# Find if there is a subarray with 0 sum

Given an array of positive and negative numbers, find if there is a subarray (of size at least one) with 0 sum.

**Examples:**

Input:{4, 2, -3, 1, 6}Output:trueExplanation:

There is a subarray with zero sum from index 1 to 3.

Input:{4, 2, 0, 1, 6}Output: trueExplanation: The third element is zero. A single element is also a sub-array.

Input:{-3, 2, 3, 1, 6}Output:false

__Naive approach:__

__Naive approach:__

consider all subarrays one by one and check the sum of every subarray. Run two loops: the outer loop picks a starting point i and the inner loop tries all subarrays starting from i (See this for implementation).

**Time Complexity:** O(N^{2})**Auxiliary Space:** O(1)

__Find if there is a subarray with 0 sum using hashing:__

The idea is to iterate through the array and for every element arr[i], calculate the sum of elements from 0 to i (this can simply be done as sum += arr[i]). If the current sum has been seen before, then there is a zero-sum array. Hashing is used to store the sum values so that sum can be stored quickly and find out whether the current sum is seen before or not.

Follow the given steps to solve the problem:

- Declare a variable sum, to store the sum of prefix elements
- Traverse the array and at each index, add the element into the sum and check if this sum exists earlier. If the sum exists, then return true
- Also, insert every prefix sum into a map, so that later on it can be found whether the current sum is seen before or not
- At the end return false, as no such subarray is found

**Illustration:**

arr[] = {1, 4, -2, -2, 5, -4, 3}

Consider all prefix sums, one can notice that there is a subarray with 0 sum when :

- Either a prefix sum repeats or
- Or prefix sum becomes 0.
Prefix sums for above array are:

1, 5, 3,1, 6, 2, 5

Since prefix sum 1 repeats, we have a subarray with 0 sum.

Below is the Implementation of the above approach:

## C++

`// C++ program to find if` `// there is a zero sum subarray` `#include <bits/stdc++.h>` `using` `namespace` `std;` `bool` `subArrayExists(` `int` `arr[], ` `int` `N)` `{` ` ` `unordered_set<` `int` `> sumSet;` ` ` `// Traverse through array` ` ` `// and store prefix sums` ` ` `int` `sum = 0;` ` ` `for` `(` `int` `i = 0; i < N; i++) {` ` ` `sum += arr[i];` ` ` `// If prefix sum is 0 or` ` ` `// it is already present` ` ` `if` `(sum == 0 || sumSet.find(sum) != sumSet.end())` ` ` `return` `true` `;` ` ` `sumSet.insert(sum);` ` ` `}` ` ` `return` `false` `;` `}` `// Driver's code` `int` `main()` `{` ` ` `int` `arr[] = {-3, 2, 3, 1, 6};` ` ` `int` `N = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `// Function call` ` ` `if` `(subArrayExists(arr, N))` ` ` `cout << ` `"Found a subarray with 0 sum"` `;` ` ` `else` ` ` `cout << ` `"No Such Sub Array Exists!"` `;` ` ` `return` `0;` `}` |

## Java

`// Java program to find` `// if there is a zero sum subarray` `import` `java.util.HashSet;` `import` `java.util.Set;` `class` `ZeroSumSubarray {` ` ` ` ` `// Returns true if arr[]` ` ` `// has a subarray with sero sum` ` ` `static` `Boolean subArrayExists(` `int` `arr[])` ` ` `{` ` ` `// Creates an empty hashset hs` ` ` `Set<Integer> hs = ` `new` `HashSet<Integer>();` ` ` `// Initialize sum of elements` ` ` `int` `sum = ` `0` `;` ` ` `// Traverse through the given array` ` ` `for` `(` `int` `i = ` `0` `; i < arr.length; i++) {` ` ` `// Add current element to sum` ` ` `sum += arr[i];` ` ` `// Return true in following cases` ` ` `// a) Current element is 0` ` ` `// b) sum of elements from 0 to i is 0` ` ` `// c) sum is already present in hash set` ` ` `if` `(arr[i] == ` `0` `|| sum == ` `0` `|| hs.contains(sum))` ` ` `return` `true` `;` ` ` `// Add sum to hash set` ` ` `hs.add(sum);` ` ` `}` ` ` `// We reach here only when there is` ` ` `// no subarray with 0 sum` ` ` `return` `false` `;` ` ` `}` ` ` `// Driver's code` ` ` `public` `static` `void` `main(String arg[])` ` ` `{` ` ` `int` `arr[] = {-` `3` `, ` `2` `, ` `3` `, ` `1` `, ` `6` `};` ` ` `// Function call` ` ` `if` `(subArrayExists(arr))` ` ` `System.out.println(` ` ` `"Found a subarray with 0 sum"` `);` ` ` `else` ` ` `System.out.println(` `"No Such Sub Array Exists!"` `);` ` ` `}` `}` |

## Python3

`# python3 program to find if` `# there is a zero sum subarray` `def` `subArrayExists(arr, N):` ` ` `# traverse through array` ` ` `# and store prefix sums` ` ` `n_sum ` `=` `0` ` ` `s ` `=` `set` `()` ` ` `for` `i ` `in` `range` `(N):` ` ` `n_sum ` `+` `=` `arr[i]` ` ` `# If prefix sum is 0 or` ` ` `# it is already present` ` ` `if` `n_sum ` `=` `=` `0` `or` `n_sum ` `in` `s:` ` ` `return` `True` ` ` `s.add(n_sum)` ` ` `return` `False` `# Driver's code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `arr ` `=` `[` `-` `3` `, ` `2` `, ` `3` `, ` `1` `, ` `6` `]` ` ` `N ` `=` `len` `(arr)` ` ` `# Function call` ` ` `if` `subArrayExists(arr, N) ` `=` `=` `True` `:` ` ` `print` `(` `"Found a sunbarray with 0 sum"` `)` ` ` `else` `:` ` ` `print` `(` `"No Such sub array exits!"` `)` `# This code is contributed by Shrikant13` |

## C#

`// C# program to find if there` `// is a zero sum subarray` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG {` ` ` `// Returns true if arr[] has` ` ` `// a subarray with sero sum` ` ` `static` `bool` `SubArrayExists(` `int` `[] arr)` ` ` `{` ` ` `// Creates an empty HashSet hM` ` ` `HashSet<` `int` `> hs = ` `new` `HashSet<` `int` `>();` ` ` `// Initialize sum of elements` ` ` `int` `sum = 0;` ` ` `// Traverse through the given array` ` ` `for` `(` `int` `i = 0; i < arr.Length; i++) {` ` ` `// Add current element to sum` ` ` `sum += arr[i];` ` ` `// Return true in following cases` ` ` `// a) Current element is 0` ` ` `// b) sum of elements from 0 to i is 0` ` ` `// c) sum is already present in hash set` ` ` `if` `(arr[i] == 0 || sum == 0 || hs.Contains(sum))` ` ` `return` `true` `;` ` ` `// Add sum to hash set` ` ` `hs.Add(sum);` ` ` `}` ` ` `// Reach here only when there is` ` ` `// no subarray with 0 sum` ` ` `return` `false` `;` ` ` `}` ` ` `// Driver's code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `[] arr = {-3, 2, 3, 1, 6};` ` ` `// Function call` ` ` `if` `(SubArrayExists(arr))` ` ` `Console.WriteLine(` ` ` `"Found a subarray with 0 sum"` `);` ` ` `else` ` ` `Console.WriteLine(` `"No Such Sub Array Exists!"` `);` ` ` `}` `}` |

## Javascript

`// A Javascript program to` `// find if there is a zero sum subarray` `const subArrayExists = (arr) => {` ` ` `const sumSet = ` `new` `Set();` ` ` `// Traverse through array` ` ` `// and store prefix sums` ` ` `let sum = 0;` ` ` `for` `(let i = 0 ; i < arr.length ; i++)` ` ` `{` ` ` `sum += arr[i];` ` ` `// If prefix sum is 0` ` ` `// or it is already present` ` ` `if` `(sum === 0 || sumSet.has(sum))` ` ` `return` `true` `;` ` ` `sumSet.add(sum);` ` ` `}` ` ` `return` `false` `;` `}` `// Driver code` `const arr = [-3, 2, 3, 1, 6];` `if` `(subArrayExists(arr))` ` ` `console.log(` `"Found a subarray with 0 sum"` `);` `else` ` ` `console.log(` `"No Such Sub Array Exists!"` `);` |

**Output**

No Such Sub Array Exists!

**Time Complexity: **O(N) under the assumption that a good hashing function is used, that allows insertion and retrieval operations in O(1) time. **Auxiliary Space:** O(N) Here extra space is required for hashing

This article is contributed by **Chirag Gupta**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above