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# Maximize count of non-overlapping subarrays with sum K

• Difficulty Level : Medium
• Last Updated : 18 May, 2021

Given an array arr[] and an integer K, the task is to print the maximum number of non-overlapping subarrays with a sum equal to K.

Examples:

Input: arr[] = {-2, 6, 6, 3, 5, 4, 1, 2, 8}, K = 10
Output: 3
Explanation: All possible non-overlapping subarrays with sum K(= 10) are {-2, 6, 6}, {5, 4, 1}, {2, 8}. Therefore, the required count is 3.

Input: arr[] = {1, 1, 1}, K = 2
Output: 1

Approach: The problem can be solved using the concept of prefix sum. Follow the below steps to solve the problem:

1. Initialize a set to store all the prefix sums obtained up to the current element.
2. Initialize variables prefixSum and res, to store the prefix sum of the current subarray and the count of subarrays with a sum equal to K respectively.
3. Iterate over the array and for each array element, update prefixSum by adding to it the current element. Now, check if the value prefixSum – K is already present in the set or not. If found to be true, increment res, clear the set, and reset the value of prefixSum.
4. Repeat the above steps until the entire array is traversed. Finally, print the value of res.

## C++14

 `// C++ Program to implement``// the above approach` `#include ``using` `namespace` `std;` `// Function to count the maximum``// number of subarrays with sum K``int` `CtSubarr(``int` `arr[], ``int` `N, ``int` `K)``{` `    ``// Stores all the distinct``    ``// prefixSums obtained``    ``unordered_set<``int``> st;` `    ``// Stores the prefix sum``    ``// of the current subarray``    ``int` `prefixSum = 0;` `    ``st.insert(prefixSum);` `    ``// Stores the count of``    ``// subarrays with sum K``    ``int` `res = 0;` `    ``for` `(``int` `i = 0; i < N; i++) {``        ``prefixSum += arr[i];` `        ``// If a subarray with sum K``        ``// is already found``        ``if` `(st.count(prefixSum - K)) {` `            ``// Increase count``            ``res += 1;` `            ``// Reset prefix sum``            ``prefixSum = 0;` `            ``// Clear the set``            ``st.clear();``            ``st.insert(0);``        ``}` `        ``// Insert the prefix sum``        ``st.insert(prefixSum);``    ``}``    ``return` `res;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { -2, 6, 6, 3, 5, 4, 1, 2, 8 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``int` `K = 10;``    ``cout << CtSubarr(arr, N, K);``}`

## Java

 `// Java Program to implement``// the above approach``import` `java.util.*;``class` `GFG{``    ``// Function to count the maximum``    ``// number of subarrays with sum K``    ``static` `int` `CtSubarr(``int``[] arr,``                        ``int` `N, ``int` `K)``    ``{``        ``// Stores all the distinct``        ``// prefixSums obtained``        ``Set st = ``new` `HashSet();` `        ``// Stores the prefix sum``        ``// of the current subarray``        ``int` `prefixSum = ``0``;` `        ``st.add(prefixSum);` `        ``// Stores the count of``        ``// subarrays with sum K``        ``int` `res = ``0``;` `        ``for` `(``int` `i = ``0``; i < N; i++)``        ``{``            ``prefixSum += arr[i];` `            ``// If a subarray with sum K``            ``// is already found``            ``if` `(st.contains(prefixSum - K))``            ``{``                ``// Increase count``                ``res += ``1``;` `                ``// Reset prefix sum``                ``prefixSum = ``0``;` `                ``// Clear the set``                ``st.clear();``                ``st.add(``0``);``            ``}` `            ``// Insert the prefix sum``            ``st.add(prefixSum);``        ``}``        ``return` `res;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = {-``2``, ``6``, ``6``, ``3``,``                     ``5``, ``4``, ``1``, ``2``, ``8``};``        ``int` `N = arr.length;``        ``int` `K = ``10``;``        ``System.out.println(CtSubarr(arr, N, K));``    ``}``}` `// This code is contributed by Chitranayal`

## Python3

 `# Python3 program to implement``# the above approach` `# Function to count the maximum``# number of subarrays with sum K``def` `CtSubarr(arr, N, K):` `    ``# Stores all the distinct``    ``# prefixSums obtained``    ``st ``=` `set``()` `    ``# Stores the prefix sum``    ``# of the current subarray``    ``prefixSum ``=` `0` `    ``st.add(prefixSum)` `    ``# Stores the count of``    ``# subarrays with sum K``    ``res ``=` `0` `    ``for` `i ``in` `range``(N):``        ``prefixSum ``+``=` `arr[i]` `        ``# If a subarray with sum K``        ``# is already found``        ``if``((prefixSum ``-` `K) ``in` `st):` `            ``# Increase count``            ``res ``+``=` `1` `            ``# Reset prefix sum``            ``prefixSum ``=` `0` `            ``# Clear the set``            ``st.clear()``            ``st.add(``0``)` `        ``# Insert the prefix sum``        ``st.add(prefixSum)` `    ``return` `res` `# Driver Code``arr ``=` `[ ``-``2``, ``6``, ``6``, ``3``, ``5``, ``4``, ``1``, ``2``, ``8` `]``N ``=` `len``(arr)``K ``=` `10` `# Function call``print``(CtSubarr(arr, N, K))` `# This code is contributed by Shivam Singh`

## C#

 `// C# program to implement``// the above approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG{``    ` `// Function to count the maximum``// number of subarrays with sum K``static` `int` `CtSubarr(``int``[] arr,``                    ``int` `N, ``int` `K)``{``    ` `    ``// Stores all the distinct``    ``// prefixSums obtained``    ``HashSet<``int``> st = ``new` `HashSet<``int``>();` `    ``// Stores the prefix sum``    ``// of the current subarray``    ``int` `prefixSum = 0;` `    ``st.Add(prefixSum);` `    ``// Stores the count of``    ``// subarrays with sum K``    ``int` `res = 0;` `    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ``prefixSum += arr[i];` `        ``// If a subarray with sum K``        ``// is already found``        ``if` `(st.Contains(prefixSum - K))``        ``{``            ` `            ``// Increase count``            ``res += 1;` `            ``// Reset prefix sum``            ``prefixSum = 0;` `            ``// Clear the set``            ``st.Clear();``            ``st.Add(0);``        ``}` `        ``// Insert the prefix sum``        ``st.Add(prefixSum);``    ``}``    ``return` `res;``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { -2, 6, 6, 3,``                   ``5, 4, 1, 2, 8};``    ``int` `N = arr.Length;``    ``int` `K = 10;``    ` `    ``Console.WriteLine(CtSubarr(arr, N, K));``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:
`3`

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

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