Maximum difference between adjacent elements of list

Maximum difference between adjacent elements of list is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Find maximum difference between adjacent elements of list.

The list may have negative values, zero values, real numbers.

List   =   [1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3]

Output would be   (which could have more verbiage):

  2,9 ==> 7
  1,8 ==> 7
  10,3 ==> 7

ALGOL 68

<lang algol68>BEGIN # find the maximum difference between consecutive list elements #

   # returns the maximum difference between pairs of elements of list        #
   OP   MAXDELTA = ( []REAL list )REAL:
        BEGIN
           REAL max diff := 0;
           FOR i FROM LWB list TO UPB list - 1 DO
               REAL delta = ABS ( list[ i ] - list[ i + 1 ] );
               IF delta > max diff THEN
                   max diff := delta # found a higher difference             #
               FI
           OD;
           max diff
        END; # MAXDELTA #
   # returns r converted to a string with trailing 0 decimal places removed  #
   OP   TOSTRING = ( REAL r )STRING:
        BEGIN
           STRING result  := fixed( r, 0, 10 );
           IF result[ LWB result ] = "." THEN result := "0" + result FI;
           INT    r end   := UPB result;
           INT    r start := LWB result;
           WHILE IF r end <= r start THEN FALSE ELSE result[ r end ] = "0" FI DO
              r end -:= 1
           OD;
           IF r end > LWB result THEN
               # if all decimal places were "0", remove the "." as well      #
               IF result[ r end ] = "." THEN r end -:= 1 FI
           FI;
           result[ r start : r end ]
        END; # TOSTRING #
   # test the MAXDELTA operator                                              #
   PROC test max delta = ( []REAL list )VOID:
        BEGIN
           REAL max diff = MAXDELTA list;
           print( ( "Max difference [" ) );
           FOR i FROM LWB list TO UPB list DO
               print( ( " ", TOSTRING list[ i ] ) )
           OD;
           print( ( " ] is ", TOSTRING max diff, ":",  newline ) );
           FOR i FROM LWB list TO UPB list - 1 DO
               IF REAL diff = ABS ( list[ i ] - list[ i + 1 ] );
                  diff = max diff
               THEN
                   print( ( "    ", TOSTRING list[ i ], ", ", TOSTRING list[ i + 1 ]
                          , " ==> ", TOSTRING diff
                          , newline
                          )
                        )
               FI
           OD
        END; # test max delta #
   # task test case                                                          #
   test max delta( ( 1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3 ) );
   # additional test cases                                                   #
   test max delta( ( -1.1, -1.2 ) ); test max delta( ( pi, pi, pi ) );
   test max delta( ( )            ); test max delta( ( 776.591 )    )

END</lang>

Output:

Max difference [ 1 8 2 -3 0 1 1 -2.3 0 5.5 8 6 2 9 11 10 3 ] is 7:
    1, 8 ==> 7
    2, 9 ==> 7
    10, 3 ==> 7
Max difference [ -1.1 -1.2 ] is 0.1:
    -1.1, -1.2 ==> 0.1
Max difference [ 3.1415926536 3.1415926536 3.1415926536 ] is 0:
    3.1415926536, 3.1415926536 ==> 0
    3.1415926536, 3.1415926536 ==> 0
Max difference [ ] is 0:
Max difference [ 776.591 ] is 0:

ALGOL W

<lang algolw>begin % find the maximum difference between consecutive list elements  %

   % returns the maximum difference between pairs of elements of list        %
   %         the lower and upper bounds of list must be specified in lb & ub %
   real procedure maxDelta ( real    array list ( * )
                           ; integer value lb, ub
                           ) ;
   begin
       real maxDiff;
       maxDiff := 0;
       for i := lb until ub - 1 do begin
           real delta;
           delta := abs ( list( i ) - list( i + 1 ) );
           if delta > maxDiff then maxDiff := delta % found a higher difference %
       end for_i;
       maxDiff
   end maxDelta;
   % test the maxDelta procedure                                             %
   procedure testMaxDelta ( real    array list ( * )
                          ; integer value lb, ub, rw, dp
                          ) ;
   begin
       real maxDiff;
       maxDiff := maxDelta( list, lb, ub );
       write( s_w := 0, "Max difference [" );
       for i := lb until ub do begin
           writeon( r_format := "A", r_w := rw, r_d := dp, s_w := 0, " ", list( i ) );
       end for_i;
       writeon( r_format := "A", r_w := rw, r_d := dp, s_w := 0, " ] is ", maxDiff, ":" );
       for i := lb until ub - 1 do begin
           real diff;
           diff := abs ( list( i ) - list( i + 1 ) );
           if diff = maxDiff then begin
               write( r_format := "A", r_w := rw, r_d := dp, s_w := 0, "    ", list( i ), ", ", list( i + 1 ), " ==> ", diff );
           end if_diff_eq_maxDiff
        end for_i
   end testMaxDelta;
   begin % task test case                                                    %
       integer tPos;
       real array tc( 1 :: 17 );
       tPos := 0;
       for i := 1, 8, 2, -3, 0, 1, 1, -23, 0, 55, 8, 6, 2, 9, 11, 10, 3 do begin
           tPos       := tPos + 1;
           tc( tPos ) := i
       end for_i;
       tc( 8 ) := -2.3; tc( 10 ) := 5.5;
       testMaxDelta( tc, 1, 17, 4, 1 )
   end;
   begin % additional test cases                                             %
       integer tPos;
       real array tc( 1 :: 3 );
       tc( 1 ) := -1.1; tc( 2 ) := -1.2; testMaxDelta( tc, 1, 2, 4, 1  );
       for i := 1 until 3 do tc( i ) := pi;
       testMaxDelta( tc, 1, 3, 6, 4 );
       testMaxDelta( tc, 1, 0, 3, 1 );
       tc( 1 ) := 776.591;
       testMaxDelta( tc, 1, 1, 6, 3 )
   end

end.</lang>

Output:

Max difference [  1.0  8.0  2.0 -3.0  0.0  1.0  1.0 -2.3  0.0  5.5  8.0  6.0  2.0  9.0 11.0 10.0  3.0 ] is  7.0:
     1.0,  8.0 ==>  7.0
     2.0,  9.0 ==>  7.0
    10.0,  3.0 ==>  7.0
Max difference [ -1.1 -1.2 ] is  0.1:
    -1.1, -1.2 ==>  0.1
Max difference [ 3.1416 3.1416 3.1416 ] is 0.0000:
    3.1416, 3.1416 ==> 0.0000
    3.1416, 3.1416 ==> 0.0000
Max difference [ ] is 0.0:
Max difference [ 776.591 ] is  0.000:

Factor

Works with: Factor version 0.99 2021-06-02

<lang factor>USING: assocs grouping math prettyprint sequences ;

max-diff ( seq -- assoc )

   2 clump [ first2 - abs ] collect-by >alist supremum ;

{ 1 8 2 -3 0 1 1 -2.3 0 5.5 8 6 2 9 11 10 3 } max-diff .</lang>

Output:

{ 7 V{ { 1 8 } { 2 9 } { 10 3 } } }

Go

<lang go>package main

import (

   "fmt"
   "math"

)

func main() {

   list := []float64{1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3}
   maxDiff := -1.0
   var maxPairs [][2]float64
   for i := 1; i < len(list); i++ {
       diff := math.Abs(list[i-1] - list[i])
       if diff > maxDiff {
           maxDiff = diff
           maxPairs = [][2]float64{{list[i-1], list[i]}}
       } else if diff == maxDiff {
           maxPairs = append(maxPairs, [2]float64{list[i-1], list[i]})
       }
   }
   fmt.Println("The maximum difference between adjacent pairs of the list is:", maxDiff)
   fmt.Println("The pairs with this difference are:", maxPairs)

}</lang>

Output:

The maximum difference between adjacent pairs of the list is: 7
The pairs with this difference are: [[1 8] [2 9] [10 3]]

Haskell

<lang haskell>import Data.List (maximumBy) import Data.Ord (comparing)

maxDeltas :: [Float] -> [(Float, (Float, Float))] maxDeltas xs = filter ((delta ==) . fst) pairs

 where
   pairs =
     zipWith
       (\a b -> (abs (a - b), (a, b)))
       xs
       (tail xs)
   delta = fst $ maximumBy (comparing fst) pairs

main :: IO () main =

 mapM_ print $
   maxDeltas [1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3]</lang>

Output:

(7.0,(1.0,8.0))
(7.0,(2.0,9.0))
(7.0,(10.0,3.0))

Julia

<lang julia> function maxadjacentdiffs(list)

   pairs, maxδ = Pair{eltype(list)}[], abs(zero(eltype(list)))
   for i in eachindex(list[begin:end-1])
       x, y = list[i], list[i + 1]
       if (δ = abs(x - y)) == maxδ
           push!(pairs, x => y)
       elseif δ > maxδ
           maxδ, pairs = δ, [x => y]
       end
   end
   return maxδ, pairs

end

diff, pairs = maxadjacentdiffs([1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3])

foreach(p -> println(p[1], ", ", p[2], " ==> ", diff), pairs)

</lang>

Output:

1.0, 8.0 ==> 7.0
2.0, 9.0 ==> 7.0
10.0, 3.0 ==> 7.0

Nim

<lang Nim>import strformat, strutils

type Pair = (float, float)

func `$`(p: Pair): string = &"({p[0]:g}, {p[1]:g})"

func maxdiff(list: openArray[float]): tuple[diff: float; list: seq[Pair]] =

 assert list.len >= 2
 result = (diff: -1.0, list: @[])
 var prev = list[0]
 for n in list[1..^1]:
   let d = abs(n - prev)
   if d > result.diff:
     result.diff = d
     result.list = @[(prev, n)]
   elif d == result.diff:
     result.list.add (prev, n)
   prev = n

let list = [float 1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3] let (diff, pairs) = list.maxdiff()

echo &"The maximum difference between adjacent pairs of the list is: {diff:g}" echo "The pairs with this difference are: ", pairs.join(" ")</lang>

Output:

The maximum difference between adjacent pairs of the list is: 7
The pairs with this difference are: (1, 8) (2, 9) (10, 3)

Phix

procedure differences(sequence s)
    sequence d, mx = {0,""}, mn = mx
    atom av = 0
    function fall(integer fn, sequence d, s)
        atom m = fn(d)
        sequence p = find_all(m,d)
        for i=1 to length(p) do
            integer pi = p[i], pj = pi+1
            p[i] = sprintf("s[%d..%d]=%V",{pi,pj,s[pi..pj]})
        end for
        return {m,", occurring at "&join(p,", ")}
    end function
    if length(s)>=2 then
        d = sq_abs(sq_sub(s[1..-2],s[2..-1]))
        mx = fall(maxsq, d, s)
        mn = fall(minsq, d, s)
        av = sum(d)/length(d)
    end if
    printf(1,"sequence: %V\n",{s})
    printf(1,"max difference is %g%s\n",mx)
    printf(1,"min difference is %g%s\n",mn)
    printf(1,"avg difference is %.7g\n\n",av)
end procedure
differences({1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3})
differences({-1.1,-1.2})
differences({})
differences({776.591})

Output:

sequence: {1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3}
max difference is 7, occurring at s[1..2]={1,8}, s[13..14]={2,9}, s[16..17]={10,3}
min difference is 0, occurring at s[6..7]={1,1}
avg difference is 3.6625

sequence: {-1.1,-1.2}
max difference is 0.1, occurring at s[1..2]={-1.1,-1.2}
min difference is 0.1, occurring at s[1..2]={-1.1,-1.2}
avg difference is 0.1

sequence: {}
max difference is 0
min difference is 0
avg difference is 0

sequence: {776.591}
max difference is 0
min difference is 0
avg difference is 0

Python

<lang python>Maximum difference between adjacent numbers in list

1. maxDeltas [Float] -> [(Float, (Float, Float))]

def maxDeltas(ns):

   Each of the maximally differing successive pairs
      in ns, each preceded by the value of the difference.
   
   pairs = [
       (abs(a - b), (a, b)) for a, b
       in zip(ns, ns[1:])
   ]
   delta = max(pairs, key=lambda ab: ab[0])[0]

   return [
       ab for ab in pairs
       if delta == ab[0]
   ]

1. ------------------------- TEST -------------------------
2. main :: IO ()

def main():

   Each of the maximally differing pairs in a list

   maxPairs = maxDeltas([
       1, 8, 2, -3, 0, 1, 1, -2.3, 0,
       5.5, 8, 6, 2, 9, 11, 10, 3
   ])

   for ab in maxPairs:
       print(ab)

1. MAIN ---

if __name__ == '__main__':

   main()</lang>

Output:

(7, (1, 8))
(7, (2, 9))
(7, (10, 3))

Raku

<lang perl6>sub max-diff (*@list) {

  return 0 if +@list < 2;
  my $max = @list.rotor(2 => -1).max({ (.[0] - .[1]).abs }).map( (* - *).abs )[0];
  "$max @ elements { @list.rotor(2 => -1).grep( { (.[0] - .[1]).abs == $max } ).gist }"

}

sub min-diff (*@list) {

  return 0 if +@list < 2;
  my $min = @list.rotor(2 => -1).min({ (.[0] - .[1]).abs }).map( (* - *).abs )[0];
  "$min @ elements { @list.rotor(2 => -1).grep( { (.[0] - .[1]).abs == $min } ).gist }"

}

sub avg-diff (*@list) { (+@list > 1) ?? (@list.sum / +@list) !! 0 }

1. TESTING

for (

     [ 1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3 ]
    ,[(rand × 1e6) xx 6]
    ,[ e, i, τ, π, ∞ ]
    ,[ 1.9+3.7i, 2.07-13.2i, 0.2+-2.2i, 4.6+0i ]
    ,[ 6 ]
    ,[]
    ,[<One Two Three>]
   )

-> @list {

   say 'List: ', ~ @list.raku;
   for ('  Maximum', &max-diff ,'Minimumum', &min-diff, '  Average', &avg-diff)
   -> $which, &sub {
       say "$which distance between list elements: " ~ &sub(@list);
   }
   say ;

}</lang>

Output:

List: [1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3]
  Maximum distance between list elements: 7 @ elements ((1 8) (2 9) (10 3))
Minimumum distance between list elements: 0 @ elements ((1 1))
  Average distance between list elements: 3.658824

List: [480470.3324944039e0, 719954.3173377671e0, 648221.5674277907e0, 340053.78585537826e0, 540629.6741075241e0, 4336.700602958543e0]
  Maximum distance between list elements: 536292.9735045655 @ elements ((540629.6741075241 4336.700602958543))
Minimumum distance between list elements: 71732.74990997638 @ elements ((719954.3173377671 648221.5674277907))
  Average distance between list elements: 455611.06297097047

List: [2.718281828459045e0, <0+1i>, 6.283185307179586e0, 3.141592653589793e0, Inf]
  Maximum distance between list elements: Inf @ elements ((3.141592653589793 Inf))
Minimumum distance between list elements: 2.896386731590008 @ elements ((2.718281828459045 0+1i))
  Average distance between list elements: Inf+0.2i

List: [<1.9+3.7i>, <2.07-13.2i>, <0.2-2.2i>, <4.6+0i>]
  Maximum distance between list elements: 16.900855007957436 @ elements ((1.9+3.7i 2.07-13.2i))
Minimumum distance between list elements: 4.919349550499537 @ elements ((0.2-2.2i 4.6+0i))
  Average distance between list elements: 2.1925-2.925i

List: [6]
  Maximum distance between list elements: 0
Minimumum distance between list elements: 0
  Average distance between list elements: 0

List: []
  Maximum distance between list elements: 0
Minimumum distance between list elements: 0
  Average distance between list elements: 0

List: ["One", "Two", "Three"]
Cannot convert string to number: base-10 number must begin with valid digits or '.' in '⏏Two' (indicated by ⏏)
  in sub max-diff at listdiff.p6 line 3
  in block  at listdiff.p6 line 33
  in block <unit> at listdiff.p6 line 20

REXX

Some basic error checking was made   (non─numeric element,   not enough elements).

This REXX version was optimized to handle very large lists. <lang rexx>/*REXX program finds/displays the maximum difference between adjacent elements of a list*/ parse arg $ /*obtain optional arguments from the CL*/ if $= | S=="," then $= , /*Not specified? Then use the default.*/

    '1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3' /*commas are optional;  blanks are OK. */

w= 0 /*the maximum width of any element num.*/ $= translate($, , ',') /*elide optional commas between numbers*/

1. = words($) /*number of elements in the $ list. */

            do i=1  for words($); x= word($, i) /*examine each element, ensure a number*/
            @.i= x;     w= max(w, length(x) )   /*assign element #; find maximum width.*/
            if datatype(x, 'N')  then iterate   /*Is it numeric?   Yes, then continue. */
            say '***error***  element #'i    " isn't numeric: "    x
            exit 13
            end   /*i*/

n= 0 /*N: # sets of (difference) elements.*/ if #<2 then do; say '***error*** not enough elements were specified, minimum is two.'

                  exit 13
            end

say ' list of elements: ' space($) /*show the list of numbers in list.*/ say ' number of elements: ' # /*show " number " elements " " */ d= -1; /*d: maximum difference found (so far)*/

       do j=1  for #-1;   jp= j + 1;   a= @.j   /*obtain the  "A"  element.            */
                                       b= @.jp  /*   "    "   "B"     "                */
       newD= abs(a - b)                         /*obtain difference between 2 elements.*/
       if newD<d  then iterate                  /*Is this  not  a new max difference ? */
       d= newD                                  /*assign new maximum difference,  and  */
       n= n + 1                                 /*bump the # of (difference) sets.     */
       aa.n= a;        bb.n= b                  /*  the elements that had the max diff.*/
       end   /*j*/

say say 'The maximum difference of the elements in the list is: ' d

       do k=1  for n
       say 'and is between the elements: '   right(aa.k, w)    " and "     right(bb.k, w)
       end   /*k*/

exit 0 /*stick a fork in it, we're all done. */</lang>

output   when using the default input:

   list  of elements:  1 8 2 -3 0 1 1 -2.3 0 5.5 8 6 2 9 11 10 3
  number of elements:  17

The maximum difference of the elements in the list is:   7
and is between the elements:     1  and     8
and is between the elements:     2  and     9
and is between the elements:    10  and     3

Ring

<lang ring> see "working..." + nl strList = "[1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3]" see "Maximum difference between adjacent elements of list is:" + nl + nl see "Input list = " + strList + nl + nl see "Output:" + nl sList = [1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3] sortList = []

for n = 1 to len(sList)-1

   diff = fabs(sList[n]-sList[n+1])
   oldDiff = diff
   first = sList[n]
   second = sList[n+1]
   add(sortList,[oldDiff,first,second])

next

sortList = sort(sortlist,1) sortList = reverse(sortlist) flag = 1

for n=1 to len(sortList)-1

   oldDiff1 = sortlist[n][1]
   oldDiff2 = sortlist[n+1][1] 
   first1 = sortlist[n][2]
   second1 = sortlist[n][3]
   first2 = sortlist[n+1][2]
   second2 = sortlist[n+1][3]
   if n = 1 and oldDiff1 != oldDiff2
      see "" + first1 + "," + second1 + " ==> " + oldDiff1 + nl 
   ok
   if oldDiff1 = oldDiff2
      if flag = 1
         flag = 0
         see "" + first1 + "," + second1 + " ==> " + oldDiff1 + nl   
         see "" + first2 + "," + second2 + " ==> " + oldDiff2 + nl
      else
         see "" + first2 + "," + second2 + " ==> " + oldDiff2 + nl
      ok
   else
      exit
   ok

next

see "done..." + nl </lang>

Output:

working...
Maximum difference between adjacent elements of list is:

Input list = [1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3]

Output:
2,9 ==> 7
1,8 ==> 7
10,3 ==> 7
done...

Wren

<lang ecmascript>var list = [1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8,6, 2, 9, 11, 10, 3] var maxDiff = -1 var maxPairs = [] for (i in 1...list.count) {

   var diff = (list[i-1] - list[i]).abs
   if (diff > maxDiff) {
       maxDiff = diff
       maxPairs = [[list[i-1], list[i]]]
   } else if (diff == maxDiff) {
       maxPairs.add([list[i-1], list[i]])
   }

} System.print("The maximum difference between adjacent pairs of the list is: %(maxDiff)") System.print("The pairs with this difference are: %(maxPairs)")</lang>

Output:

The maximum difference between adjacent pairs of the list is: 7
The pairs with this difference are: [[1, 8], [2, 9], [10, 3]]

XPL0

<lang XPL0>real List, Dist, MaxDist; int I; [List:= [1., 8., 2., -3., 0., 1., 1., -2.3, 0., 5.5, 8., 6., 2., 9., 11., 10., 3.]; MaxDist:= 0.; for I:= 0 to 17-2 do

   [Dist:= abs(List(I) - List(I+1));
   if Dist > MaxDist then
       MaxDist:= Dist;
   ];

Format(1, 0); for I:= 0 to 17-2 do

   [Dist:= abs(List(I) - List(I+1));
   if Dist = MaxDist then
       [RlOut(0, List(I));  Text(0, ", ");  RlOut(0, List(I+1));
       Text(0, " ==> ");  RlOut(0, MaxDist);  CrLf(0);
       ];
   ];

]</lang>

Output:

1, 8 ==> 7
2, 9 ==> 7
10, 3 ==> 7