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

Following solution finds max length subarray with a given sum k without using dynamic programming, but using simple rescursion. Here i_s is start index and i_e is end index for the current value of sum

##Input the array and sum to be found(0 in your case)
a = map(int,raw_input().split())
k = int(raw_input())

##initialize total sum=0
totalsum=0

##Recursive function to find max len 0
def findMaxLen(sumL,i_s,i_e):
    if i_s0: 
        if sumL==k:
            print i_s, i_e
            return (i_s,i_e)
        else:
            x = findMaxLen(sumL-a[i_s],i_s+1,i_e)
            y = findMaxLen(sumL-a[i_e],i_s,i_e-1)
            if x[1]-x[0]>y[1]-y[0]:
                return x
            else:
                return y
    else:
        ##Result not there
        return (-1,-1)


## find total sum
for i in range(len(a)):
    totalsum += a[i]

##if totalsum==0, max array is array itself
if totalsum == k:
    print "seq found at",0,len(a)-1

##else use recursion
else:
    print findMaxLen(totalsum,0,len(a)-1)

Time complexity is O(n) and space complexity is O(n) due to recursive memory stack