# Print all subarrays with 0 sum

• Difficulty Level : Hard
• Last Updated : 01 Jun, 2021

Given an array, print all subarrays in the array which has sum 0.
Examples:

```Input:  arr = [6, 3, -1, -3, 4, -2, 2,
4, 6, -12, -7]
Output:
Subarray found from Index 2 to 4
Subarray found from Index 2 to 6
Subarray found from Index 5 to 6
Subarray found from Index 6 to 9
Subarray found from Index 0 to 10```

Related posts: Find if there is a subarray with 0 sum

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A simple solution is to consider all subarrays one by one and check if sum of every subarray is equal to 0 or not. The complexity of this solution would be O(n^2).
A better approach is to use Hashing.
Do following for each element in the array

1. Maintain sum of elements encountered so far in a variable (say sum).
2. If current sum is 0, we found a subarray starting from index 0 and ending at index current index
3. Check if current sum exists in the hash table or not.
4. If current sum already exists in the hash table then it indicates that this sum was the sum of some sub-array elements arr…arr[i] and now the same sum is obtained for the current sub-array arr…arr[j] which means that the sum of the sub-array arr[i+1]…arr[j] must be 0.
5. Insert current sum into the hash table

Below is a dry run of the above approach: Below is the implementation of the above approach:

## C++

 `// C++ program to print all subarrays``// in the array which has sum 0``#include ``using` `namespace` `std;`` ` `// Function to print all subarrays in the array which``// has sum 0``vector< pair<``int``, ``int``> > findSubArrays(``int` `arr[], ``int` `n)``{``    ``// create an empty map``    ``unordered_map<``int``, vector<``int``> > map;`` ` `    ``// create an empty vector of pairs to store``    ``// subarray starting and ending index``    ``vector > out;`` ` `    ``// Maintains sum of elements so far``    ``int` `sum = 0;`` ` `    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``// add current element to sum``        ``sum += arr[i];`` ` `        ``// if sum is 0, we found a subarray starting``        ``// from index 0 and ending at index i``        ``if` `(sum == 0)``            ``out.push_back(make_pair(0, i));`` ` `        ``// If sum already exists in the map there exists``        ``// at-least one subarray ending at index i with``        ``// 0 sum``        ``if` `(map.find(sum) != map.end())``        ``{``            ``// map[sum] stores starting index of all subarrays``            ``vector<``int``> vc = map[sum];``            ``for` `(``auto` `it = vc.begin(); it != vc.end(); it++)``                ``out.push_back(make_pair(*it + 1, i));``        ``}`` ` `        ``// Important - no else``        ``map[sum].push_back(i);``    ``}`` ` `    ``// return output vector``    ``return` `out;``}`` ` `// Utility function to print all subarrays with sum 0``void` `print(vector> out)``{``    ``for` `(``auto` `it = out.begin(); it != out.end(); it++)``        ``cout << ``"Subarray found from Index "` `<<``            ``it->first << ``" to "` `<< it->second << endl;``}`` ` `// Driver code``int` `main()``{``    ``int` `arr[] = {6, 3, -1, -3, 4, -2, 2, 4, 6, -12, -7};``    ``int` `n = ``sizeof``(arr)/``sizeof``(arr);`` ` `    ``vector > out = findSubArrays(arr, n);`` ` `    ``// if we didn’t find any subarray with 0 sum,``    ``// then subarray doesn’t exists``    ``if` `(out.size() == 0)``        ``cout << ``"No subarray exists"``;``    ``else``        ``print(out);`` ` `    ``return` `0;``}`

## Java

 `// Java program to print all subarrays``// in the array which has sum 0``import` `java.io.*;``import` `java.util.*;` `// User defined pair class``class` `Pair``{``    ``int` `first, second;``    ``Pair(``int` `a, ``int` `b)``    ``{``        ``first = a;``        ``second = b;``    ``}``}` `public` `class` `GFG``{``    ``// Function to print all subarrays in the array which``    ``// has sum 0``    ``static` `ArrayList findSubArrays(``int``[] arr, ``int` `n)``    ``{``            ``// create an empty map``            ``HashMap> map = ``new` `HashMap<>();` `            ``// create an empty vector of pairs to store``            ``// subarray starting and ending index``            ``ArrayList out = ``new` `ArrayList<>();` `            ``// Maintains sum of elements so far``            ``int` `sum = ``0``;` `            ``for` `(``int` `i = ``0``; i < n; i++)``            ``{``                ``// add current element to sum``                ``sum += arr[i];` `                ``// if sum is 0, we found a subarray starting``                ``// from index 0 and ending at index i``                ``if` `(sum == ``0``)``                    ``out.add(``new` `Pair(``0``, i));``                ``ArrayList al = ``new` `ArrayList<>();``                ` `                ``// If sum already exists in the map there exists``                ``// at-least one subarray ending at index i with``                ``// 0 sum``                ``if` `(map.containsKey(sum))``                ``{``                    ``// map[sum] stores starting index of all subarrays``                    ``al = map.get(sum);``                    ``for` `(``int` `it = ``0``; it < al.size(); it++)``                    ``{``                            ``out.add(``new` `Pair(al.get(it) + ``1``, i));``                    ``}``                ``}``                ``al.add(i);``                ``map.put(sum, al);``            ``}``            ``return` `out;``    ``}` `    ``// Utility function to print all subarrays with sum 0``    ``static` `void` `print(ArrayList out)``    ``{``            ``for` `(``int` `i = ``0``; i < out.size(); i++)``            ``{``                ``Pair p = out.get(i);``                ``System.out.println(``"Subarray found from Index "``                        ``+ p.first + ``" to "` `+ p.second);``            ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String args[])``    ``{``            ``int``[] arr = {``6``, ``3``, -``1``, -``3``, ``4``, -``2``, ``2``, ``4``, ``6``, -``12``, -``7``};``            ``int` `n = arr.length;``            ` `            ``ArrayList out = findSubArrays(arr, n);``            ` `            ``// if we did not find any subarray with 0 sum,``            ``// then subarray does not exists``            ``if` `(out.size() == ``0``)``                ``System.out.println(``"No subarray exists"``);``            ``else``                ``print(out);``    ``}``}` `// This code is contributed by rachana soma`

## Python3

 `# Python3 program to print all subarrays``# in the array which has sum 0` `# Function to get all subarrays``# in the array which has sum 0``def` `findSubArrays(arr,n):` `    ``# create a python dict``    ``hashMap ``=` `{}``    ` `    ``# create a python list``    ``# equivalent to ArrayList``    ``out ``=` `[]``    ` `    ``# tracker for sum of elements``    ``sum1 ``=` `0``    ``for` `i ``in` `range``(n):``        ` `        ``# increment sum by element of array``        ``sum1 ``+``=` `arr[i]``        ` `        ``# if sum is 0, we found a subarray starting``        ``# from index 0 and ending at index i``        ``if` `sum1 ``=``=` `0``:``            ``out.append((``0``, i))``        ``al ``=` `[]``        ` `        ``# If sum already exists in the map``        ``# there exists at-least one subarray``        ``# ending at index i with 0 sum``        ``if` `sum1 ``in` `hashMap:``            ` `            ``# map[sum] stores starting index``            ``# of all subarrays``            ``al ``=` `hashMap.get(sum1)``            ``for` `it ``in` `range``(``len``(al)):``                ``out.append((al[it] ``+` `1``, i))``        ``al.append(i)``        ``hashMap[sum1] ``=` `al``    ``return` `out` `# Utility function to print``# all subarrays with sum 0``def` `printOutput(output):``    ``for` `i ``in` `output:``        ``print` `(``"Subarray found from Index "` `+``                ``str``(i[``0``]) ``+` `" to "` `+` `str``(i[``1``]))` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=` `[``6``, ``3``, ``-``1``, ``-``3``, ``4``, ``-``2``,``              ``2``, ``4``, ``6``, ``-``12``, ``-``7``]``    ``n ``=` `len``(arr)``    ``out ``=` `findSubArrays(arr, n)``    ` `    ``# if we did not find any subarray with 0 sum,``    ``# then subarray does not exists``    ``if` `(``len``(out) ``=``=` `0``):``        ``print` `(``"No subarray exists"``)``    ``else``:``        ``printOutput (out)` `# This code is contributed by Vikas Chitturi`

## C#

 `// C# program to print all subarrays``// in the array which has sum 0``using` `System;``using` `System.Collections.Generic;` `// User defined pair class``class` `Pair``{``    ``public` `int` `first, second;``    ``public` `Pair(``int` `a, ``int` `b)``    ``{``        ``first = a;``        ``second = b;``    ``}``}` `class` `GFG``{``    ``// Function to print all subarrays``    ``// in the array which has sum 0``    ``static` `List findSubArrays(``int``[] arr, ``int` `n)``    ``{``        ``// create an empty map``        ``Dictionary<``int``, List<``int``>> map =``                   ``new` `Dictionary<``int``, List<``int``>>();` `        ``// create an empty vector of pairs to store``        ``// subarray starting and ending index``        ``List outt = ``new` `List();` `        ``// Maintains sum of elements so far``        ``int` `sum = 0;` `        ``for` `(``int` `i = 0; i < n; i++)``        ``{``            ``// add current element to sum``            ``sum += arr[i];` `            ``// if sum is 0, we found a subarray starting``            ``// from index 0 and ending at index i``            ``if` `(sum == 0)``                ``outt.Add(``new` `Pair(0, i));``            ``List<``int``> al = ``new` `List<``int``>();``            ` `            ``// If sum already exists in the map there exists``            ``// at-least one subarray ending at index i with``            ``// 0 sum``            ``if` `(map.ContainsKey(sum))``            ``{``                ``// map[sum] stores starting index``                ``// of all subarrays``                ``al = map[sum];``                ``for` `(``int` `it = 0; it < al.Count; it++)``                ``{``                    ``outt.Add(``new` `Pair(al[it] + 1, i));``                ``}``            ``}``            ``al.Add(i);``            ``if``(map.ContainsKey(sum))``                ``map[sum] = al;``            ``else``                ``map.Add(sum, al);``        ``}``        ``return` `outt;``    ``}` `    ``// Utility function to print all subarrays with sum 0``    ``static` `void` `print(List outt)``    ``{``        ``for` `(``int` `i = 0; i < outt.Count; i++)``        ``{``            ``Pair p = outt[i];``            ``Console.WriteLine(``"Subarray found from Index "` `+``                               ``p.first + ``" to "` `+ p.second);``        ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String []args)``    ``{``        ``int``[] arr = {6, 3, -1, -3, 4, -2,``                        ``2, 4, 6, -12, -7};``        ``int` `n = arr.Length;``        ` `        ``List outt = findSubArrays(arr, n);``        ` `        ``// if we did not find any subarray with 0 sum,``        ``// then subarray does not exists``        ``if` `(outt.Count == 0)``            ``Console.WriteLine(``"No subarray exists"``);``        ``else``            ``print(outt);``    ``}``}` `// This code is contributed by Rajput-Ji`

Output:

```Subarray found from Index 2 to 4
Subarray found from Index 2 to 6
Subarray found from Index 5 to 6
Subarray found from Index 6 to 9
Subarray found from Index 0 to 10```

Time Complexity: O(N^2)
Auxiliary Space: O(N)