Print all subarrays with 0 sum

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

This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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My Personal Notes

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

C++

Java

Python3

C#

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