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# Subarray with 0 sum

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

Examples:

Input: {4, 2, -3, 1, 6}
Output: true
Explanation:
There is a subarray with zero sum from index 1 to 3.

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

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

Recommended Practice

## Subarray with 0 sum using Nested loop:

Generate every subarray and calcuate the sum of each subarray. Check if subarray sum is 0 then return true. Otherwise, if no such subarray found then return false.

Below is the implementation of the above approach:

## C++

 `// C++ program to find if``// there is a zero sum subarray``#include ``using` `namespace` `std;` `bool` `subArrayExists(``int` `arr[], ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++) {``      ` `        ``// starting point of the sub arrray and``        ``// sum is initialized with first element of subarray``        ``// a[i]``        ``int` `sum = arr[i];``        ``if` `(sum == 0)``            ``return` `true``;``        ``for` `(``int` `j = i + 1; j < n; j++) {``          ` `            ``// we are finding the sum till jth index``            ``// starting from ith index``            ``sum += arr[j];``            ``if` `(sum == 0)``                ``return` `true``;``        ``}``    ``}``    ``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;``}` `// This code is contributed by Tapesh(tapeshdua420)`

## Java

 `// Java program to find if``// there is a zero sum subarray``import` `java.util.Arrays;` `public` `class` `Main {` `public` `static` `boolean` `subArrayExists(``int` `arr[], ``int` `n)``{``    ``for` `(``int` `i = ``0``; i < n; i++) {``        ``int` `sum = arr[i];``        ``if` `(sum == ``0``)``            ``return` `true``;``        ``for` `(``int` `j = i + ``1``; j < n; j++) {``            ``sum += arr[j];``            ``if` `(sum == ``0``)``                ``return` `true``;``        ``}``    ``}``    ``return` `false``;``}` `// Driver's code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { -``3``, ``2``, ``3``, ``1``, ``6` `};``    ``int` `N = arr.length;` `    ``// Function call``    ``if` `(subArrayExists(arr, N))``        ``System.out.println(``"Found a subarray with 0 sum"``);``    ``else``        ``System.out.println(``"No Such Sub Array Exists!"``);` `}``}` `// This code is contributed by Utkarsh Kumar`

## Python3

 `def` `subArrayExists(arr, n):``    ``for` `i ``in` `range``(n):``        ``# Starting point of the subarray and``        ``# sum is initialized with the first element of subarray``        ``sum` `=` `arr[i]``        ``if` `sum` `=``=` `0``:``            ``return` `True``        ``for` `j ``in` `range``(i ``+` `1``, n):``            ``# We are finding the sum till the jth index``            ``# starting from the ith index``            ``sum` `+``=` `arr[j]``            ``if` `sum` `=``=` `0``:``                ``return` `True``    ``return` `False` `# Driver's code``if` `__name__ ``=``=` `"__main__"``:``    ``arr ``=` `[``-``3``, ``2``, ``3``, ``1``, ``6``]``    ``N ``=` `len``(arr)` `    ``# Function call``    ``if` `subArrayExists(arr, N):``        ``print``(``"Found a subarray with 0 sum"``)``    ``else``:``        ``print``(``"No Such Sub Array Exists!"``)`

## C#

 `// C# program to find if``// there is a zero sum subarray``using` `System;` `public` `class` `GFG {` `public` `static` `bool` `subArrayExists(``int``[] arr, ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++) {``        ``int` `sum = arr[i];``        ``if` `(sum == 0)``            ``return` `true``;``        ``for` `(``int` `j = i + 1; j < n; j++) {``            ``sum += arr[j];``            ``if` `(sum == 0)``                ``return` `true``;``        ``}``    ``}``    ``return` `false``;``}` `// Driver's code``public` `static` `void` `Main()``{``    ``int``[] arr = { -3, 2, 3, 1, 6 };``    ``int` `N = arr.Length;` `    ``// Function call``    ``if` `(subArrayExists(arr, N))``        ``Console.WriteLine(``"Found a subarray with 0 sum"``);``    ``else``        ``Console.WriteLine(``"No Such Sub Array Exists!"``);` `}``}` `// This code is contributed by Pushpesh Raj`

Output

```No Such Sub Array Exists!

```

Time Complexity: O(N2)
Auxiliary Space: O(1)

## 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 must be a zero-sum subarray. 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, 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 ``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 hs = ``new` `HashSet();` `        ``// 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 subarray 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