Find maximal subsequence of array with indexes

Question

I would like to find the maximal subsequence S(h,k) in an array of integer. I already have the code (in Java) to find the maximum value and it works fine, but how can I get the two indexes h and k from the following?

int []a = {-2, 1, -3, 4, -1, 2, 1, -5, 4 };
int max_so_far = 0, max_ending_here = 0;
for(int i=0; i<a.length; i++) {
    max_ending_here = Math.max(0, max_ending_here + a[i]);
    max_so_far = Math.max(max_so_far, max_ending_here);
}
System.out.println("The maximal sum of subsequence is = "+max_so_far)";

is this what you looking for? http://www.geeksforgeeks.org/largest-sum-contiguous-subarray/ — Shreyas Sarvothama, Oct 26 '16 at 17:10
No it's not. But I found on this site the correct solution, working also with all the numbers negative. http://code.geeksforgeeks.org/o4cxS2 — Gio Bact, Oct 26 '16 at 17:21

score 0 · Answer 1 · answered Oct 26 '16 at 17:23

You can get the subsequence itself by storing the last index at which you improved max_so_far, and "unraveling" the sequence from the back:

int []a = {-2, 1, -3, 4, -1, 2, 1, -5, 4 };
int max_so_far = 0, max_ending_here = 0, index_max = 0;
for(int i=0; i<a.length; i++) {
    max_ending_here = Math.max(0, max_ending_here + a[i]);
    if (max_so_far < max_ending_here) {
        max_so_far = max_ending_here;
        index_max = i;
    }
}
System.out.print("The maximal sum of subsequence is = "+max_so_far);
int j = index_max;
while (j >= 0 && max_so_far > 0) {
    max_so_far -= a[j--];
}
System.out.println(", from = "+(j+1)+" to "+index_max+", inclusive");

Demo.

Note: Unraveling from the back using a marker is a common theme in dynamic programming algorithms. In your simple case index_max plays the role of a special marker, from which you look backward for the index that runs max_so_far into zero.

Gio Bact · Answer 2 · 2016-10-26T17:52:32.590

Thank to Shreyas Sarvothama and dasblinkenlight for their answers. I found a good solution this code written by Utsav Chokshi on the geeksforgeeks.org website.

The solution is:

int []a = {-2, 1, -3, 4, -1, 2, 1, -5, 4 };
int max_so_far = a[0], max_ending_here = a[0];
int curStartIndex = 0;
int maxStartIndex = 0;
int maxEndIndex = 0;

for(int i=1; i<a.length; i++) {
        max_ending_here = Math.max(a[i], max_ending_here + a[i]);
        if(max_ending_here > max_so_far){
             max_so_far = max_ending_here;
             maxStartIndex = curStartIndex;
             maxEndIndex = i;
        }
        if(max_ending_here < 0){
            curStartIndex = i+1;
        }
}

Find maximal subsequence of array with indexes

2 Answers2