maxsum=: ((] + #@] {. [)2 >./\ ])/</syntaxhighlight>

However, this turns out to be a slightly slower approach, because we are doing a little more work for each row.

(Note that the cost of padding every row to the same width averages out to an average 2x cost in space and time. So what we are saying here is that the interpreter overhead for changing the size of the memory region used in each operation with each row winds up being more than a 2x cost. You can probably beat that using compiled code, but of course the cost of compiling the program will itself be more than 2x - so not worth paying in a one-off experiment. You wind up with similar issues in any system involving one-off tests.)

=={{header|Java}}==
{{works with|Java|8}}
<syntaxhighlight lang="java">import java.nio.file.*;
import static java.util.Arrays.stream;

public class MaxPathSum {

    public static void main(String[] args) throws Exception {
        int[][] data = Files.lines(Paths.get("triangle.txt"))
                .map(s -> stream(s.trim().split("\\s+"))
                        .mapToInt(Integer::parseInt)
                        .toArray())
                .toArray(int[][]::new);

        for (int r = data.length - 1; r > 0; r--)
            for (int c = 0; c < data[r].length - 1; c++)
                data[r - 1][c] += Math.max(data[r][c], data[r][c + 1]);

        System.out.println(data[0][0]);
    }
}</syntaxhighlight>

<pre>1320</pre>

=={{header|Javascript}}==
===ES5===
====Imperative====
<syntaxhighlight lang="javascript">
var arr = [
[55],
[94, 48],
[95, 30, 96],
[77, 71, 26, 67],
[97, 13, 76, 38, 45],
[07, 36, 79, 16, 37, 68],
[48, 07, 09, 18, 70, 26, 06],
[18, 72, 79, 46, 59, 79, 29, 90],
[20, 76, 87, 11, 32, 07, 07, 49, 18],
[27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
[14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
[02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23],
[92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42],
[56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72],
[44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
[85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52],
[06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15],
[27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
];

while (arr.length !== 1) {
  var len = arr.length;
  var row = [];
  var current = arr[len-2];
  var currentLen = current.length - 1;
  var end = arr[len-1];

  for ( var i = 0; i <= currentLen; i++ ) {
    row.push(Math.max(current[i] + end[i] || 0, current[i] + end[i+1] || 0) )
  }

  arr.pop();
  arr.pop();

  arr.push(row);
}

console.log(arr);
</syntaxhighlight>

{{out}}
<syntaxhighlight lang="javascript">
[ [ 1320 ] ]
</syntaxhighlight>

====Functional====
{{trans|Haskell}}
<syntaxhighlight lang="javascript">(function () {

  // Right fold using final element as initial accumulator
  // (a -> a -> a) -> t a -> a
  function foldr1(f, lst) {
    return lst.length > 1 ? (
      f(lst[0], foldr1(f, lst.slice(1)))
    ) : lst[0];
  }

  // function of arity 3 mapped over nth items of each of 3 lists
  // (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
  function zipWith3(f, xs, ys, zs) {
    return zs.length ? [f(xs[0], ys[0], zs[0])].concat(
      zipWith3(f, xs.slice(1), ys.slice(1), zs.slice(1))) : [];
  }

  // Evaluating from bottom up (right fold)
  // and with recursion left to right (head and first item of tail at each stage)
  return foldr1(
    function (xs, ys) {
      return zipWith3(
        function (x, y, z) {
          return x + (y < z ? z : y);
        },
        xs, ys, ys.slice(1) // item above, and larger of two below
      );
    }, [
        [55],
        [94, 48],
        [95, 30, 96],
        [77, 71, 26, 67],
        [97, 13, 76, 38, 45],
        [07, 36, 79, 16, 37, 68],
        [48, 07, 09, 18, 70, 26, 06],
        [18, 72, 79, 46, 59, 79, 29, 90],
        [20, 76, 87, 11, 32, 07, 07, 49, 18],
        [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
        [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
        [02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23],
        [92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42],
        [56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72],
        [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
        [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52],
        [06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15],
        [27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
    ]
  )[0];

})();</syntaxhighlight>
{{out}}
<syntaxhighlight lang="javascript">1320</syntaxhighlight>

===ES6===
====Imperative====
<syntaxhighlight lang="javascript">function maximumTrianglePathSum(triangle) {

  function distilLastLine() {
    let lastLine = triangle.pop(),
        aboveLine = triangle.pop();
    for (let i = 0; i < aboveLine.length; i++)
      aboveLine[i] = Math.max(
        aboveLine[i] + lastLine[i],
        aboveLine[i] + lastLine[i + 1]
      );
    triangle.push(aboveLine);
  }
  
  do {
    distilLastLine();
  } while (triangle.length > 1);
  return triangle[0][0];
}

// testing
let theTriangle = [
[55],
[94, 48],
[95, 30, 96],
[77, 71, 26, 67],
[97, 13, 76, 38, 45],
[ 7, 36, 79, 16, 37, 68],
[48,  7,  9, 18, 70, 26,  6],
[18, 72, 79, 46, 59, 79, 29, 90],
[20, 76, 87, 11, 32,  7,  7, 49, 18],
[27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
[14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
[ 2, 90,  3, 60, 48, 49, 41, 46, 33, 36, 47, 23],
[92, 50, 48,  2, 36, 59, 42, 79, 72, 20, 82, 77, 42],
[56, 78, 38, 80, 39, 75,  2, 71, 66, 66,  1,  3, 55, 72],
[44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
[85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17,  1,  1, 99, 89, 52],
[ 6, 71, 28, 75, 94, 48, 37, 10, 23, 51,  6, 48, 53, 18, 74, 98, 15],
[27,  2, 92, 23,  8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
];

console.log(maximumTrianglePathSum(theTriangle));</syntaxhighlight>
{{out}}
<syntaxhighlight lang="javascript">1320</syntaxhighlight>
====Functional====
{{Trans|Haskell}}
<syntaxhighlight lang="javascript">(() => {
    "use strict";

    // ------------------ MAX PATH SUM -------------------

    // Working from the bottom of the triangle upwards,
    // summing each number with the larger of the two below
    // until the maximum emerges at the top.

    // maxPathSum ::[[Int]] -> Int
    const maxPathSum = xss =>
        // A list of lists folded down to a list of just one
        // remaining integer.
        foldr1(
            // The accumulator, zipped with the tail of the
            // accumulator, yields pairs of adjacent sums.
            (ys, xs) => zipWith3(

                // Plus greater of two below
                (a, b, c) => a + Math.max(b, c)
            )(xs)(ys)(ys.slice(1))
        )(xss)[0];


    // ---------------- GENERIC FUNCTIONS ----------------

    // foldr1 :: (a -> a -> a) -> [a] -> a
    const foldr1 = f =>
        xs => 0 < xs.length ? (
            xs.slice(0, -1).reduceRight(
                f, xs.slice(-1)[0]
            )
        ) : [];


    // zipWith3 :: (a -> b -> c -> d) ->
    // [a] -> [b] -> [c] -> [d]
    const zipWith3 = f =>
        xs => ys => zs => Array.from({
            length: Math.min(
                ...[xs, ys, zs].map(x => x.length)
            )
        }, (_, i) => f(xs[i], ys[i], zs[i]));


    // ---------------------- TEST -----------------------
    return maxPathSum([
        [55],
        [94, 48],
        [95, 30, 96],
        [77, 71, 26, 67],
        [97, 13, 76, 38, 45],
        [7, 36, 79, 16, 37, 68],
        [48, 7, 9, 18, 70, 26, 6],
        [18, 72, 79, 46, 59, 79, 29, 90],
        [20, 76, 87, 11, 32, 7, 7, 49, 18],
        [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
        [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
        [2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23],
        [92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42],
        [56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72],
        [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
        [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52],
        [6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15],
        [27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
    ]);
})();</syntaxhighlight>
{{Out}}
<pre>1320</pre>

=={{header|jq}}==
The following implementation illustrates the use of an inner function as a helper function, which is used here mainly for clarity. The inner function in effect implements the inner loop;
the outer loop is implemented using <tt>reduce</tt>.

The input array is identical to that in the Javascript section and is therefore omitted here.<syntaxhighlight lang="jq"># Usage: TRIANGLE | solve
def solve: 

  # update(next) updates the input row of maxima:
  def update(next):
    . as $maxima
    | [ range(0; next|length)
       | next[.] + ([$maxima[.], $maxima[. + 1]] | max) ];
  
  . as $in
  | reduce range(length -2; -1; -1) as $i 
      ($in[-1];  update( $in[$i] ) ) ;</syntaxhighlight>

=={{header|Julia}}==
{{works with|Julia|0.6}}

<syntaxhighlight lang="julia"># dynamic solution
function maxpathsum(t::Array{Array{I, 1}, 1}) where I
    T = deepcopy(t)
    for r in length(T)-1:-1:1
        for c in linearindices(T[r])
            T[r][c] += max(T[r+1][c], T[r+1][c+1])
        end
    end
    return T[1][1]
end

test = [[55],
        [94, 48],
        [95, 30, 96],
        [77, 71, 26, 67],
        [97, 13, 76, 38, 45],
        [07, 36, 79, 16, 37, 68],
        [48, 07, 09, 18, 70, 26, 06],
        [18, 72, 79, 46, 59, 79, 29, 90],
        [20, 76, 87, 11, 32, 07, 07, 49, 18],
        [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
        [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
        [02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23],
        [92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42],
        [56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72],
        [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
        [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52],
        [06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15],
        [27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]]

@show maxpathsum(test)</syntaxhighlight>

{{out}}
<pre>maxpathsum(test) = 1320</pre>

=={{header|Kotlin}}==
{{trans|C}}
<syntaxhighlight lang="scala">// version 1.1.2

val tri = intArrayOf(
    55,
    94, 48,
    95, 30, 96,
    77, 71, 26, 67,
    97, 13, 76, 38, 45,
     7, 36, 79, 16, 37, 68,
    48,  7,  9, 18, 70, 26,  6,
    18, 72, 79, 46, 59, 79, 29, 90,
    20, 76, 87, 11, 32,  7,  7, 49, 18,
    27, 83, 58, 35, 71, 11, 25, 57, 29, 85,
    14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55,
     2, 90,  3, 60, 48, 49, 41, 46, 33, 36, 47, 23,
    92, 50, 48,  2, 36, 59, 42, 79, 72, 20, 82, 77, 42,
    56, 78, 38, 80, 39, 75,  2, 71, 66, 66,  1,  3, 55, 72,
    44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36,
    85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17,  1,  1, 99, 89, 52,
     6, 71, 28, 75, 94, 48, 37, 10, 23, 51,  6, 48, 53, 18, 74, 98, 15,
    27,  2, 92, 23,  8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93
)

fun main(args: Array<String>) {
    val triangles = arrayOf(tri.sliceArray(0..9), tri)
    for (triangle in triangles) {
        val size  = triangle.size
        val base  = ((Math.sqrt(8.0 * size + 1.0) - 1.0)/ 2.0).toInt()
        var step  = base - 1
        var stepc = 0
        for (i in (size - base - 1) downTo 0) {
            triangle[i] += maxOf(triangle[i + step], triangle[i + step + 1])
            if (++stepc == step) {
                step--
                stepc = 0
            }
        }
        println("Maximum total  = ${triangle[0]}")
    }
}</syntaxhighlight>

{{out}}
<pre>
Maximum total  = 321
Maximum total  = 1320
</pre>

=={{header|Lua}}==

While the solutions here are clever, I found most of them to be hard to follow. In fact, none of them are very good for showing how the algorithm works. So I wrote this Lua version for maximum readability.

<syntaxhighlight lang="lua">local triangleSmall = {
    { 55 },
    { 94, 48 },
    { 95, 30, 96 },
    { 77, 71, 26, 67 },
}

local triangleLarge = {
    { 55 },
    { 94, 48 },
    { 95, 30, 96 },
    { 77, 71, 26, 67 },
    { 97, 13, 76, 38, 45 },
    {  7, 36, 79, 16, 37, 68 },
    { 48,  7,  9, 18, 70, 26,  6 },
    { 18, 72, 79, 46, 59, 79, 29, 90 },
    { 20, 76, 87, 11, 32,  7,  7, 49, 18 },
    { 27, 83, 58, 35, 71, 11, 25, 57, 29, 85 },
    { 14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55 },
    {  2, 90,  3, 60, 48, 49, 41, 46, 33, 36, 47, 23 },
    { 92, 50, 48,  2, 36, 59, 42, 79, 72, 20, 82, 77, 42 },
    { 56, 78, 38, 80, 39, 75,  2, 71, 66, 66,  1,  3, 55, 72 },
    { 44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36 },
    { 85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17,  1,  1, 99, 89, 52 },
    {  6, 71, 28, 75, 94, 48, 37, 10, 23, 51,  6, 48, 53, 18, 74, 98, 15 },
    { 27,  2, 92, 23,  8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93 },
};

function solve(triangle)

    -- Get total number of rows in triangle.
    local nRows = table.getn(triangle)

    -- Start at 2nd-to-last row and work up to the top.
    for row = nRows-1, 1, -1 do

        -- For each value in row, add the max of the 2 children beneath it.
        for i = 1, row do
            local child1 = triangle[row+1][i]
            local child2 = triangle[row+1][i+1]
            triangle[row][i] = triangle[row][i] + math.max(child1, child2)
        end

    end

    -- The top of the triangle now holds the answer.
    return triangle[1][1];

end

print(solve(triangleSmall))
print(solve(triangleLarge))
</syntaxhighlight>

{{out}}
<pre>321
1320</pre>

=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">nums={{55},{94,48},{95,30,96},{77,71,26,67},{97,13,76,38,45},{7,36,79,16,37,68},{48,7,9,18,70,26,6},{18,72,79,46,59,79,29,90},{20,76,87,11,32,7,7,49,18},{27,83,58,35,71,11,25,57,29,85},{14,64,36,96,27,11,58,56,92,18,55},{2,90,3,60,48,49,41,46,33,36,47,23},{92,50,48,2,36,59,42,79,72,20,82,77,42},{56,78,38,80,39,75,2,71,66,66,1,3,55,72},{44,25,67,84,71,67,11,61,40,57,58,89,40,56,36},{85,32,25,85,57,48,84,35,47,62,17,1,1,99,89,52},{6,71,28,75,94,48,37,10,23,51,6,48,53,18,74,98,15},{27,2,92,23,8,71,76,84,15,52,92,63,81,10,44,10,69,93}};
ClearAll[DoStep,MaximumTrianglePathSum]
DoStep[lst1_List,lst2_List]:=lst2+Join[{First[lst1]},Max/@Partition[lst1,2,1],{Last[lst1]}]
MaximumTrianglePathSum[triangle_List]:=Max[Fold[DoStep,First[triangle],Rest[triangle]]]</syntaxhighlight>
{{out}}
<pre>MaximumTrianglePathSum[nums]
1320</pre>

=={{header|Nim}}==
{{trans|Python}}
<syntaxhighlight lang="nim">import sequtils, strutils, sugar

proc solve(tri: seq[seq[int]]): int =
  var tri = tri
  while tri.len > 1:
    let t0 = tri.pop
    for i, t in tri[tri.high]: tri[tri.high][i] = max(t0[i], t0[i+1]) + t
  tri[0][0]

const data = """
                          55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"""

echo solve data.splitLines.map((x: string) => x.strip.split.map parseInt)
</syntaxhighlight>

{{out}}
<pre>1320</pre>

=={{header|PARI/GP}}==
<syntaxhighlight lang="parigp">V=[[55],[94,48],[95,30,96],[77,71,26,67],[97,13,76,38,45],[07,36,79,16,37,68],[48,07,09,18,70,26,06],[18,72,79,46,59,79,29,90],[20,76,87,11,32,07,07,49,18],[27,83,58,35,71,11,25,57,29,85],[14,64,36,96,27,11,58,56,92,18,55],[02,90,03,60,48,49,41,46,33,36,47,23],[92,50,48,02,36,59,42,79,72,20,82,77,42],[56,78,38,80,39,75,02,71,66,66,01,03,55,72],[44,25,67,84,71,67,11,61,40,57,58,89,40,56,36],[85,32,25,85,57,48,84,35,47,62,17,01,01,99,89,52],[06,71,28,75,94,48,37,10,23,51,06,48,53,18,74,98,15],[27,02,92,23,08,71,76,84,15,52,92,63,81,10,44,10,69,93]];
forstep(i=#V,2,-1,V[i-1]+=vector(i-1,j,max(V[i][j],V[i][j+1]))); V[1][1]</syntaxhighlight>
{{out}}
<pre>%1 = 1320</pre>

=={{header|Pascal}}==
testet with freepascal, should run under Turbo Pascal, therefore using static array and val,  and Delphi too.
<syntaxhighlight lang="pascal">program TriSum;
{'triangle.txt'
* one element per line
55
94
48
95
30
96
...}
const
 cMaxTriHeight = 18;
 cMaxTriElemCnt = (cMaxTriHeight+1)*cMaxTriHeight DIV 2 +1;
type
  tElem = longint;
  tbaseRow =  array[0..cMaxTriHeight] of tElem;
  tmyTri   =  array[0..cMaxTriElemCnt] of tElem;

function ReadTri(     fname:string;
                  out     t:tmyTri):integer;
{read triangle values into t and returns height}
var
  f : text;
  s : string;
  i : integer;
  ValCode : word;
begin
  i := 0;
  fillchar(t,Sizeof(t),#0);

  Assign(f,fname);
  {$I-}
  reset(f);
  IF ioResult <> 0 then
  begin
    writeln('IO-Error ',ioResult);
    close(f);
    ReadTri := i;
    EXIT;
  end;
  {$I+}

  while NOT(EOF(f)) AND (i<cMaxTriElemCnt) do
  begin
    readln(f,s);
    val(s,t[i],ValCode);
    inc(i);
    IF ValCode <> 0 then
    begin
      writeln(ValCode,' conversion error at line ',i);
      fillchar(t,Sizeof(t),#0);
      i := 0;
      BREAK;
    end;
  end;
  close(f);
  ReadTri := round(sqrt(2*(i-1)));
end;

function TriMaxSum(var t: tmyTri;hei:integer):integer;
{sums up higher values bottom to top}
var
  i,r,h,tmpMax : integer;
  idxN : integer;
  sumrow : tbaseRow;
begin
  h := hei;
  idxN := (h*(h+1)) div 2 -1;
  {copy base row}
  move(t[idxN-h+1],sumrow[0],SizeOf(tElem)*h);
  dec(h);
{  for r := 0 to h do write(sumrow[r]:4);writeln;}
  idxN := idxN-h;
  while idxN >0 do
  begin
    i := idxN-h;
    r := 0;
    while r < h do
    begin
      tmpMax:= sumrow[r];
      IF tmpMax<sumrow[r+1] then
        tmpMax:=sumrow[r+1];
      sumrow[r]:= tmpMax+t[i];
      inc(i);
      inc(r);
    end;
    idxN := idxN-h;
    dec(h);
{  for r := 0 to h do write(sumrow[r]:4);writeln;}
  end;
  TriMaxSum := sumrow[0];
end;

var
  h : integer;
  triangle : tmyTri;
Begin
{  writeln(TriMaxSum(triangle,ReadTri('triangle.txt',triangle))); -> 1320}
  h := ReadTri('triangle.txt',triangle);
  writeln('height sum');
  while h > 0 do
  begin
    writeln(h:4,TriMaxSum(triangle,h):7);
    dec(h);
  end;
end.</syntaxhighlight>
{{out}}
<pre>height sum
  18   1320
  17   1249
....
   4    321
   3    244
   2    149
   1     55</pre>

=={{header|Perl}}==
<syntaxhighlight lang="perl">use 5.10.0;
use List::Util 'max';

my @sum;
while (<>) {
	my @x = split;
	@sum = ($x[0] + $sum[0],
		map($x[$_] + max(@sum[$_-1, $_]), 1 .. @x-2),
		$x[-1] + $sum[-1]);
}

say max(@sum);</syntaxhighlight>
{{out}}
<pre>
% perl maxpath.pl triangle.txt
1320
</pre>

=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
 <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">tri</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">55</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">94</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">48</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">95</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">96</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">77</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">71</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">26</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">67</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">97</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">13</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">76</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">38</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">45</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">36</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">79</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">16</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">37</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">68</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">48</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">70</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">26</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">6</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">18</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">72</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">79</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">46</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">79</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">90</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">76</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">87</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">32</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">49</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">27</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">83</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">58</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">35</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">71</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">57</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">85</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">14</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">64</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">36</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">96</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">27</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">58</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">56</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">92</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">55</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">90</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">60</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">48</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">49</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">41</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">46</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">33</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">36</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">47</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">92</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">50</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">48</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">36</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">42</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">79</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">72</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">82</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">77</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">42</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">56</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">78</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">38</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">80</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">39</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">75</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">71</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">66</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">66</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">55</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">72</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">44</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">67</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">84</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">71</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">67</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">61</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">40</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">57</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">58</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">89</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">40</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">56</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">36</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">85</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">32</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">85</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">57</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">48</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">84</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">35</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">47</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">62</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">99</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">89</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">52</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">71</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">28</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">75</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">94</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">48</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">37</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">51</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">48</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">53</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">74</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">98</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">15</span><span style="color: #0000FF;">},</span>
                 <span style="color: #0000FF;">{</span><span style="color: #000000;">27</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">92</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23</span><span style="color: #0000FF;">,</span>  <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">71</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">76</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">84</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">15</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">52</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">92</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">63</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">81</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">44</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">69</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">93</span><span style="color: #0000FF;">}}</span>
  
 <span style="color: #000080;font-style:italic;">-- update each row from last but one upwards, with the larger 
 --  child, so the first step is to replace 6 with 6+27 or 6+2.</span>
 <span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tri</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
         <span style="color: #000000;">tri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">..</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
 <span style="color: #0000FF;">?</span><span style="color: #000000;">tri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
1320
</pre>

=={{header|Picat}}==
===Mode directed tabling===
<syntaxhighlight lang="picat">table (+,+,+,max)  
pp(Row,_Column,Tri,Sum),Row>Tri.length => Sum=0.
pp(Row,Column,Tri,Sum) ?=> 
  pp(Row+1,Column,Tri,Sum1),
  Sum = Sum1+Tri[Row,Column].
pp(Row,Column,Tri,Sum) => 
  pp(Row+1,Column+1,Tri,Sum1),
  Sum = Sum1+Tri[Row,Column].</syntaxhighlight>

===Loop based approach===
<syntaxhighlight lang="picat">pp2(Row, Column, Sum, Tri, M) =>
  if Sum > M.get(max_val,0) then
     M.put(max_val,Sum)
  end,
  Row := Row + 1,
  if Row <= Tri.length then
    foreach(I in 0..1) 
       pp2(Row,Column+I, Sum+Tri[Row,Column+I], Tri, M)
     end
  end.</syntaxhighlight>

===Recursion===
{{trans|Prolog}}
<syntaxhighlight lang="picat">max_path(N, V) :-
	data(N, T),
	path(1, T, V).
 
path(_N, [], 0) .
path(N, [H | T], V) :-
	nth(N, H, V0),
	N1 is N+1,
	path(N, T, V1),
	path(N1, T, V2),
	V = V0 +  max(V1, V2).
  
data(2, P) :-
	P =
	[ [55],
	  [94, 48],
	  [95, 30, 96],
	  [77, 71, 26, 67],
	  [97, 13, 76, 38, 45],
	  [7, 36, 79, 16, 37, 68],
	  [48, 7, 9, 18, 70, 26, 6],
	  [18, 72, 79, 46, 59, 79, 29, 90],
	  [20, 76, 87, 11, 32, 7, 7, 49, 18],
	  [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
	  [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
	  [2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23],
	  [92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42],
	  [56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72],
	  [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
	  [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52],
	  [6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15],
	  [27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]].</syntaxhighlight>

===Test===
<syntaxhighlight lang="picat">import util.

go =>
  tri(Tri),

  println("Mode directed tabling:"),
  pp(1,1,Tri,Sum),
  writeln(max_val=Sum),
  nl,

  println("Loop based:"),
  M = new_map([max_val=0]),
  pp2(1,1, Tri[1,1], Tri, M),
  writeln(max_val=M.get(max_val)),
  nl,

  println("Adapted the Prolog solution:"),
  max_path(2, V2),
  println(max_val=V2),
  nl.

tri(Tri) =>
 Tri =
{
{55},
{94,48},
{95,30,96},
{77,71,26,67},
{97,13,76,38,45},
{07,36,79,16,37,68},
{48,07,09,18,70,26,06},
{18,72,79,46,59,79,29,90},
{20,76,87,11,32,07,07,49,18},
{27,83,58,35,71,11,25,57,29,85},
{14,64,36,96,27,11,58,56,92,18,55},
{02,90,03,60,48,49,41,46,33,36,47,23},
{92,50,48,02,36,59,42,79,72,20,82,77,42},
{56,78,38,80,39,75,02,71,66,66,01,03,55,72},
{44,25,67,84,71,67,11,61,40,57,58,89,40,56,36},
{85,32,25,85,57,48,84,35,47,62,17,01,01,99,89,52},
{06,71,28,75,94,48,37,10,23,51,06,48,53,18,74,98,15},
{27,02,92,23,08,71,76,84,15,52,92,63,81,10,44,10,69,93}
}.</syntaxhighlight>

{{out}}
<pre>Mode directed tabling:
max_val = 1320

Loop based:
max_val = 1320

Adapted the Prolog solution:
max_val = 1320</pre>

=={{header|PicoLisp}}==
{{trans|Common Lisp}}
<syntaxhighlight lang="picolisp">(de maxpath (Lst)
   (let (Lst (reverse Lst)  R (car Lst))
      (for I (cdr Lst)
         (setq R
            (mapcar
               +
               (maplist
                  '((L)
                     (and (cdr L) (max (car L) (cadr L))) )
                  R )
               I ) ) )
      (car R) ) )</syntaxhighlight>

=={{header|PL/I}}==
{{trans|REXX}}
<syntaxhighlight lang="pli">*process source xref attributes or(!);
 triang: Proc Options(Main);
 Dcl nn(18,18)  Bin Fixed(31);
 Dcl (rows,i,j) Bin Fixed(31);
 Dcl (p,k,kn)   Bin Fixed(31);
 Call f_r(1 ,'                           55                         ');
 Call f_r(2 ,'                         94 48                        ');
 Call f_r(3 ,'                        95 30 96                      ');
 Call f_r(4 ,'                      77 71 26 67                     ');
 Call f_r(5 ,'                     97 13 76 38 45                   ');
 Call f_r(6 ,'                   07 36 79 16 37 68                  ');
 Call f_r(7 ,'                  48 07 09 18 70 26 06                ');
 Call f_r(8 ,'                18 72 79 46 59 79 29 90               ');
 Call f_r(9 ,'               20 76 87 11 32 07 07 49 18             ');
 Call f_r(10,'             27 83 58 35 71 11 25 57 29 85            ');
 Call f_r(11,'            14 64 36 96 27 11 58 56 92 18 55          ');
 Call f_r(12,'          02 90 03 60 48 49 41 46 33 36 47 23         ');
 Call f_r(13,'         92 50 48 02 36 59 42 79 72 20 82 77 42       ');
 Call f_r(14,'       56 78 38 80 39 75 02 71 66 66 01 03 55 72      ');
 Call f_r(15,'      44 25 67 84 71 67 11 61 40 57 58 89 40 56 36    ');
 Call f_r(16,'    85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52   ');
 Call f_r(17,'   06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15 ');
 Call f_r(18,' 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93');
 rows=hbound(nn,1);

 do r=rows by -1 to 2;
   p=r-1;                           /*traipse through triangle rows. */
   do k=1 to p;
     kn=k+1;                        /*re-calculate the previous row. */
     nn(p,k)=max(nn(r,k),nn(r,kn))+nn(p,k);  /*replace previous nn   */
     end;
   end;
 Put Edit('maximum path sum:',nn(1,1))(Skip,a,f(5)); /*display result*/
 f_r: Proc(r,vl);
 /* fill row r with r values */
 Dcl r Bin Fixed(31);
 Dcl vl Char(*);
 Dcl vla Char(100) Var;
 vla=' '!!trim(vl);
 get string(vla) Edit((nn(r,j) Do j=1 To r))(f(3));
 End;
 End;</syntaxhighlight>
{{out}}
<pre>maximum path sum: 1320</pre>

=={{header|Prolog}}==
<syntaxhighlight lang="prolog">max_path(N, V) :-
	data(N, T),
	path(0, T, V).

path(_N, [], 0) .
path(N, [H | T], V) :-
	nth0(N, H, V0),
	N1 is N+1,
	path(N, T, V1),
	path(N1, T, V2),
	V is V0 +  max(V1, V2).

data(1, P) :-
	P =
	[ [55],
	  [94, 48],
	  [95, 30, 96],
	  [77, 71, 26, 67]].


data(2, P) :-
	P =
	[ [55],
	  [94, 48],
	  [95, 30, 96],
	  [77, 71, 26, 67],
	  [97, 13, 76, 38, 45],
	  [7, 36, 79, 16, 37, 68],
	  [48, 7, 9, 18, 70, 26, 6],
	  [18, 72, 79, 46, 59, 79, 29, 90],
	  [20, 76, 87, 11, 32, 7, 7, 49, 18],
	  [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
	  [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
	  [2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23],
	  [92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42],
	  [56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72],
	  [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
	  [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52],
	  [6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15],
	  [27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]].

</syntaxhighlight>
{{out}}
<pre> ?- max_path(1, V).
V = 321 .

 ?- max_path(2, V).
V = 1320 .

</pre>

=={{header|Python}}==
A simple mostly imperative solution:
<syntaxhighlight lang="python">def solve(tri):
    while len(tri) > 1:
        t0 = tri.pop()
        t1 = tri.pop()
        tri.append([max(t0[i], t0[i+1]) + t for i,t in enumerate(t1)])
    return tri[0][0]


data = """                55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"""

print solve([map(int, row.split()) for row in data.splitlines()])</syntaxhighlight>
{{out}}
<pre>1320</pre>

A more functional version, similar to the Haskell entry (same output):
<syntaxhighlight lang="python">from itertools import imap

f = lambda x, y, z: x + max(y, z)
g = lambda xs, ys: list(imap(f, ys, xs, xs[1:]))
data = [map(int, row.split()) for row in open("triangle.txt")][::-1]
print reduce(g, data)[0]</syntaxhighlight>

And, updating a little for Python 3 (in which ''itertools'' no longer defines '''imap''', and '''reduce''' now has to be imported from ''functools''), while inlining the data for ease of testing:
{{Trans|Haskell}}
{{Trans|JavaScript}}
{{Works with|Python|3|7}}
<syntaxhighlight lang="python">'''Maximum triangle path sum'''

from functools import (reduce)


# maxPathSum :: [[Int]] -> Int
def maxPathSum(rows):
    '''The maximum total among all possible
       paths from the top to the bottom row.
    '''
    return reduce(
        lambda xs, ys: [
            a + max(b, c) for (a, b, c)
            in zip(ys, xs, xs[1:])
        ],
        reversed(rows[:-1]), rows[-1]
    )[0]


# ------------------------- TEST -------------------------
print(
    maxPathSum([
        [55],
        [94, 48],
        [95, 30, 96],
        [77, 71, 26, 67],
        [97, 13, 76, 38, 45],
        [7, 36, 79, 16, 37, 68],
        [48, 7, 9, 18, 70, 26, 6],
        [18, 72, 79, 46, 59, 79, 29, 90],
        [20, 76, 87, 11, 32, 7, 7, 49, 18],
        [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
        [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
        [2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23],
        [92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42],
        [56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72],
        [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
        [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52],
        [6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15],
        [27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
    ])
)</syntaxhighlight>
{{Out}}
<pre>1320</pre>

=={{header|Quackery}}==

<syntaxhighlight lang="Quackery">  [ [] swap
    behead swap
    witheach
      [ tuck max
        rot swap join
        swap ]
    drop ]                   is pairwise-max ( [ --> [ )

  [ [] unrot
    witheach
      [ dip behead +
        rot swap join
        swap ]
    drop ]                   is add-items    ( [ --> [ )

  [ behead dip
      [ reverse
        behead
        pairwise-max
        swap witheach
          [ add-items
            pairwise-max ] ]
        add-items
        0 peek ]             is mtps         ( [ --> n )

' [ [ 55 ]
    [ 94 48 ]
    [ 95 30 96 ]
    [ 77 71 26 67 ]
    [ 97 13 76 38 45 ]
    [ 07 36 79 16 37 68 ]
    [ 48 07 09 18 70 26 06 ]
    [ 18 72 79 46 59 79 29 90 ]
    [ 20 76 87 11 32 07 07 49 18 ]
    [ 27 83 58 35 71 11 25 57 29 85 ]
    [ 14 64 36 96 27 11 58 56 92 18 55 ]
    [ 02 90 03 60 48 49 41 46 33 36 47 23 ]
    [ 92 50 48 02 36 59 42 79 72 20 82 77 42 ]
    [ 56 78 38 80 39 75 02 71 66 66 01 03 55 72 ]
    [ 44 25 67 84 71 67 11 61 40 57 58 89 40 56 36 ]
    [ 85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52 ]
    [ 06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15 ]
    [ 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93 ] ]
mtps echo</syntaxhighlight>

{{out}}

<pre>1320</pre>

=={{header|Racket}}==
<syntaxhighlight lang="racket">#lang racket
(require math/number-theory)

(define (trinv n) ; OEIS A002024
  (exact-floor (/ (+ 1 (sqrt (* 1 (* 8 n)))) 2)))

(define (triangle-neighbour-bl n)
  (define row (trinv n))
  (+ n (- (triangle-number row) (triangle-number (- row 1)))))

(define (maximum-triangle-path-sum T)
  (define n-rows (trinv (vector-length T)))
  (define memo# (make-hash))
  (define (inner i)
    (hash-ref!
     memo# i
     (λ ()
       (+ (vector-ref T (sub1 i)) ; index is 1-based (so vector-refs need -1'ing)
          (cond [(= (trinv i) n-rows) 0]
                [else
                 (define bl (triangle-neighbour-bl i))
                 (max (inner bl) (inner (add1 bl)))])))))
  (inner 1))

(module+ main
  (maximum-triangle-path-sum
   #(55
     94 48
     95 30 96
     77 71 26 67
     97 13 76 38 45
     07 36 79 16 37 68
     48 07 09 18 70 26 06
     18 72 79 46 59 79 29 90
     20 76 87 11 32 07 07 49 18
     27 83 58 35 71 11 25 57 29 85
     14 64 36 96 27 11 58 56 92 18 55
     02 90 03 60 48 49 41 46 33 36 47 23
     92 50 48 02 36 59 42 79 72 20 82 77 42
     56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
     85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
     06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
     27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93)))

(module+ test
  (require rackunit)
  (check-equal? (for/list ((n (in-range 1 (add1 10)))) (trinv n)) '(1 2 2 3 3 3 4 4 4 4))
  ;    1
  ;   2 3
  ;  4 5 6
  ; 7 8 9 10
  (check-eq? (triangle-neighbour-bl 1) 2)
  (check-eq? (triangle-neighbour-bl 3) 5)
  (check-eq? (triangle-neighbour-bl 5) 8)
  (define test-triangle
    #(55   94 48   95 30 96   77 71 26 67))
  (check-equal? (maximum-triangle-path-sum test-triangle) 321)
  )</syntaxhighlight>
{{out}}
<pre>1320</pre>

=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2018.03}}
The <tt>Z+</tt> and <tt>Zmax</tt> are examples of the zipwith metaoperator. Note also we can use the <tt>Zmax</tt> metaoperator form because <tt>max</tt> is define as an infix in Perl 6.
<syntaxhighlight lang="raku" line>my $triangle = q|         55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93|;


my @rows = $triangle.lines.map: { [.words] }
while @rows > 1 {
    my @last := @rows.pop;
    @rows[*-1] = (@rows[*-1][] Z+ (@last Zmax @last[1..*])).List;
}
put @rows;


# Here's a more FPish version. We define our own operator and the use it in the reduction metaoperator form, [op], which turns any infix into a list operator. 
sub infix:<op>(@a,@b) { (@a Zmax @a[1..*]) Z+ @b }
put [op] $triangle.lines.reverse.map: { [.words] }


# Or, instead of using reverse, one could also define the op as right-associative.
sub infix:<rop>(@a,@b) is assoc('right') { @a Z+ (@b Zmax @b[1..*]) }
put [rop] $triangle.lines.map: { [.words] }</syntaxhighlight>

{{out}}
<pre>1320
1320
1320</pre>

=={{header|REXX}}==
The method used is very efficient and performs very well for triangles that have thousands of rows (lines).
<br>For an expanded discussion of the program method's efficiency, see the discussion page.   
<syntaxhighlight lang="rexx">/*REXX program finds the  maximum sum  of a  path of numbers  in a pyramid of numbers.  */
@.=.;                   @.1  =                            55
                        @.2  =                          94 48
                        @.3  =                         95 30 96
                        @.4  =                       77 71 26 67
                        @.5  =                      97 13 76 38 45
                        @.6  =                    07 36 79 16 37 68
                        @.7  =                   48 07 09 18 70 26 06
                        @.8  =                 18 72 79 46 59 79 29 90
                        @.9  =                20 76 87 11 32 07 07 49 18
                        @.10 =              27 83 58 35 71 11 25 57 29 85
                        @.11 =             14 64 36 96 27 11 58 56 92 18 55
                        @.12 =           02 90 03 60 48 49 41 46 33 36 47 23
                        @.13 =          92 50 48 02 36 59 42 79 72 20 82 77 42
                        @.14 =        56 78 38 80 39 75 02 71 66 66 01 03 55 72
                        @.15 =       44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
                        @.16 =     85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
                        @.17 =    06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
                        @.18 =  27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
#.=0
      do    r=1  while  @.r\==.                  /*build another version of the pyramid.*/
         do k=1  for r;    #.r.k=word(@.r, k)    /*assign a number to an array number.  */
         end   /*k*/
      end      /*r*/

      do    r=r-1  by -1  to 2;         p=r-1    /*traipse through the pyramid rows.    */
         do k=1    for p;               _=k+1    /*re─calculate the previous pyramid row*/
         #.p.k=max(#.r.k, #.r._)    +   #.p.k    /*replace the previous number.         */
         end   /*k*/
      end      /*r*/
                                                 /*stick a fork in it,  we're all done. */
say 'maximum path sum: '       #.1.1             /*show the top (row 1) pyramid number. */</syntaxhighlight>
'''output''' &nbsp; using the data within the REXX program:
<pre>
maximum path sum:  1320
</pre>

=={{header|Ring}}==
<syntaxhighlight lang="ring">
# Project : Maximum triangle path sum

load "stdlib.ring"
ln = list(19)
ln[1] = "                   55"
ln[2] = "                  94 48"
ln[3] = "                95 30 96"
ln[4] = "               77 71 26 67"
ln[5] = "              97 13 76 38 45"
ln[6] = "             07 36 79 16 37 68"
ln[7] = "            48 07 09 18 70 26 06"
ln[8] = "           18 72 79 46 59 79 29 90"
ln[9] = "          20 76 87 11 32 07 07 49 18"
ln[10] = "         27 83 58 35 71 11 25 57 29 85"
ln[11] = "        14 64 36 96 27 11 58 56 92 18 55"
ln[12] = "       02 90 03 60 48 49 41 46 33 36 47 23"
ln[13] = "      92 50 48 02 36 59 42 79 72 20 82 77 42"
ln[14] = "     56 78 38 80 39 75 02 71 66 66 01 03 55 72"
ln[15] = "    44 25 67 84 71 67 11 61 40 57 58 89 40 56 36"
ln[16] = "   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52"
ln[17] = "  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15"
ln[18] = " 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
ln[19] = "end"  
 
matrix = newlist(20,20)
x = 1
size = 0
 
for n = 1 to len(ln) - 1
     ln2 = ln[n]
     ln2 = trim(ln2)
     for y = 1 to x
          matrix[x][y] = number(left(ln2,2))
          if len(ln2) > 4
              ln2 = substr(ln2,4,len(ln2)-4)
          ok
     next
     x = x + 1
     size = size + 1
next
 
for x = size - 1 to 1 step - 1
     for y = 1 to x
          s1 = matrix[x+1][y]
          s2 = matrix[x+1][y+1]
          if s1 > s2 
             matrix[x][y] = matrix[x][y] + s1
          else
             matrix[x][y] = matrix[x][y] + s2
          ok
     next
next
 
see "maximum triangle path sum = " + matrix[1][1]
</syntaxhighlight>
Output:
<pre>
maximum triangle path sum = 1320
</pre>

=={{header|RPL}}==
{{works with|HP|48G}}
 « DUP TAIL
   0 + « MAX » DOLIST 
   1 OVER SIZE 1 - SUB
 » '<span style="color:blue">MAX2L</span>' STO
 
 « → t
   « t SIZE LASTARG OVER GET 
     SWAP 1 - 1 '''FOR''' j 
        <span style="color:blue">MAX2L</span> t j GET ADD  
     -1 '''STEP''' 
     HEAD
 » » '<span style="color:blue">P018</span>' STO

 {{ 55 }
 { 94 48 }
 { 95 30 96 }
 { 77 71 26 67 }
 { 97 13 76 38 45 }
 { 07 36 79 16 37 68 }
 { 48 07 09 18 70 26 06 }
 { 18 72 79 46 59 79 29 90 }
 { 20 76 87 11 32 07 07 49 18 }
 { 27 83 58 35 71 11 25 57 29 85 }
 { 14 64 36 96 27 11 58 56 92 18 55 }
 { 02 90 03 60 48 49 41 46 33 36 47 23 }
 { 92 50 48 02 36 59 42 79 72 20 82 77 42 }
 { 56 78 38 80 39 75 02 71 66 66 01 03 55 72 }
 { 44 25 67 84 71 67 11 61 40 57 58 89 40 56 36 }
 { 85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52 }
 { 06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15 }
 { 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93 }} <span style="color:blue">P018</span>
{{out}}
<pre>
1: 1320
</pre>

=={{header|Ruby}}==
<syntaxhighlight lang="ruby">triangle = 
"                         55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"

ar = triangle.each_line.map{|line| line.split.map(&:to_i)}
puts ar.inject([]){|res,x|
  maxes = [0, *res, 0].each_cons(2).map(&:max)
  x.zip(maxes).map{|a,b| a+b}
}.max
# => 1320</syntaxhighlight>

=={{header|Rust}}==
{{works with|Rust|1.3}}
<syntaxhighlight lang="rust">use std::cmp::max;

fn max_path(vector: &mut Vec<Vec<u32>>) -> u32 {
    
    while vector.len() > 1 {
        
        let last = vector.pop().unwrap();
        let ante = vector.pop().unwrap();
        
        let mut new: Vec<u32> = Vec::new();
        
        for (i, value) in ante.iter().enumerate() {
            new.push(max(last[i], last[i+1]) + value);
        };
        
        vector.push(new);
    };
    
    vector[0][0]
}

fn main() {
    let mut data = "55
94 48
95 30 96
77 71 26 67
97 13 76 38 45
07 36 79 16 37 68
48 07 09 18 70 26 06
18 72 79 46 59 79 29 90
20 76 87 11 32 07 07 49 18
27 83 58 35 71 11 25 57 29 85
14 64 36 96 27 11 58 56 92 18 55
02 90 03 60 48 49 41 46 33 36 47 23
92 50 48 02 36 59 42 79 72 20 82 77 42
56 78 38 80 39 75 02 71 66 66 01 03 55 72
44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93";

    let mut vector = data.split("\n").map(|x| x.split(" ").map(|s: &str| s.parse::<u32>().unwrap())
        .collect::<Vec<u32>>()).collect::<Vec<Vec<u32>>>();
    
    let max_value = max_path(&mut vector);
    
    println!("{}", max_value);
    //=> 7273
}</syntaxhighlight>

=={{header|Scala}}==
<syntaxhighlight lang="scala">object MaximumTrianglePathSum extends App {
    // Solution:
    def sum(triangle: Array[Array[Int]]) =
        triangle.reduceRight((upper, lower) =>
            upper zip (lower zip lower.tail)
            map {case (above, (left, right)) => above + Math.max(left, right)}
        ).head

    // Tests:
    def triangle = """   
                          55
                        94 48
                       95 30 96
                     77 71 26 67
    """
    def parse(s: String) = s.trim.split("\\s+").map(_.toInt)
    def parseLines(s: String) = s.trim.split("\n").map(parse)
    def parseFile(f: String) = scala.io.Source.fromFile(f).getLines.map(parse).toArray
    println(sum(parseLines(triangle)))
    println(sum(parseFile("triangle.txt")))
}</syntaxhighlight>
{{out}}
<pre>321
1320</pre>

=={{header|Sidef}}==
{{trans|Perl}}

Iterative solution:
<syntaxhighlight lang="ruby">var sum = [0]

ARGF.each {  |line|
    var x = line.words.map{.to_n}
    sum = [
            x.first + sum.first,
            1 ..^ x.end -> map{|i| x[i] + [sum[i-1, i]].max}...,
            x.last + sum.last,
          ]
}

say sum.max</syntaxhighlight>

Recursive solution:
<syntaxhighlight lang="ruby">var triangle = ARGF.slurp.lines.map{.words.map{.to_n}}
 
func max_value(i=0, j=0) is cached {
    i == triangle.len && return 0
    triangle[i][j] + [max_value(i+1, j), max_value(i+1, j+1)].max
}
 
say max_value()</syntaxhighlight>
{{out}}
<pre>% sidef maxpath.sf triangle.txt
1320</pre>

=={{header|Stata}}==
<syntaxhighlight lang="stata">import delimited triangle.txt, delim(" ") clear
mata
a = st_data(.,.)
n = rows(a)
for (i=n-1; i>=1; i--) {
	for (j=1; j<=i; j++) {
		a[i,j] = a[i,j]+max((a[i+1,j],a[i+1,j+1]))
	}
}
a[1,1]
end</syntaxhighlight>

'''Output'''

<pre>1320</pre>

=={{header|Tcl}}==
{{works with|Tcl|8.6}}
<syntaxhighlight lang="tcl">package require Tcl 8.6

proc maxTrianglePathSum {definition} {
    # Parse the definition, stripping whitespace and leading zeroes.
    set lines [lmap line [split [string trim $definition] "\n"] {
	lmap val $line {scan $val %d}
    }]
    # Paths are bit strings (0 = go left, 1 = go right).
    # Enumerate the possible paths.
    set numPaths [expr {2 ** [llength $lines]}]
    for {set path 0; set max -inf} {$path < $numPaths} {incr path} {
	# Work out how much the current path costs.
	set sum [set idx [set row 0]]
	for {set bit 1} {$row < [llength $lines]} {incr row} {
	    incr sum [lindex $lines $row $idx]
	    if {$path & $bit} {incr idx}
	    set bit [expr {$bit << 1}]
	}
	# Remember the max so far.
	if {$sum > $max} {set max $sum}
    }
    return $max
}

puts [maxTrianglePathSum {
                          55
                        94 48
                       95 30 96
                     77 71 26 67
                    97 13 76 38 45
                  07 36 79 16 37 68
                 48 07 09 18 70 26 06
               18 72 79 46 59 79 29 90
              20 76 87 11 32 07 07 49 18
            27 83 58 35 71 11 25 57 29 85
           14 64 36 96 27 11 58 56 92 18 55
         02 90 03 60 48 49 41 46 33 36 47 23
        92 50 48 02 36 59 42 79 72 20 82 77 42
      56 78 38 80 39 75 02 71 66 66 01 03 55 72
     44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
   85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
  06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
}]
# Reading from a file is left as an exercise…</syntaxhighlight>
{{out}}
<pre>
1320
</pre>

=={{header|VBScript}}==
<syntaxhighlight lang="vb">
'Solution derived from http://stackoverflow.com/questions/8002252/euler-project-18-approach.

Set objfso = CreateObject("Scripting.FileSystemObject")
Set objinfile = objfso.OpenTextFile(objfso.GetParentFolderName(WScript.ScriptFullName) &_
	"\triangle.txt",1,False)
	
row = Split(objinfile.ReadAll,vbCrLf)

For i = UBound(row) To 0 Step -1
	row(i) = Split(row(i)," ")
	If i < UBound(row) Then
		For j = 0 To UBound(row(i))
			If (row(i)(j) + row(i+1)(j)) > (row(i)(j) + row(i+1)(j+1)) Then
				row(i)(j) = CInt(row(i)(j)) + CInt(row(i+1)(j))
			Else
				row(i)(j) = CInt(row(i)(j)) + CInt(row(i+1)(j+1))
			End If
		Next
	End If	
Next

WScript.Echo row(0)(0)

objinfile.Close
Set objfso = Nothing
</syntaxhighlight>

{{In}}
Input file
<pre>
55
94 48
95 30 96
77 71 26 67
97 13 76 38 45
07 36 79 16 37 68
48 07 09 18 70 26 06
18 72 79 46 59 79 29 90
20 76 87 11 32 07 07 49 18
27 83 58 35 71 11 25 57 29 85
14 64 36 96 27 11 58 56 92 18 55
02 90 03 60 48 49 41 46 33 36 47 23
92 50 48 02 36 59 42 79 72 20 82 77 42
56 78 38 80 39 75 02 71 66 66 01 03 55 72
44 25 67 84 71 67 11 61 40 57 58 89 40 56 36
85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52
06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15
27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93
</pre>

{{Out}}
<pre>1320</pre>

=={{header|Wren}}==
{{trans|Go}}
<syntaxhighlight lang="wren">var lines = [
    "                 55",
    "                94 48",
    "               95 30 96",
    "              77 71 26 67",
    "             97 13 76 38 45",
    "            07 36 79 16 37 68",
    "           48 07 09 18 70 26 06",
    "          18 72 79 46 59 79 29 90",
    "         20 76 87 11 32 07 07 49 18",
    "        27 83 58 35 71 11 25 57 29 85",
    "       14 64 36 96 27 11 58 56 92 18 55",
    "      02 90 03 60 48 49 41 46 33 36 47 23",
    "     92 50 48 02 36 59 42 79 72 20 82 77 42",
    "    56 78 38 80 39 75 02 71 66 66 01 03 55 72",
    "   44 25 67 84 71 67 11 61 40 57 58 89 40 56 36",
    "  85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52",
    " 06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15",
    "27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93"
]
var f = lines[-1].split(" ")
var d = f.map { |s| Num.fromString(s) }.toList
for (row in lines.count-2..0) {
    var l = d[0]
    var i = 0
    for (s in lines[row].trimStart().split(" ")) {
        var u = Num.fromString(s)
        var r = d[i+1]
        d[i] = (l > r) ? u + l : u + r
        l = r
        i = i + 1
    }
}
System.print(d[0])</syntaxhighlight>

{{out}}
<pre>
1320
</pre>

=={{header|XPL0}}==
{{trans|Ada}}
<syntaxhighlight lang "XPL0">function Max(A, B);
int A, B;
return if A > B then A else B;

int Triangle, Last, Tn, N, I;
begin
Triangle:= [0,
                                      55,
                                    94, 48,
                                  95, 30, 96,
                                77, 71, 26, 67,
                              97, 13, 76, 38, 45,
                            07, 36, 79, 16, 37, 68,
                          48, 07, 09, 18, 70, 26, 06,
                        18, 72, 79, 46, 59, 79, 29, 90,
                      20, 76, 87, 11, 32, 07, 07, 49, 18,
                    27, 83, 58, 35, 71, 11, 25, 57, 29, 85,
                  14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55,
                02, 90, 03, 60, 48, 49, 41, 46, 33, 36, 47, 23,
              92, 50, 48, 02, 36, 59, 42, 79, 72, 20, 82, 77, 42,
            56, 78, 38, 80, 39, 75, 02, 71, 66, 66, 01, 03, 55, 72,
          44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36,
        85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 01, 01, 99, 89, 52,
      06, 71, 28, 75, 94, 48, 37, 10, 23, 51, 06, 48, 53, 18, 74, 98, 15,
    27, 02, 92, 23, 08, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93];

   Last  := (18*18+18)/2;
   Tn    := 1;

   while (Tn * (Tn + 1) / 2) < Last  do
      Tn := Tn + 1;
   for N:= Tn downto 2 do begin
      for I:= 2 to N do begin
         Triangle (Last - N) := Triangle (Last - N) +
           Max(Triangle (Last - 1), Triangle (Last));
         Last := Last - 1;
      end;
      Last := Last - 1;
   end;
   IntOut(0, Triangle(1));
   CrLf(0);
end;</syntaxhighlight>
{{out}}
<pre>
1320
</pre>

=={{header|Z80 Assembly}}==
{{works with|CP/M 3.1|YAZE-AG-2.51.2 Z80 emulator}}
{{works with|ZSM4 macro assembler|YAZE-AG-2.51.2 Z80 emulator}}
Use the /S8 switch on the ZSM4 assembler for 8 significant characters for labels and names<br><br>
No attempt is made to check for and handle incomplete triangles, and the number of elements must be defined in code.<br>
<syntaxhighlight lang="z80">
	;
	; Find maximum triangle path sum using Z80 assembly language
	;
	; Runs under CP/M 3.1 on YAZE-AG-2.51.2 Z80 emulator
	; Assembled with zsm4 on same emulator/OS, uses macro capabilities of said assembler
	; Created with vim under Windows
	;
	; Thanks to https://wikiti.brandonw.net for the idea for the conversion routine hl -> decimal ASCII
	;
	;
	; 2023-04-28 Xorph
	;

	;
	; Useful definitions
	;

	bdos	equ 05h		; Call to CP/M BDOS function
	strdel	equ 6eh		; Set string delimiter
	wrtstr	equ 09h		; Write string to console

	nul	equ 00h		; ASCII control characters
	cr	equ 0dh
	lf	equ 0ah

	cnull	equ '0'		; ASCII character constants

	trisize	equ 171		; Number of elements in triangle, must be counted manually - elements are 16 bit words

	;
	; Macros for BDOS calls
	;

setdel 	macro	char		; Set string delimiter to char
	ld	c,strdel
	ld	e,char
	call	bdos
	endm

print 	macro	msg		; Output string to console
	ld	c,wrtstr
	ld	de,msg
	call	bdos
	endm

newline	macro			; Print newline
	ld	c,wrtstr
	ld	de,crlf
	call	bdos
	endm

pushall	macro			; Save all registers to stack
	push	af
	push	bc
	push	de
	push	hl
	push	ix
	push	iy
	endm

popall	macro			; Recall all registers from stack
	pop	iy
	pop	ix
	pop	hl
	pop	de
	pop	bc
	pop	af
	endm

	;
	; =====================
	; Start of main program
	; =====================
	;

	cseg

	;
	; The total number of elements in a triangle with N rows is the sum of the numbers 1..N, and we need to
	; determine N for the given number of elements (trisize from above).
	; Since the Z80 has no multiplication instruction, we can not use the Gauss formula N * (N + 1) / 2. Instead, we
	; just sum up all the numbers beginning with 1, until we exceed the number of elements.
	;

	ld	a,trisize	; a holds number of elements for comparison
	ld	de,1		; de is the counter from 1..N
	ld	hl,0		; hl holds the accumulated sum. Since a must be used for comparison, we need hl as accumulator 

sum1toN:
	add	hl,de		; Add next number to hl
	cp	l		; Comparison is only 8 bit! The maximum number of elements is limited to 255
	jr	c,foundN	; If l exceeds trisize, we are finished and need to reduce de again
	inc	de		; Otherwise, increase de and repeat
	jr	sum1toN

foundN:
	dec	de		; We overshot the target and need to reduce de again. de now holds N, the number of rows = elements in last row
	ld	b,e		; Our actual counters will be b and c

	ld	ix,triangle	; Set ix to LSB of very last element (16 bit word) of triangle
	ld	de,2*trisize-2
	add	ix,de		; Everything is 0-based! Here we need the bytes instead of the number of elements

	push	ix		; Set iy to last element of penultimate row
	pop	hl		; Need to use hl for subtraction of number of bytes in last row
	ld	c,b		; Get number of bytes in c, b shall keep the number of elements
	sla	c		; bytes = 2 * elements
	ld	d,0		; Use de for 16 bit subtraction of c from hl
	ld	e,c
	sbc	hl,de		
	push	hl		; and then move it to iy via stack, no direct load
	pop	iy

	dec	b		; b runs over the penultimate row, which has 1 element less
	ld	c,b		; c is the row counter, b the element counter - each row contains as many elements as is its number

loop:				; Loop entry point is the same for inner and outer loop
	push	bc		; Save bc to stack, it will hold the maximum of right and left successor
	ld	l,(ix)		; Right successor of iy
	ld	h,(ix+1)
	ld	e,(ix-2)	; Left successor of iy
	ld	d,(ix-1)
	push	hl		; Save hl, it is modified by the comparison/subtraction
	or	a		; Clear carry flag
	sbc	hl,de		; 16 bit comparison by subtracting left from right
	pop	hl		; Restore hl
	jr	c,delarger	; If carry, then the left successor in de is larger

	push	hl		; hl is larger, move it to bc
	pop	bc
	jr	addmax

delarger:
	push	de		; de is larger, move it to bc
	pop	bc

addmax:
	ld	l,(iy)		; Get "parent" element into hl and add maximum of its two successors
	ld	h,(iy+1)
	add	hl,bc		; Add maximum, which is in bc
	ld	(iy),l		; Store hl back to triangle
	ld	(iy+1),h
	pop	bc		; Restore bc with loop counters

	dec	ix		; Decrement element pointers (by 2 bytes)
	dec	ix
	dec	iy
	dec	iy

	dec	b		; Decrement element counter
	jp	nz,loop		; Check if penultimate row finished - this is the inner loop

	ld	b,c		; Restore inner loop counter, check if more rows above current
	dec	ix		; Decrement element pointer of row below again (by 2 bytes), skip leftmost element
	dec	ix
	dec	b		; Decrement loop counters, first the element counter
	dec	c		; ...then the row counter
	jp	nz,loop		; Check if triangle finished - this is the outer loop

	ld	hl,(triangle)	; Root element now contains maximum sum
	ld	ix,buffer	; Set ix to output buffer
	call	dispHL		; Create decimal representation

	setdel	nul		; Set string delimiter to 00h
	print	buffer		; Display result
	newline

	ret			; Return to CP/M

	;
	; ===================
	; End of main program
	; ===================
	;

	;
	; Helper routines - notice that the Z80 does not have a divide instruction
	; Notice further that CP/M does not have any support for pretty-printing
	; formatted numbers and stuff like that. So we have to do all this by hand...
	;

	;
	; Converts the value (unsigned int) in register hl to its decimal representation
	; Register ix has memory address of target for converted value
	; String is terminated with nul character (\0)
	;

dispHL:
	pushall
	ld	b,1		; Flag for leading '0'
	irp	x,<-10000,-1000,-100,-10,-1>
	ld	de,x		; Subtract powers of 10 and determine digit
	call	calcdig
	endm

	ld	a,nul		; Terminate result string with nul
	ld	(ix+0),a

	popall
	ret			; End of conversion routine

calcdig:
	ld	a,cnull-1	; Determine the digit character
incrdig:
	inc	a		; Start with '0'
	add	hl,de		; As long as subtraction is possible, increment digit character
	jr	c,incrdig

	sbc	hl,de		; If negative, undo last subtraction and continue with remainder
	cp	cnull		; Check for leading '0', these are ignored
	jr	nz,adddig
	bit	0,b		; Use bit instruction for check if flag set, register a contains digit
	ret	nz		; If '0' found and flag set, it is a leading '0' and we return
adddig:
	ld	b,0		; Reset flag for leading '0', we are now outputting digits
	ld	(ix+0),a	; Store character in memory and set ix to next location
	inc	ix

	ret			; End of conversion helper routine

	;
	; ================
	; Data definitions
	; ================
	;

	dseg

crlf:	defb	cr,lf,nul	; Generic newline
buffer:	defs	10		; Buffer for conversion of number to text

triangle:			; Triangle data, number of elements is "trisize" equ further above
	defw	55
	defw	94
	defw	48
	defw	95
	defw	30
	defw	96
	defw	77
	defw	71
	defw	26
	defw	67
	defw	97
	defw	13
	defw	76
	defw	38
	defw	45
	defw	07
	defw	36
	defw	79
	defw	16
	defw	37
	defw	68
	defw	48
	defw	07
	defw	09
	defw	18
	defw	70
	defw	26
	defw	06
	defw	18
	defw	72
	defw	79
	defw	46
	defw	59
	defw	79
	defw	29
	defw	90
	defw	20
	defw	76
	defw	87
	defw	11
	defw	32
	defw	07
	defw	07
	defw	49
	defw	18
	defw	27
	defw	83
	defw	58
	defw	35
	defw	71
	defw	11
	defw	25
	defw	57
	defw	29
	defw	85
	defw	14
	defw	64
	defw	36
	defw	96
	defw	27
	defw	11
	defw	58
	defw	56
	defw	92
	defw	18
	defw	55
	defw	02
	defw	90
	defw	03
	defw	60
	defw	48
	defw	49
	defw	41
	defw	46
	defw	33
	defw	36
	defw	47
	defw	23
	defw	92
	defw	50
	defw	48
	defw	02
	defw	36
	defw	59
	defw	42
	defw	79
	defw	72
	defw	20
	defw	82
	defw	77
	defw	42
	defw	56
	defw	78
	defw	38
	defw	80
	defw	39
	defw	75
	defw	02
	defw	71
	defw	66
	defw	66
	defw	01
	defw	03
	defw	55
	defw	72
	defw	44
	defw	25
	defw	67
	defw	84
	defw	71
	defw	67
	defw	11
	defw	61
	defw	40
	defw	57
	defw	58
	defw	89
	defw	40
	defw	56
	defw	36
	defw	85
	defw	32
	defw	25
	defw	85
	defw	57
	defw	48
	defw	84
	defw	35
	defw	47
	defw	62
	defw	17
	defw	01
	defw	01
	defw	99
	defw	89
	defw	52
	defw	06
	defw	71
	defw	28
	defw	75
	defw	94
	defw	48
	defw	37
	defw	10
	defw	23
	defw	51
	defw	06
	defw	48
	defw	53
	defw	18
	defw	74
	defw	98
	defw	15
	defw	27
	defw	02
	defw	92
	defw	23
	defw	08
	defw	71
	defw	76
	defw	84
	defw	15
	defw	52
	defw	92
	defw	63
	defw	81
	defw	10
	defw	44
	defw	10
	defw	69
	defw	93
</syntaxhighlight>

{{out}}
<pre>
E>maxtri
1320
</pre>

=={{header|zkl}}==
{{trans|Python}}
The two Python solutions:
<syntaxhighlight lang="zkl">tri:=File("triangle.txt").pump(List,fcn(s){ s.strip().split(" ").apply("toInt") }).copy();
while(tri.len()>1){
   t0:=tri.pop();
   t1:=tri.pop();
   tri.append( [[(it); t1.enumerate(); 
	'wrap([(i,t)]){ t + t0[i].max(t0[i+1]) }]])
}
tri[0][0].println();</syntaxhighlight>
<syntaxhighlight lang="zkl">data:=File("triangle.txt").pump(List,fcn(s){ s.strip().split(" ").apply("toInt") });
fcn f(x,y,z){ x + y.max(z) }
fcn g(xs,ys){ Utils.zipWith(f,ys,xs,xs[1,*]); }
data.reverse().reduce(g)[0].println();</syntaxhighlight>
{{trans|Go}}
<syntaxhighlight lang="zkl">lines:=File("triangle.txt").pump(List,fcn(s){ s.strip().split(" ").apply("toInt") });
d:=lines[-1].copy();
foreach row in ([lines.len()-2..0,-1]){
   d1:=d[1,*];
   l :=d[0];
   foreach i,u in (lines[row].enumerate()){
       d[i] = u + l.max(r:=d1[i]);
       l    = r;
    }
}
println(d[0]);</syntaxhighlight>
{{out}}
<pre>
1320
1320
1320
</pre>