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Number of subarrays having sum exactly equal to k

  • Difficulty Level : Medium
  • Last Updated : 07 May, 2021

Given an unsorted array of integers, find the number of subarrays having sum exactly equal to a given number k.

Examples: 

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Input : arr[] = {10, 2, -2, -20, 10}, 
        k = -10
Output : 3
Subarrays: arr[0...3], arr[1...4], arr[3..4]
have sum exactly equal to -10.

Input : arr[] = {9, 4, 20, 3, 10, 5},
            k = 33
Output : 2
Subarrays : arr[0...2], arr[2...4] have sum
exactly equal to 33.

Naive Solution – 
A simple solution is to traverse all the subarrays and calculate their sum. If the sum is equal to the required sum then increment the count of subarrays. Print final count of subarray. Following is the naive implementation – 



C++




// C++ program for
// the above approach
#include <bits/stdc++.h>
using namespace std;
int main()
{
  int arr[] = {10, 2, -2, -20, 10};
  int k = -10;
  int n = sizeof(arr) / sizeof(arr[0]);
  int res = 0;
 
  // Calculate all subarrays
  for (int i = 0; i < n; i++)
  {
    int sum = 0;
    for (int j = i; j < n; j++)
    {
      // Calculate required sum
      sum += arr[j];
 
      // Check if sum is equal to
      // required sum
      if (sum == k)
        res++;
    }
  }
  cout << (res) << endl;
}
 
// This code is contributed by Chitranayal

Java




// Java program for
// the above approach
import java.util.*;
class Solution {
     
    public static void main(String[] args)
    {
        int arr[] = { 10, 2, -2, -20, 10 };
        int k = -10;
        int n = arr.length;
        int res = 0;
         
        // calculate all subarrays
        for (int i = 0; i < n; i++) {
             
            int sum = 0;
            for (int j = i; j < n; j++) {
                 
                // calculate required sum
                sum += arr[j];
                 
                // check if sum is equal to
                // required sum
                if (sum == k)
                    res++;
            }
        }
        System.out.println(res);
    }
}

Python3




# Python3 program for
# the above approach
arr = [ 10, 2, -2, -20, 10 ]
n = len(arr)
k = -10
res = 0
 
# Calculate all subarrays
for i in range(n):
    summ = 0           
    for j in range(i, n):
         
        # Calculate required sum
        summ += arr[j]
 
        # Check if sum is equal to
        # required sum
        if summ == k:
            res += 1
 
print(res)
 
# This code is contributed by kavan155gondalia

C#




// C# program for
// the above approach
using System;
using System.Collections.Generic;
class GFG {
     
  static void Main() {
      int[] arr = {10, 2, -2, -20, 10};
      int k = -10;
      int n = arr.Length;
      int res = 0;
      
      // Calculate all subarrays
      for (int i = 0; i < n; i++)
      {
        int sum = 0;
        for (int j = i; j < n; j++)
        {
           
          // Calculate required sum
          sum += arr[j];
      
          // Check if sum is equal to
          // required sum
          if (sum == k)
            res++;
        }
      }
      Console.WriteLine(res);
  }
}
 
// This code is contributed by divyesh072019

Javascript




<script>
     
// Javascript program for
// the above approach
let arr = [ 10, 2, -2, -20, 10 ];
let k = -10;
let n = arr.length;
let res = 0;
 
// Calculate all subarrays
for(let i = 0; i < n; i++)
{
    let sum = 0;
    for(let j = i; j < n; j++)
    {
         
        // Calculate required sum
        sum += arr[j];
         
        // Check if sum is equal to
        // required sum
        if (sum == k)
            res++;
    }
}
document.write(res);
 
// This code is contributed by suresh07
   
</script>
Output: 
3

 

Efficient Solution – 
An efficient solution is while traversing the array, store sum so far in currsum. Also, maintain the count of different values of currsum in a map. If the value of currsum is equal to the desired sum at any instance increment count of subarrays by one. The value of currsum exceeds the desired sum by currsum – sum. If this value is removed from currsum then the desired sum can be obtained. From the map find the number of subarrays previously found having sum equal to currsum-sum. Excluding all those subarrays from the current subarray, gives new subarrays having the desired sum. So increase count by the number of such subarrays. Note that when currsum is equal to the desired sum then also check the number of subarrays previously having a sum equal to 0. Excluding those subarrays from the current subarray gives new subarrays having the desired sum. Increase count by the number of subarrays having sum 0 in that case.

C++




// C++ program to find number of subarrays
// with sum exactly equal to k.
#include <bits/stdc++.h>
using namespace std;
 
// Function to find number of subarrays
// with sum exactly equal to k.
int findSubarraySum(int arr[], int n, int sum)
{
    // STL map to store number of subarrays
    // starting from index zero having
    // particular value of sum.
    unordered_map<int, int> prevSum;
 
    int res = 0;
 
    // Sum of elements so far.
    int currsum = 0;
 
    for (int i = 0; i < n; i++) {
 
        // Add current element to sum so far.
        currsum += arr[i];
 
        // If currsum is equal to desired sum,
        // then a new subarray is found. So
        // increase count of subarrays.
        if (currsum == sum)
            res++;
 
        // currsum exceeds given sum by currsum
        //  - sum. Find number of subarrays having
        // this sum and exclude those subarrays
        // from currsum by increasing count by
        // same amount.
        if (prevSum.find(currsum - sum) != prevSum.end())
            res += (prevSum[currsum - sum]);
 
        // Add currsum value to count of
        // different values of sum.
        prevSum[currsum]++;
    }
 
    return res;
}
 
int main()
{
    int arr[] = { 10, 2, -2, -20, 10 };
    int sum = -10;
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << findSubarraySum(arr, n, sum);
    return 0;
}

Java




// Java program to find number of subarrays
// with sum exactly equal to k.
import java.util.HashMap;
import java.util.Map;
 
public class GfG {
 
    // Function to find number of subarrays
    // with sum exactly equal to k.
    static int findSubarraySum(int arr[], int n, int sum)
    {
        // HashMap to store number of subarrays
        // starting from index zero having
        // particular value of sum.
        HashMap<Integer, Integer> prevSum = new HashMap<>();
 
        int res = 0;
 
        // Sum of elements so far.
        int currsum = 0;
 
        for (int i = 0; i < n; i++) {
 
            // Add current element to sum so far.
            currsum += arr[i];
 
            // If currsum is equal to desired sum,
            // then a new subarray is found. So
            // increase count of subarrays.
            if (currsum == sum)
                res++;
 
            // currsum exceeds given sum by currsum
            //  - sum. Find number of subarrays having
            // this sum and exclude those subarrays
            // from currsum by increasing count by
            // same amount.
            if (prevSum.containsKey(currsum - sum))
                res += prevSum.get(currsum - sum);
 
            // Add currsum value to count of
            // different values of sum.
            Integer count = prevSum.get(currsum);
            if (count == null)
                prevSum.put(currsum, 1);
            else
                prevSum.put(currsum, count + 1);
        }
 
        return res;
    }
 
    public static void main(String[] args)
    {
 
        int arr[] = { 10, 2, -2, -20, 10 };
        int sum = -10;
        int n = arr.length;
        System.out.println(findSubarraySum(arr, n, sum));
    }
}
 
// This code is contributed by Rituraj Jain

Python3




# Python3 program to find the number of
# subarrays with sum exactly equal to k.
from collections import defaultdict
 
# Function to find number of subarrays 
# with sum exactly equal to k.
def findSubarraySum(arr, n, Sum):
  
    # Dictionary to store number of subarrays
    # starting from index zero having 
    # particular value of sum.
    prevSum = defaultdict(lambda : 0)
   
    res = 0
   
    # Sum of elements so far.
    currsum = 0
   
    for i in range(0, n): 
   
        # Add current element to sum so far.
        currsum += arr[i]
   
        # If currsum is equal to desired sum,
        # then a new subarray is found. So
        # increase count of subarrays.
        if currsum == Sum
            res += 1        
   
        # currsum exceeds given sum by currsum  - sum.
        # Find number of subarrays having 
        # this sum and exclude those subarrays
        # from currsum by increasing count by 
        # same amount.
        if (currsum - Sum) in prevSum:
            res += prevSum[currsum - Sum]
           
   
        # Add currsum value to count of 
        # different values of sum.
        prevSum[currsum] += 1
      
    return res
  
if __name__ == "__main__":
 
    arr =  [10, 2, -2, -20, 10
    Sum = -10
    n = len(arr)
    print(findSubarraySum(arr, n, Sum))
     
# This code is contributed by Rituraj Jain

C#




// C# program to find number of subarrays
// with sum exactly equal to k.
using System;
using System.Collections.Generic;
 
class GFG {
    // Function to find number of subarrays
    // with sum exactly equal to k.
    public static int findSubarraySum(int[] arr,
                                      int n, int sum)
    {
 
        // HashMap to store number of subarrays
        // starting from index zero having
        // particular value of sum.
        Dictionary<int, int> prevSum = new Dictionary<int, int>();
 
        int res = 0;
 
        // Sum of elements so far
        int currsum = 0;
 
        for (int i = 0; i < n; i++) {
 
            // Add current element to sum so far.
            currsum += arr[i];
 
            // If currsum is equal to desired sum,
            // then a new subarray is found. So
            // increase count of subarrays.
            if (currsum == sum)
                res++;
 
            // currsum exceeds given sum by currsum
            // - sum. Find number of subarrays having
            // this sum and exclude those subarrays
            // from currsum by increasing count by
            // same amount.
            if (prevSum.ContainsKey(currsum - sum))
                res += prevSum[currsum - sum];
 
            // Add currsum value to count of
            // different values of sum.
            if (!prevSum.ContainsKey(currsum))
                prevSum.Add(currsum, 1);
            else {
                int count = prevSum[currsum];
                prevSum[currsum] = count + 1;
            }
        }
        return res;
    }
 
    // Driver Code
    public static void Main()
    {
        int[] arr = { 10, 2, -2, -20, 10 };
        int sum = -10;
        int n = arr.Length;
        Console.Write(findSubarraySum(arr, n, sum));
    }
}
 
// This code is contributed by
// sanjeev2552

Javascript




<script>
// Javascript program to find number of subarrays
// with sum exactly equal to k.
     
    // Function to find number of subarrays
    // with sum exactly equal to k.
    function findSubarraySum(arr,n,sum)
    {
     
        // HashMap to store number of subarrays
        // starting from index zero having
        // particular value of sum.
        let prevSum = new Map();
        let res = 0;
  
        // Sum of elements so far.
        let currsum = 0;
        for (let i = 0; i < n; i++)
        {
  
            // Add current element to sum so far.
            currsum += arr[i];
  
            // If currsum is equal to desired sum,
            // then a new subarray is found. So
            // increase count of subarrays.
            if (currsum == sum)
                res++;
  
            // currsum exceeds given sum by currsum
            //  - sum. Find number of subarrays having
            // this sum and exclude those subarrays
            // from currsum by increasing count by
            // same amount.
            if (prevSum.has(currsum - sum))
                res += prevSum.get(currsum - sum);
  
            // Add currsum value to count of
            // different values of sum.
            let count = prevSum.get(currsum);
            if (count == null)
                prevSum.set(currsum, 1);
            else
                prevSum.set(currsum, count + 1);
        }
        return res;
    }
     
    let arr = [10, 2, -2, -20, 10];
    let sum = -10;
    let n = arr.length;
    document.write(findSubarraySum(arr, n, sum));
     
    // This code is contributed by avanitrachhadiya2155.
</script>
Output: 
3

 

Time Complexity: O(n) 
Auxiliary Space: O(n)




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