Print all subarrays with 0 sum

Difficulty Level : Hard
Last Updated : 09 May, 2020

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

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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

Maintain sum of elements encountered so far in a variable (say sum).
If current sum is 0, we found a subarray starting from index 0 and ending at index current index
Check if current sum exists in the hash table or not.
If current sum already exists in the hash table then it indicates that this sum was the sum of some sub-array elements arr[0]…arr[i] and now the same sum is obtained for the current sub-array arr[0]…arr[j] which means that the sum of the sub-array arr[i+1]…arr[j] must be 0.
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 <bits/stdc++.h>
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 <pair<int, int>> 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<pair<int, int>> 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[0]);
   
    vector<pair<int, int> > 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<Pair> findSubArrays(int[] arr, int n)
    {
            // create an empty map 
            HashMap<Integer,ArrayList<Integer>> map = new HashMap<>();
  
            // create an empty vector of pairs to store 
            // subarray starting and ending index 
            ArrayList<Pair> 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<Integer> 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<Pair> 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<Pair> 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<Pair> 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<Pair> outt = new List<Pair>();
  
        // 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<Pair> 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<Pair> 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

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