Maximum difference between adjacent elements of list
Find 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
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):
1,8 ==> 7 2,9 ==> 7 10,3 ==> 7
11l
F maxDeltas(ns)
V pairs = zip(ns, ns[1..]).map((a, b) -> (abs(a - b), (a, b)))
V delta = max(pairs, key' ab -> ab[0])[0]
R pairs.filter(ab -> @delta == ab[0])
V maxPairs = maxDeltas([Float(1), 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3])
L(ab) maxPairs
print(ab)- Output:
(7, (1, 8)) (7, (2, 9)) (7, (10, 3))
Action!
INCLUDE "H6:REALMATH.ACT"
DEFINE PTR="CARD"
PTR FUNC GetPtr(BYTE ARRAY a INT index)
RETURN (a+index*6)
PROC MaxDifference(BYTE ARRAY a INT len REAL POINTER maxDiff)
INT i
REAL diff
REAL POINTER r1,r2
IntToReal(0,maxDiff)
FOR i=0 TO len-2
DO
r1=GetPtr(a,i)
r2=GetPtr(a,i+1)
RealAbsDiff(r1,r2,diff)
IF RealGreaterOrEqual(diff,maxDiff) THEN
RealAssign(diff,maxDiff)
FI
OD
RETURN
PROC PrintPairs(BYTE ARRAY a INT len,maxDiff)
INT i
REAL diff
REAL POINTER r1,r2
FOR i=0 TO len-2
DO
r1=GetPtr(a,i)
r2=GetPtr(a,i+1)
RealAbsDiff(r1,r2,diff)
IF RealEqual(diff,maxDiff) THEN
Print(" AbsDiff(") PrintR(r1)
Print(", ") PrintR(r2)
Print(") = ") PrintRE(maxDiff)
FI
OD
RETURN
PROC Decode(CHAR ARRAY s BYTE ARRAY a INT POINTER len)
BYTE i,start,length
CHAR ARRAY item,tmp(10)
REAL POINTER r
len^=0 i=1
WHILE i<=s(0)
DO
start=i
WHILE i<=s(0) AND s(i)#32
DO
i==+1
OD
length=i-start
SCopyS(tmp,s,start,i-1)
r=GetPtr(a,len^)
ValR(tmp,r)
len^==+1
i==+1
OD
RETURN
PROC Test(CHAR ARRAY s)
BYTE ARRAY a(200)
INT len
REAL maxDiff
PrintF("Max difference in [%S] is ",s)
Decode(s,a,@len)
MaxDifference(a,len,maxDiff)
PrintRE(maxDiff)
PrintPairs(a,len,maxDiff) PutE()
RETURN
PROC Main()
Put(125) PutE() ;clear the screen
Test("1 8 2 -3 0 1 1 -2.3 0 5.5 8 6 2 9 11 10 3")
Test("0.12 -0.04 0.34 0.72 0.34 0.27 -0.1")
Test("10E30 20E30 15E30 5E30 -5E30")
RETURN- Output:
Screenshot from Atari 8-bit computer
Max difference in [1 8 2 -3 0 1 1 -2.3 0 5.5 8 6 2 9 11 10 3] is 7 AbsDiff(1, 8) = 7 AbsDiff(2, 9) = 7 AbsDiff(10, 3) = 7 Max difference in [0.12 -0.04 0.34 0.72 0.34 0.27 -0.1] is .38 AbsDiff(-0.04, .34) = .38 AbsDiff(.34, .72) = .38 AbsDiff(.72, .34) = .38 Max difference in [10E30 20E30 15E30 5E30 -5E30] is 1.0E+31 AbsDiff(1.0E+31, 2.0E+31) = 1.0E+31 AbsDiff(1.5E+31, 5E+30) = 1.0E+31 AbsDiff(5E+30, -5E+30) = 1.0E+31
Ada
-- Find the maximum absolute difference between adjacent values in a list, and output all pairs with that difference
-- J. Carter 2023 Apr
-- Uses the PragmAda Reusable Components (https://github.com/jrcarter/PragmARC)
with Ada.Text_IO;
with PragmARC.Images;
procedure List_Max_Diff is
function Float_Image is new PragmARC.Images.Float_Image (Number => Float);
function Image (Number : in Float) return String;
-- Returns the image of Number without a decimal point or fractional digits if the fractional part is zero
function Image (Number : in Float) return String is
Result : constant String := Float_Image (Number, Aft => 0, Exp => 0);
begin -- Image
if Result'Length > 1 and then Result (Result'Last - 1 .. Result'Last) = ".0" then
return Result (Result'First .. Result'Last - 2);
end if;
return Result;
end Image;
type Float_List is array (Positive range <>) of Float with Dynamic_Predicate => Float_List'First = 1;
List : constant Float_List := (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);
Max : Float := -1.0;
begin -- List_Max_Diff
Find : for I in 1 .. List'Last - 1 loop
Max := Float'Max (abs (List (I) - List (I + 1) ), Max);
end loop Find;
Print : for I in 1 .. List'Last - 1 loop
if abs (List (I) - List (I + 1) ) = Max then
Ada.Text_IO.Put_Line (Item => Image (List (I) ) & ',' & Image (List (I + 1) ) & " ==> " & Image (Max) );
end if;
end loop Print;
end List_Max_Diff;- Output:
1,8 ==> 7 2,9 ==> 7 10,3 ==> 7
ALGOL 68
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- 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
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.- 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:
APL
maxdiff ← (⊢((⌈/⊢),⊣(⌿⍨)⊢=(⌈/⊢))(|-)/)∘(↑2,/⊢)
- Output:
maxdiff 1 8 2 ¯3 0 1 1 ¯2.3 0 5.5 8 6 2 9 11 10 3 7 1 8 7 2 9 7 10 3
Arturo
maximumAdjacentDifference: function [L][
result: [[[] 0]]
loop 0..(size L)-2 'a [
diff: abs (y: <= L\[a+1]) - (x: <= L\[a])
if diff >= last maximum result => last ->
result: (select result 'x -> diff = last x) ++ @[@[@[x,y], diff]]
]
maxLen: result\0\1
result: @[unique map result 'x -> first x, maxLen]
return result
]
lst: @[1,8,2,neg 3,0,1,1,neg 2.3,0,5.5,8,6,2,9,11,10,3]
diffs: maximumAdjacentDifference lst
loop diffs\0 'd ->
print [d "->" diffs\1]
- Output:
[1 8] -> 7 [2 9] -> 7 [10 3] -> 7
AutoHotkey
List := [1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3]
mxDiff := []
loop % List.Count() -1
mxDiff[d := Abs(list[A_Index+1] - list[A_Index])] .= list[A_Index] ", " list[A_Index+1] " ==> " d "`n"
MsgBox % result := Trim(mxDiff[mxDiff.MaxIndex()], "`n")
- Output:
1, 8 ==> 7 2, 9 ==> 7 10, 3 ==> 7
AWK
# syntax: GAWK -f MAXIMUM_DIFFERENCE_BETWEEN_ADJACENT_ELEMENTS_OF_LIST.AWK
BEGIN {
list = "1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3"
n = split(list,arr,",")
for (i=1; i<n; i++) {
a = arr[i]
b = arr[i+1]
if (abs(a-b) == highest) {
sets = sprintf("%s%s,%s ",sets,a,b)
}
else if (abs(a-b) > highest) {
highest = abs(a-b)
sets = sprintf("%s,%s ",a,b)
}
}
printf("%s: %s\n",highest,sets)
exit(0)
}
function abs(x) { if (x >= 0) { return x } else { return -x } }
- Output:
7: 1,8 2,9 10,3
BASIC
QBasic
maxdist = 0
DIM lista(0 TO 16)
FOR i = 0 TO UBOUND(lista)
READ lista(i)
NEXT i
PRINT "Maximum difference between adjacent elements of lista is:"
FOR i = 0 TO UBOUND(lista) - 1
dist = ABS(lista(i) - lista(i + 1))
IF dist > maxdist THEN maxdist = dist
NEXT i
FOR i = 0 TO UBOUND(lista) - 1
dist = ABS(lista(i) - lista(i + 1))
IF dist = maxdist THEN PRINT lista(i); ", "; lista(i + 1); " ==> "; maxdist
NEXT i
DATA 1., 8., 2., -3., 0., 1., 1., -2.3, 0., 5.5, 8., 6., 2., 9., 11., 10., 3.
- Output:
Same as FreeBASIC entry.
BASIC256
arraybase 1
maxdist = 0
dim lista = {1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3}
print "Maximum difference between adjacent elements of lista is:"
for i = 1 to lista[?]-1
dist = abs(lista[i] - lista[i+1])
if dist > maxdist then maxdist = dist
next i
for i = 1 to lista[?]-1
dist = abs(lista[i] - lista[i+1])
if dist = maxdist then print lista[i] & ", " & lista[i+1] & " ==> " & maxdist
next i- Output:
Same as FreeBASIC entry.
True BASIC
LET maxdist = 0
DIM lista(0 TO 16)
FOR i = 0 TO UBOUND(lista)
READ lista(i)
NEXT i
PRINT "Maximum difference between adjacent elements of lista is:"
FOR i = 0 TO UBOUND(lista)-1
LET dist = ABS(lista(i)-lista(i+1))
IF dist > maxdist THEN LET maxdist = dist
NEXT i
FOR i = 0 TO UBOUND(lista)-1
LET dist = ABS(lista(i)-lista(i+1))
IF dist = maxdist THEN PRINT lista(i); ", "; lista(i+1); " ==> "; maxdist
NEXT i
DATA 1., 8., 2., -3., 0., 1., 1., -2.3, 0., 5.5, 8., 6., 2., 9., 11., 10., 3.
END
- Output:
Same as FreeBASIC entry.
Yabasic
maxdist = 0
dim lista(16)
lista(0) = 1 : lista(1) = 8
lista(2) = 2 : lista(3) = -3
lista(4) = 0 : lista(5) = 1
lista(6) = 1 : lista(7) = -2.3
lista(8) = 0 : lista(9) = 5.5
lista(10) = 8 : lista(11) = 6
lista(12) = 2 : lista(13) = 9
lista(14) = 11 : lista(15) = 10
lista(16) = 3
print "Maximum difference between adjacent elements of lista is:"
for i = 0 to arraysize(lista(),1)-1
dist = abs(lista(i) - lista(i+1))
if dist > maxdist maxdist = dist
next i
for i = 0 to arraysize(lista(),1)-1
dist = abs(lista(i) - lista(i+1))
if dist = maxdist print lista(i), ", ", lista(i+1), " ==> ", maxdist
next i- Output:
Same as FreeBASIC entry.
C
#include <stdio.h>
#include <math.h>
typedef struct {
double x;
double y;
} pair;
int main() {
double list[17] = {1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8,6, 2, 9, 11, 10, 3};
double diff, maxDiff = -1;
pair maxPairs[5];
int i, count = 0;
for (i = 1; i < 17; ++i) {
diff = fabs(list[i-1] - list[i]);
if (diff > maxDiff) {
maxDiff = diff;
maxPairs[count++] = (pair){list[i-1], list[i]};
} else if (diff == maxDiff) {
maxPairs[count++] = (pair){list[i-1], list[i]};
}
}
printf("The maximum difference between adjacent pairs of the list is: %g\n", maxDiff);
printf("The pairs with this difference are: ");
for (i = 0; i < count; ++i) printf("[%g, %g] ", maxPairs[i].x, maxPairs[i].y);
printf("\n");
return 0;
}
- Output:
The maximum difference between adjacent pairs of the list is: 7 The pairs with this difference are: [1, 8] [2, 9] [10, 3]
C++
#include <iostream>
#include <iterator>
#include <vector>
#include <utility>
#include <cstdlib>
#include <algorithm>
//supposing example numbers are entered!
int main( ) {
std::cout << "Enter some doubles, separated by blanks, e to end!\n" ;
std::vector<double> numbers { std::istream_iterator<double>{ std::cin } ,
std::istream_iterator<double>{} } ;
std::vector<std::pair<int , int>> neighbours ;
for ( int i = 0 ; i < numbers.size( ) - 1 ; i++ )
neighbours.push_back( std::make_pair( numbers[i] , numbers[ i + 1 ] )) ;
std::sort( neighbours.begin( ) , neighbours.end( ) , []( auto p1 , auto p2 ) {
return std::abs( p1.first - p1.second ) > std::abs( p2.first - p2.second )
; } ) ;
double maximum = std::abs( neighbours[0].first - neighbours[0].second ) ;
int pos = 0 ;
while ( std::abs(neighbours[pos].first - neighbours[pos].second ) == maximum ) {
std::cout << neighbours[pos].first << ',' << neighbours[pos].second <<
" ==> " << maximum << '\n' ;
pos++ ;
}
return 0 ;
}
- Output:
1,8 ==> 7 2,9 ==> 7 10,3 ==> 7
Delphi
{Data type to hold difference info}
type TDiffInfo = record
Diff,N1,N2: double;
end;
{Array of different info}
type TDiffArray = array of TDiffInfo;
procedure FindMaximumDifference(List: array of double; var DiffArray: TDiffArray);
{Analyze data and return list of differnces}
var I: integer;
var Diff,MaxDiff: double;
begin
MaxDiff:=0;
for I:=0 to High(List)-1 do
begin
Diff:=Abs(List[I+1]-List[I]);
if Diff>=MaxDiff then
begin
MaxDiff:=Diff;
SetLength(DiffArray,Length(DiffArray)+1);
DiffArray[High(DiffArray)].Diff:=MaxDiff;
DiffArray[High(DiffArray)].N1:=List[I];
DiffArray[High(DiffArray)].N2:=List[I+1];
end
end;
end;
procedure MaximumAdjacentDifference(Memo: TMemo);
var DA: TDiffArray;
var I: integer;
begin
FindMaximumDifference([1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3],DA);
for I:=0 to High(DA) do
begin
Memo.Lines.Add(Format('abs(%4.1f - %4.1f) = %4.1f',[DA[I].N1,DA[I].N2,DA[I].Diff]));
end;
end;
- Output:
abs( 1.0 - 8.0) = 7.0 abs( 2.0 - 9.0) = 7.0 abs(10.0 - 3.0) = 7.0
EasyLang
list[] = [ 1 8 2 -3 0 1 1 -2.3 0 5.5 8 6 2 9 11 10 3 ]
for i = 2 to len list[]
dist = abs (list[i - 1] - list[i])
max = higher dist max
.
for i = 2 to len list[]
if abs (list[i - 1] - list[i]) = max
print list[i - 1] & "," & list[i] & " ==> " & dist
.
.- Output:
1,8 ==> 7 2,9 ==> 7 10,3 ==> 7
F#
// Max diff 'twix adj elems. Nigel Galloway: July 18th., 2021
let n,g=[1;8;2;-3;0;1;1;-2;3;0;5;5;8;6;2;9;11;10;3]|>List.pairwise|>List.groupBy(fun(n,g)->abs(n-g))|>List.maxBy fst in printfn "Pairs %A have the max diff of %d" g n
- Output:
Pairs [(1, 8); (2, 9); (10, 3)] have the max diff of 7
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 .
- Output:
{ 7 V{ { 1 8 } { 2 9 } { 10 3 } } }
Free Pascal
program maximumDifferenceBetweenAdjacentElementsOfList(output);
type
tmyReal = extended;
tmyList = array of tmyReal;
const
input: tmyList = (1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3);
procedure OutSameDistanceInList(Dist:tmyReal;const list: tmyList);
var
currentDistance : tmyReal;
i : integer;
begin
for i := 0 to High(List) - 1 do
begin
currentDistance := abs(list[i] - list[succ(i)]);
if currentDistance = dist then
writeln('idx : ',i:4,' values ',list[i],' ',list[i+1]);
end;
writeln;
end;
function internalDistance(const list: tmyList): tmyReal;
var
i: integer;
maximumDistance, currentDistance: tmyReal;
begin
maximumDistance := 0.0;
for i := 0 to High(List) - 1 do
begin
currentDistance := abs(list[i] - list[succ(i)]);
if currentDistance > maximumDistance then
begin
maximumDistance := currentDistance;
end;
end;
internalDistance := maximumDistance;
end;
var
list: tmyList;
foundDistance : tmyReal;
begin
list := input;
if length(list) > 0 then
Begin
foundDistance := internalDistance(list);
OutSameDistanceInList(foundDistance,list);
end;
{$IFDEF WINDOWS}
readln;
{$ENDIF}
end.
- Output:
idx : 0 values 1.0000000000000000E+000 8.0000000000000000E+000 idx : 12 values 2.0000000000000000E+000 9.0000000000000000E+000 idx : 15 values 1.0000000000000000E+001 3.0000000000000000E+000
FreeBASIC
Dim As Single Dist, MaxDist = 0
Dim As Single List(16) => {1., 8., 2., -3., 0., 1., 1., -2.3, 0., 5.5, 8., 6., 2., 9., 11., 10., 3.}
Print !"Maximum difference between adjacent elements of list is:"
For i As Integer = 0 To Ubound(List)
Dist = Abs(List(i) - List(i+1))
If Dist > MaxDist Then MaxDist = Dist
Next i
For i As Integer = 0 To Ubound(List)
Dist = Abs(List(i) - List(i+1))
If Dist = MaxDist Then Print List(i) & ", " & List(i+1) & " ==> " & MaxDist
Next i- Output:
Maximum difference between adjacent elements of lista is: 1, 8 ==> 7 2, 9 ==> 7 10, 3 ==> 7
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)
}
- 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
import Data.List (maximumBy)
import Data.Ord (comparing)
maxDeltas :: (Num a, Ord a) => [a] -> [(a, (a, a))]
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]
- Output:
(7.0,(1.0,8.0)) (7.0,(2.0,9.0)) (7.0,(10.0,3.0))
J
maxdiff=: [: (,.|@-/"1) 2(,/\ (#~ (=>./)@:|) -/\) ]
- Output:
maxdiff 1 8 2 _3 0 1 1 _2.3 0 5.5 8 6 2 9 11 10 3
1 8 7
2 9 7
10 3 7
(}:,&":' ==> ',&":{:)"1 maxdiff 1 8 2 _3 0 1 1 _2.3 0 5.5 8 6 2 9 11 10 3
1 8 ==> 7
2 9 ==> 7
10 3 ==> 7
jq
Works with gojq, the Go implementation of jq
def maximally_different_adjacent_pairs:
. as $in
| reduce range(1; length) as $i ({ maxDiff: -1};
(($in[$i-1] - $in[$i])|length) as $diff # length being abs
| if $diff > .maxDiff
then .maxDiff = $diff
| .maxPairs = [[$in[$i-1], $in[$i]]]
elif $diff == .maxDiff
then .maxPairs += [[$in[$i-1], $in[$i]]]
else .
end
);
# Example:
[1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8,6, 2, 9, 11, 10, 3]
| maximally_different_adjacent_pairs- Output:
{"maxDiff":7,"maxPairs":[[1,8],[2,9],[10,3]]}
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(Real[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)
- Output:
1, 8 ==> 7 2, 9 ==> 7 10, 3 ==> 7
Mathematica/Wolfram Language
l = {1, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3};
diff = Abs@Differences[l];
m = Max[diff];
pos = Flatten[Position[diff, m]];
Column[Part[l, # ;; # + 1] -> m & /@ pos]
- Output:
{1,8}->7
{2,9}->7
{10,3}->7
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(" ")
- Output:
The maximum difference between adjacent pairs of the list is: 7 The pairs with this difference are: (1, 8) (2, 9) (10, 3)
OCaml
let rec fold_pairwise f m = function
| a :: (b :: _ as t) -> fold_pairwise f (f m a b) t
| _ -> m
let pair_to_str (a, b) =
Printf.sprintf "(%g, %g)" a b
let max_diffs =
let next m a b =
match abs_float (b -. a), m with
| d', (d, _) when d' > d -> d', [a, b]
| d', (d, l) when d' = d -> d', (a, b) :: l
| _ -> m
in fold_pairwise next (0., [])
let () =
let d, l = max_diffs [1.;8.;2.;-3.;0.;1.;1.;-2.3;0.;5.5;8.;6.;2.;9.;11.;10.;3.] in
List.rev_map pair_to_str l |> String.concat " " |> Printf.printf "%g: %s\n" d
- Output:
7: (1, 8) (2, 9) (10, 3)
Pascal
The following program needs an ISO 7185 Standard “unextended” Pascal, level 1, compliant compiler.
program maximumDifferenceBetweenAdjacentElementsOfList(output);
function internalDistance(
list: array[indexMinimum..indexMaximum: integer] of real
): real;
var
i: integer;
maximumDistance, currentDistance: real;
begin
maximumDistance := 0.0;
for i := indexMinimum to pred(indexMaximum) do
begin
currentDistance := abs(list[i] - list[succ(i)]);
if currentDistance > maximumDistance then
begin
maximumDistance := currentDistance
end
end;
internalDistance := maximumDistance
end;
var
list: array[1..2] of real;
begin
list[1] := 1.0; list[2] := 8.0;
writeLn(internalDistance(list));
end.
Perl
#!/usr/bin/perl
use strict;
use warnings;
use List::Util qw( reduce max );
my @list = (1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3);
my %diffs;
reduce { $diffs{ abs $a - $b } .= " $a,$b"; $b } @list;
my $max = max keys %diffs;
print "$_ ==> $max\n" for split ' ', $diffs{ $max };
- Output:
1,8 ==> 7 2,9 ==> 7 10,3 ==> 7
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
Picat
import util.
main =>
L = [1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3],
Diffs = findall([Diff,A,B], (nextto(A,B,L), Diff = abs(A-B))),
MaxDiff = max([Diff : [Diff,_,_] in Diffs]),
println(MaxDiff=[[A,B] : [Diff,A,B] in Diffs, Diff == MaxDiff]),
nl.- Output:
7 = [[1,8],[2,9],[10,3]]
Here is an alternative way to get the pairwise differences, using zip/2:
% ...
Diffs = [[abs(A-B),A,B] : {A,B} in zip(L.butlast,L.tail)],
% ...
% Returns all element of L but the last
butlast(L) = L[1..L.len-1].
Python
'''Maximum difference between adjacent numbers in list'''
# 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]
]
# ------------------------- TEST -------------------------
# 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)
# MAIN ---
if __name__ == '__main__':
main()
- Output:
(7, (1, 8)) (7, (2, 9)) (7, (10, 3))
Raku
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 }
# 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 ,' Minimum', &min-diff, ' Average', &avg-diff)
-> $which, &sub {
say "$which distance between list elements: " ~ &sub(@list);
}
say '';
}
- 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)) Minimum 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)) Minimum 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)) Minimum 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)) Minimum 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 Minimum distance between list elements: 0 Average distance between list elements: 0 List: [] Maximum distance between list elements: 0 Minimum 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.
/*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*/
#= 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. */
- 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
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- 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...
RPL
| Code | Comments |
|---|---|
≪ DUP SIZE 0 → list len max
≪ 2 len FOR j
list j 1 - GET list j GET - ABS
IF max OVER < THEN 'max' STO
ELSE DROP END
NEXT
{} max +
2 len FOR j
list j 1 - GET list j GET
IF DUP2 - ABS max == THEN R→C +
ELSE DROP2 END
NEXT
≫ ≫ 'ADJMAX' STO
|
( {list} -- { max ( adjacent couples) }
Scan input list...
... calculate adjacent gap
... and store max value
Initialize output list
Scan input list...
Get 2 adjacent elements
If gap = max, add the 2 elements as a complex to the output list
|
The following line of code delivers what is required:
[1 8 2 -3 0 1 1 -2.3 0 5.5 8 6 2 9 11 10 3] ADJMAX
- Output:
1: { 7 (1,8) (2,9) (10,3) }
Ruby
list = [1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3]
max_dif, pairs = list.each_cons(2).group_by{|a,b| (a-b).abs}.max
puts "Maximum difference is #{max_dif}:"
pairs.each{|pair| p pair}
- Output:
Maximum difference is 7: [1, 8] [2, 9] [10, 3]
Rust
use std::io ;
use itertools::Itertools ;
fn main() {
println!("Enter some real numbers, separated by blanks!");
let mut inline : String = String::new( ) ;
io::stdin( ).read_line( &mut inline ).unwrap( ) ;
let entered_line : &str = &*inline ;
let numbers : Vec<f32> = entered_line.split_whitespace( ).map( | s |
s.trim( ). parse::<f32>( ).unwrap( ) ).collect( ) ;
let mut pairs : Vec<(&f32, &f32)> = numbers.iter( ).tuple_windows( ).collect( ) ;
let num_slice = &mut pairs[..] ;
let len = num_slice.len( ) ;
num_slice.sort_by( | a, b| (a.0 - a.1).abs( ).partial_cmp(&( &*b.0 -&*b.1).abs( ))
.unwrap( )) ;
let maximumpair = &num_slice[len - 1 .. len] ;
let maxi = maximumpair.to_vec( ) ;
let maximum : f32 = (maxi[0].0- maxi[0].1).abs( ) ;
let maxima : Vec<&(&f32, &f32)> = num_slice.iter( ).filter( |&p |
(p.0 - p.1).abs( ) == maximum ).collect( ) ;
maxima.iter( ).for_each( | p | println!("{},{} ==> {}" ,
p.0 , p.1 , maximum)) ;
}
- Output:
1,8 ==> 7 2,9 ==> 7 10,3 ==> 7
V (Vlang)
import math
fn main() {
list := [1.0, 8, 2, -3, 0, 1, 1, -2.3, 0, 5.5, 8, 6, 2, 9, 11, 10, 3]
mut max_diff := -1.0
mut max_pairs := [][2]f64{}
for i in 1..list.len {
diff := math.abs(list[i-1] - list[i])
if diff > max_diff {
max_diff = diff
max_pairs = [[list[i-1], list[i]]!]
} else if diff == max_diff {
max_pairs << [list[i-1], list[i]]!
}
}
println("The maximum difference between adjacent pairs of the list is: $max_diff")
println("The pairs with this difference are: $max_pairs")
}- Output:
The maximum difference between adjacent pairs of the list is: 7 The pairs with this difference are: [[1, 8] [2, 9] [10, 3]]
Wren
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)")
- 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
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);
];
];
]- Output:
1, 8 ==> 7 2, 9 ==> 7 10, 3 ==> 7