> For the complete documentation index, see [llms.txt](https://gl01.gitbook.io/gfg-editorials/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://gl01.gitbook.io/gfg-editorials/2023/12-2023-dec-9/10-subarray-with-0-sum.md).

# 10. Subarray with 0 sum

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/subarray-with-0-sum-1587115621/1)

![](https://badgen.net/badge/Level/Medium/yellow)

## My Approach

To check if there is a subarray with a sum of 0, I maintain a running sum while traversing the array. I use an unordered set to store the cumulative sum at each step. If, at any point, I find that the sum already exists in the set, it means there is a subarray with a sum of 0. This is because the difference between the current sum and the sum stored in the set would be 0.

## Explain with Example

Consider the array \[4, 2, -3, 1, 6]. The running sum would be \[4, 6, 3, 4, 10]. At the third step, the sum becomes 4, and we check if 4 is already in the set. Since it is, we know there is a subarray with a sum of 0 (from index 1 to 3: `2 - 3 + 1`).

## Time and Auxiliary Space Complexity

* **Time Complexity** : `O(n)`, where n is the size of the array.
* **Auxiliary Space Complexity** : `O(n)`, where n is the size of the array.

## Code (C++)

```cpp
class Solution {
public:
    bool subArrayExists(int arr[], int n) {
        int sum = 0;
        unordered_set<int> s;
        s.insert(0);
        
        for (int i = 0; i < n; i++) {
            sum += arr[i];
            if (s.find(sum) != s.end())
                return true;
            s.insert(sum);
        }
        
        return false;
    }
};
```

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