Add tasks for all the new languages
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Tina Müller
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PROGRAM MAX_SUM
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DIM A%[11],B%[10],C%[4]
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!$DYNAMIC
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DIM P%[0]
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PROCEDURE MAX_SUBSEQUENCE(P%[],N%->A$)
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LOCAL A%,B%,I%,J%,M%,S%
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A%=1
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FOR I%=0 TO N% DO
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S%=0
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FOR J%=I% TO N% DO
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S%+=P%[J%]
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IF S%>M% THEN
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M%=S%
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A%=I%
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B%=J%
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END IF
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END FOR
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END FOR
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IF A%>B% THEN A$="[]" EXIT PROCEDURE END IF
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A$="["
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FOR I%=A% TO B% DO
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A$+=STR$(P%[I%])+","
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END FOR
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A$=LEFT$(A$,LEN(A$)-1)+"]"
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END PROCEDURE
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PROCEDURE SHOW_ARRAY(P%[],N%->A$)
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LOCAL I%
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A$="["
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FOR I%=0 TO N% DO
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A$+=STR$(P%[I%])+","
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END FOR
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A$=LEFT$(A$,LEN(A$)-1)+"]"
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END PROCEDURE
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BEGIN
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A%[]=(0,1,2,-3,3,-1,0,-4,0,-1,-4,2)
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N%=UBOUND(A%,1)
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!$DIM P%[N%]
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SHOW_ARRAY(A%[],N%->A$)
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PRINT(A$;" -> ";)
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MAX_SUBSEQUENCE(A%[],N%->A$)
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PRINT(A$)
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!$ERASE P%
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B%[]=(-1,-2,3,5,6,-2,-1,4,-4,2,-1)
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N%=UBOUND(B%,1)
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!$DIM P%[N%]
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SHOW_ARRAY(B%[],N%->A$)
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PRINT(A$;" -> ";)
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MAX_SUBSEQUENCE(B%[],N%->A$)
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PRINT(A$)
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!$ERASE P%
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C%[]=(-1,-2,-3,-4,-5)
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N%=UBOUND(C%,1)
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!$DIM P%[N%]
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SHOW_ARRAY(C%[],N%->A$)
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PRINT(A$;" -> ";)
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MAX_SUBSEQUENCE(C%[],N%->A$)
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PRINT(A$)
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!$ERASE P%
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END PROGRAM
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(lib 'struct)
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(struct result (score starter))
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;; the score of i in sequence ( .. i j ...) is max (i , i + score (j))
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;; to compute score of (a b .. x y z) :
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;; start with score(z) and compute scores of y , z , ..c, b , a.
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;; this is O(n)
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;; return value of sub-sequence
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(define (max-max L into: result)
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(define value
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(if
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(empty? L) -Infinity
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(max (first L) (+ (first L) (max-max (cdr L) result )))))
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(when (> value (result-score result))
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(set-result-score! result value) ;; remember best score
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(set-result-starter! result L)) ;; and its location
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value)
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;; return (best-score (best sequence))
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(define (max-seq L)
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(define best (result -Infinity null))
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(max-max L into: best)
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(define score (result-score best))
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(list score
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(for/list (( n (result-starter best)))
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#:break (zero? score)
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(set! score (- score n))
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n)))
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(define L '(-1 -2 3 5 6 -2 -1 4 -4 2 -1))
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(max-seq L)
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→ (15 (3 5 6 -2 -1 4))
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' FB 1.05.0 Win64
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Dim As Integer seq(10) = {-1 , -2 , 3 , 5 , 6 , -2 , -1 , 4 , -4 , 2 , -1}
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Dim As Integer i, j, sum, maxSum, first, last
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maxSum = 0
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For i = LBound(seq) To UBound(seq)
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sum = 0
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For j = i To UBound(seq)
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' only proper sub-sequences are considered
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If i = LBound(seq) AndAlso j = UBound(seq) Then Exit For
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sum += seq(j)
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If sum > maxSum Then
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maxSum = sum
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first = i
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last = j
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End If
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Next j
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Next i
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If maxSum > 0 Then
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Print "Maximum subsequence is from indices"; first; " to"; last
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Print "Elements are : ";
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For i = first To last
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Print seq(i); " ";
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Next
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Print
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Print "Sum is"; maxSum
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Else
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Print "Maximum subsequence is the empty sequence which has a sum of 0"
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End If
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Print
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Print "Press any key to quit"
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Sleep
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proc maxsum(s): int =
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var maxendinghere = 0
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for x in s:
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maxendinghere = max(maxendinghere + x, 0)
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result = max(result, maxendinghere)
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echo maxsum(@[-1, -2, 3, 5, 6, -2, -1, 4, -4, 2, -1])
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function maxSubseq(sequence s)
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integer this, maxsum = 0, first = 1, last = 0
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for i=1 to length(s) do
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this = 0
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for j=i to length(s) do
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this += s[j]
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if this>maxsum then
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{maxsum,first,last} = {this,i,j}
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end if
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end for
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end for
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return s[first..last]
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end function
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? maxSubseq({-1, -2, 3, 5, 6, -2, -1, 4, -4, 2, -1})
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? maxSubseq({})
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? maxSubseq({-1, -5, -3})
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gss = (lst) :
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# Find discrete integral
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integral = (0)
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accum = 0
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lst each (n): accum = accum + n, integral append(accum).
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# Check integral[b + 1] - integral[a] for all 0 <= a <= b < N
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max = -1
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max_a = 0
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max_b = 0
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lst length times (b) :
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b times (a) :
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if (integral(b + 1) - integral(a) > max) :
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max = integral(b + 1) - integral(a)
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max_a = a
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max_b = b
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.
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.
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.
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# Print the results
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if (max >= 0) :
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(lst slice(max_a, max_b) join(" + "), " = ", max, "\n") join print
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.
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else :
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"No subsequence larger than 0\n" print
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.
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.
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gss((-1, -2, 3, 5, 6, -2, -1, 4, -4, 2, -1))
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gss((-1, -2, -3, -4, -5))
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gss((7,-6, -8, 5, -2, -6, 7, 4, 8, -9, -3, 2, 6, -4, -6))
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func maxsubseq(*a) {
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var (start, end, sum, maxsum) = (-1, -1, 0, 0);
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a.each_kv { |i, x|
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sum += x;
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if (maxsum < sum) {
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maxsum = sum;
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end = i;
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}
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elsif (sum < 0) {
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sum = 0;
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start = i;
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}
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};
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a.ft(start+1, end);
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}
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say maxsubseq(-1, -2, 3, 5, 6, -2, -1, 4, -4, 2, -1);
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say maxsubseq(-2, -2, -1, 3, 5, 6, -1, 4, -4, 2, -1);
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say maxsubseq(-2, -2, -1, -3, -5, -6, -1, -4, -4, -2, -1);
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def subarray_sum:
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. as $arr
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| reduce range(0; length) as $i
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( {"first": length, "last": 0, "curr": 0, "curr_first": 0, "max": 0};
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$arr[$i] as $e
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| (.curr + $e) as $curr
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| . + (if $e > $curr then {"curr": $e, "curr_first": $i} else {"curr": $curr} end)
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| if .curr > .max then . + {"max": $curr, "first": .curr_first, "last": $i}
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else .
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end)
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| [ .max, $arr[ .first : (1 + .last)] ];
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[1, 2, 3, 4, 5, -8, -9, -20, 40, 25, -5] | subarray_sum
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$ jq -c -n -f Greatest_subsequential_sum.jq
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[65,[40,25]]
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