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
Output: Sum found between indexes 2 and 4
Explantion: Sum of elements between indices
2 and 4 is 20 + 3 + 10 = 33

Input: arr[] = {10, 2, -2, -20, 10}, sum = -10
Output: Sum found between indexes 0 to 3
Explantion: Sum of elements between indices
0 and 3 is 10 + 2 - 2 - 20 = -10

Input: arr[] = {-10, 0, 2, -2, -20, 10}, sum = 20
Output: No subarray with given sum exists
Explantion: There is no subarray with the given sum

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

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

Approach: The idea is to store the sum of elements of every prefix of the array in a hashmap, i.e for every index store the sum of elements upto that index hashmap. So to check if there is a subarray with sum equal to s, check for every index i, and sum upto that index as x. If there is a prefix with sum equal to x – s, then the subarray with given sum is found.

Algorithm:

create a Hashmap (hm) to store key value pair, i.e, key = prefix sum and value = its index and a variable to store the current sum (sum = 0) and the sum of subarray as s
Traverse through the array from start to end.
For every element update the sum, i.e sum = sum + array[i]
If sum is equal to s then print that the subarray with given sum is from 0 to i
If there is any key in the HashMap which is equal to sum – s then print that the subarray with given sum is from hm[sum – s] to i
Put the sum and index in the hashmap as key-value pair.

Dry-run of the above approach:

Implementation:

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

Complexity Analysis:

Time complexity: O(N).
If hashing is performed with the help of an array then this the time complexity. In case the elements cannot be hashed in an array a hash map can also be used as shown in the above code.
Auxiliary space: O(n).
As a HashMap is needed, this takes a linear space.

Find subarray with given sum with negatives allowed in constant space

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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