Find subarray with given sum | Set 2 (Handles Negative Numbers)

Given an unsorted array of integers, find a subarray which adds to a given number. If there are more than one subarrays with the sum as the given number, print any of them.

Examples:

Input: arr[] = {1, 4, 20, 3, 10, 5}, sum = 33
Ouptut: Sum found between indexes 2 and 4

Input: arr[] = {10, 2, -2, -20, 10}, sum = -10
Ouptut: Sum found between indexes 0 to 3

Input: arr[] = {-10, 0, 2, -2, -20, 10}, sum = 20
Ouptut: No subarray with given sum exists

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

We have discussed a solution that do not handles negative integers here. In this post, negative integers are also handled.

A simple solution is to consider all subarrays one by one and check if sum of every subarray is equal to given sum or not. The complexity of this solution would be O(n^2).

An efficient way is to use a map. The idea is to maintain sum of elements encountered so far in a variable (say curr_sum). Let the given number is sum. Now for each element, we check if curr_sum – sum exists in the map or not. If we found it in the map that means, we have a subarray present with given sum, else we insert curr_sum into the map and proceed to next element. If all elements of the array are processed and we didn’t find any subarray with given sum, then subarray doesn’t exists.

Below is the implementation of above idea –

C++

// C++ program to print subarray with sum as given sum 
#include<bits/stdc++.h> 
using namespace std; 
  
// Function to print subarray with sum as given sum 
void subArraySum(int arr[], int n, int sum) 
{ 
    // create an empty map 
    unordered_map<int, int> map; 
  
    // Maintains sum of elements so far 
    int curr_sum = 0; 
  
    for (int i = 0; i < n; i++) 
    { 
        // add current element to curr_sum 
        curr_sum = curr_sum + arr[i]; 
  
        // if curr_sum is equal to target sum 
        // we found a subarray starting from index 0 
        // and ending at index i 
        if (curr_sum == sum) 
        { 
            cout << "Sum found between indexes "
                 << 0 << " to " << i << endl; 
            return; 
        } 
  
        // If curr_sum - sum already exists in map 
        // we have found a subarray with target sum 
        if (map.find(curr_sum - sum) != map.end()) 
        { 
            cout << "Sum found between indexes "
                 << map[curr_sum - sum] + 1 
                 << " to " << i << endl; 
            return; 
        } 
  
        map[curr_sum] = i; 
    } 
  
    // If we reach here, then no subarray exists 
    cout << "No subarray with given sum exists"; 
} 
  
// Driver program to test above function 
int main() 
{ 
    int arr[] = {10, 2, -2, -20, 10}; 
    int n = sizeof(arr)/sizeof(arr[0]); 
    int sum = -10; 
  
    subArraySum(arr, n, sum); 
  
    return 0; 
} 

Java

// Java program to print subarray with sum as given sum 
import java.util.*; 
  
class GFG { 
  
    public static void subArraySum(int[] arr, int n, int sum) { 
        //cur_sum to keep track of cummulative sum till that point 
        int cur_sum = 0; 
        int start = 0; 
        int end = -1; 
        HashMap<Integer, Integer> hashMap = new HashMap<>(); 
  
        for (int i = 0; i < n; i++) { 
            cur_sum = cur_sum + arr[i]; 
            //check whether cur_sum - sum = 0, if 0 it means 
            //the sub array is starting from index 0- so stop 
            if (cur_sum - sum == 0) { 
                start = 0; 
                end = i; 
                break; 
            } 
            //if hashMap already has the value, means we already  
            // have subarray with the sum - so stop 
            if (hashMap.containsKey(cur_sum - sum)) { 
                start = hashMap.get(cur_sum - sum) + 1; 
                end = i; 
                break; 
            } 
            //if value is not present then add to hashmap 
            hashMap.put(cur_sum, i); 
  
        } 
        // if end is -1 : means we have reached end without the sum 
        if (end == -1) { 
            System.out.println("No subarray with given sum exists"); 
        } else { 
            System.out.println("Sum found between indexes " 
                            + start + " to " + end); 
        } 
  
    } 
  
    // Driver code 
    public static void main(String[] args) { 
        int[] arr = {10, 2, -2, -20, 10}; 
        int n = arr.length; 
        int sum = -10; 
        subArraySum(arr, n, sum); 
  
    } 
} 

Python3

# Python3 program to print subarray with sum as given sum  
  
# Function to print subarray with sum as given sum  
def subArraySum(arr, n, Sum):  
   
    # create an empty map  
    Map = {}  
    
    # Maintains sum of elements so far  
    curr_sum = 0 
    
    for i in range(0,n):  
       
        # add current element to curr_sum  
        curr_sum = curr_sum + arr[i]  
    
        # if curr_sum is equal to target sum  
        # we found a subarray starting from index 0  
        # and ending at index i  
        if curr_sum == Sum:  
           
            print("Sum found between indexes 0 to", i) 
            return 
           
    
        # If curr_sum - sum already exists in map  
        # we have found a subarray with target sum  
        if (curr_sum - Sum) in Map:  
           
            print("Sum found between indexes", \ 
                   Map[curr_sum - Sum] + 1, "to", i)  
              
            return 
    
        Map[curr_sum] = i  
    
    # If we reach here, then no subarray exists  
    print("No subarray with given sum exists")  
   
    
# Driver program to test above function  
if __name__ == "__main__":  
   
    arr = [10, 2, -2, -20, 10]  
    n = len(arr)  
    Sum = -10 
    
    subArraySum(arr, n, Sum)  
    
# This code is contributed by Rituraj Jain 

C#

using System; 
using System.Collections.Generic; 
  
// C# program to print subarray with sum as given sum  
  
public class GFG 
{ 
  
    public static void subArraySum(int[] arr, int n, int sum) 
    { 
        //cur_sum to keep track of cummulative sum till that point  
        int cur_sum = 0; 
        int start = 0; 
        int end = -1; 
        Dictionary<int, int> hashMap = new Dictionary<int, int>(); 
  
        for (int i = 0; i < n; i++) 
        { 
            cur_sum = cur_sum + arr[i]; 
            //check whether cur_sum - sum = 0, if 0 it means  
            //the sub array is starting from index 0- so stop  
            if (cur_sum - sum == 0) 
            { 
                start = 0; 
                end = i; 
                break; 
            } 
            //if hashMap already has the value, means we already   
            // have subarray with the sum - so stop  
            if (hashMap.ContainsKey(cur_sum - sum)) 
            { 
                start = hashMap[cur_sum - sum] + 1; 
                end = i; 
                break; 
            } 
            //if value is not present then add to hashmap  
            hashMap[cur_sum] = i; 
  
        } 
        // if end is -1 : means we have reached end without the sum  
        if (end == -1) 
        { 
            Console.WriteLine("No subarray with given sum exists"); 
        } 
        else
        { 
            Console.WriteLine("Sum found between indexes " + start + " to " + end); 
        } 
  
    } 
  
    // Driver code  
    public static void Main(string[] args) 
    { 
        int[] arr = new int[] {10, 2, -2, -20, 10}; 
        int n = arr.Length; 
        int sum = -10; 
        subArraySum(arr, n, sum); 
  
    } 
} 
  
// This code is contributed by Shrikant13 

Output:

Sum found between indexes 0 to 3

Time complexity of above solution is O(n) as we are doing only one traversal of the array.

Auxiliary space used by the program is O(n).

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