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
Related posts: Find if there is a subarray with 0 sum
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
Time Complexity: O(N)
Auxiliary Space: O(N)
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