Maximum difference between adjacent elements of list
Find maximum difference between adjacent elements of list.
- 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 (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
<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 maxdiff(sequence s) sequence d = sq_abs(sq_sub(s[1..-2],s[2..-1])) atom m = max(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 printf(1,"max difference is %g, occurring at %s\n",{m,join(p,", ")}) end procedure maxdiff({1,8,2,-3,0,1,1,-2.3,0,5.5,8,6,2,9,11,10,3})
- Output:
max difference is 7, occurring at s[1..2]={1,8}, s[13..14]={2,9}, s[16..17]={10,3}
Python
<lang 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()</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 }
- 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 may be */
$= translate($, , ',') /*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
if datatype(x, 'N') then iterate /*Is it numeric? Yes, then continue. */
say '***error*** element #'i " isn't numeric: " x
exit 13
end /*i*/
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 " " */ aa=; bb= /*the AA and BB list(s); # pairs. */ d= -1 /*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 */
aa= aa a; bb= bb b /* the elements that had the max diff.*/
end /*j*/
say /*stick a fork in it, we're all done. */ say 'The maximum difference of the elements in the list is: ' d
do k=1 for words(aa)
say 'and is between the elements: ' word(aa, k) " and " word(bb, k)
end /*k*/
exit 0 /*stick a fork in it, we're all done. */</lang>
- output when using the default input:
<ore>
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