# Check if subarray with 0 sum is exists or not

Given an array of integers, check if array contains a sub-array having 0 sum.

For example,

Input:  { 3, 4, -7, 3, 1, 3, 1, -4, -2, -2 }

Output: Subarray with 0 sum exists

The sub-arrays with 0 sum are:

{ 3, 4, -7 }
{ 4, -7, 3 }
{ -7, 3, 1, 3 }
{ 3, 1, -4 }
{ 3, 1, 3, 1, -4, -2, -2 }
{ 3, 4, -7, 3, 1, 3, 1, -4, -2, -2 }

We can easily solve this problem in linear time by using hashing. The idea is to use set to check if sub-array with zero sum is present in the given array or not. We traverse the given array, and maintain sum of elements seen so far. If sum is seen before (i.e. sum exists in set), we return true as there exists at-least one sub-array with zero sum which ends at current index else we insert the sum into the set.

The time complexity of proposed solution is O(n) and auxiliary space used by the program is O(n).

Output:

Subarray exists

## Java

Output:

Subarray exists

Also See: Print all sub-arrays with 0 sum

Exercise: Extend the solution for non-zero sum of sub-array.

Please use ideone or C++ Shell or any other online compiler link to post code in comments.
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Guest
H. Guijt

Instead of arguments (int A[], int n), we can also use (std::initializer_list A). The function call would then be zeroSumSubArray ({4, 2, -3, -1, 0 4});, and the for-loop could use range-based for.

Guest
Sravan

Instead of checking whether sum visited previously or not,can we check sum value in each iteration and see if sum is zero .If in any iteration sum is zero then there exists sub array whose sum is 0.No?

Guest
NeelLohit

Hi, I would like to point out that your method above is predicated upon the condition that the linear addition of the elements in the array will at least once give a sum of zero. So for the array {5,1,-6,4,3} the algorithm works. But for the same elements in a different order e.g {5,1,4,-6,3}, this doesn’t work. That condition is not mentioned in the question. I think we should look for a more generalized solution to this problem and not just concentrate on the time complexity alone.

Guest
newbie

code for the extended exercise we test with the sum so far minus the given sum
code in kotlin

Guest
Roshan

int A[] = { 2, 1, -4, -1, 4 };
fails

Guest
Roshan

by mistake, ign0re

Guest

This won’t work on say [3, -50, 1, -4]

Am I right?

Guest

Yes I’m. Tested it ou your code!

Guest

Ok, I see it now, you are working only on continious sub-arrays 😉

Guest
Yusuf Belim

Below fails.
int A[] = { 3,6,-6 };

Guest
Yusuf Belim

Guest
sneh

{2, -3, 3}
the algorithm will return True but there is no subarray with zero sum.

Guest
sneh

apology, {-3, 3}

Guest
Reena Somvanshi

this code fails for [4,2,3,1,0,4], it returns true though there are no zero sum sub arrays. Sum is repeating due to 0 in the array.

Guest
Tony

There is one zero sum subarray which is {0}.