maximum subarray whose sum equals 0

Question

An array contains both positive and negative elements, find the maximum subarray whose sum equals 0.

Answer 1

Another solution to this problem could be: 1. Calculate sum for entire array 2. Now follow following formula to get the largest subarray with sum zero:

Math.max(find(a,l+1,r,sum-a[l]), find(a,l,r-1,sum-a[r]));
where l=left index, r= right index, initially their value=0 and a.length-1

Idea is simple, max size we can get with sum=0, is the size of array then we start skipping elements from left and right recursively, the moment we get sum=0 we stop. Below is the code for same:

static int find(int a[]) {
    int sum =0;
    for (int i = 0; i < a.length; i++) {
        sum = sum+a[i];
    }

    return find(a, 0, a.length-1, sum);
}


static int find(int a[], int l, int r, int sum) {
    if(l==r && sum>0) {
        return 0;
    }
    if(sum==0) {
        return r-l+1;
    }
    return Math.max(find(a,l+1,r,sum-a[l]), find(a,l,r-1,sum-a[r]));

}