# Count of substrings of a binary string containing K ones

Given a binary string of length N and an integer K, we need to find out how many substrings of this string are exist which contains exactly K ones.

**Examples:**

Input : s = “10010” K = 1 Output : 9 The 9 substrings containing one 1 are, “1”, “10”, “100”, “001”, “01”, “1”, “10”, “0010” and “010”

In this problem we need to find count of substrings which contains exactly K ones or in other words sum of digits in those substring is K. We first create a prefix sum array and loop over that and stop when sum value is greater than or equal to K. Now if sum at current index is (K + a) then we know that substring sum, from all those indices where sum is (a), till current index will be K, so count of indices having sum (a), will be added to result. This procedure is explained with an example below,

string s = “100101” K = 2 prefix sum array = [1, 1, 1, 2, 2, 3] So, at index 3, we have prefix sum 2, Now total indices from where sum is 2, is 1 so result = 1 Substring considered = [“1001”] At index 4, we have prefix sum 2, Now total indices from where sum is 2, is 1 so result = 2 Substring considered = [“1001”, “10010”] At index 5, we have prefix sum 3, Now total indices from where sum is 2, is 3 so result = 5 Substring considered = [“1001”, “10010”, “00101”, “0101”, “101”]

So we need to track two things, prefix sum and frequency of particular sum. In below code, instead of storing complete prefix sum, only prefix sum at current index is stored using one variable and frequency of sums in stored in an array. Total time complexity of solution is O(N).

## C++

// C++ program to find count of substring containing // exactly K ones #include <bits/stdc++.h> using namespace std; // method returns total number of substring having K ones int countOfSubstringWithKOnes(string s, int K) { int N = s.length(); int res = 0; int countOfOne = 0; int freq[N + 1] = {0}; // initialize index having zero sum as 1 freq[0] = 1; // loop over binary characters of string for (int i = 0; i < N; i++) { // update countOfOne variable with value // of ith character countOfOne += (s[i] - '0'); // if value reaches more than K, then // update result if (countOfOne >= K) { // add frequency of indices, having // sum (current sum - K), to the result res += freq[countOfOne - K]; } // update frequency of one's count freq[countOfOne]++; } return res; } // Driver code to test above methods int main() { string s = "10010"; int K = 1; cout << countOfSubstringWithKOnes(s, K) << endl; return 0; }

## Java

// Java program to find count of substring // containing exactly K ones import java.io.*; public class GFG { // method returns total number of // substring having K ones static int countOfSubstringWithKOnes( String s, int K) { int N = s.length(); int res = 0; int countOfOne = 0; int []freq = new int[N+1]; // initialize index having zero // sum as 1 freq[0] = 1; // loop over binary characters // of string for (int i = 0; i < N; i++) { // update countOfOne variable // with value of ith character countOfOne += (s.charAt(i) - '0'); // if value reaches more than // K, then update result if (countOfOne >= K) { // add frequency of indices, // having sum (current sum - K), // to the result res += freq[countOfOne - K]; } // update frequency of one's count freq[countOfOne]++; } return res; } // Driver code to test above methods static public void main (String[] args) { String s = "10010"; int K = 1; System.out.println( countOfSubstringWithKOnes(s, K)); } } // This code is contributed by vt_m.

## Python3

# Python 3 program to find count of # substring containing exactly K ones # method returns total number of # substring having K ones def countOfSubstringWithKOnes(s, K): N = len(s) res = 0 countOfOne = 0 freq = [0 for i in range(N + 1)] # initialize index having # zero sum as 1 freq[0] = 1 # loop over binary characters of string for i in range(0, N, 1): # update countOfOne variable with # value of ith character countOfOne += ord(s[i]) - ord('0') # if value reaches more than K, # then update result if (countOfOne >= K): # add frequency of indices, having # sum (current sum - K), to the result res += freq[countOfOne - K] # update frequency of one's count freq[countOfOne] += 1 return res # Driver code if __name__ == '__main__': s = "10010" K = 1 print(countOfSubstringWithKOnes(s, K)) # This code is contributed by # Surendra_Gangwar

## C#

// C# program to find count of substring // containing exactly K ones using System; public class GFG { // method returns total number of // substring having K ones static int countOfSubstringWithKOnes( string s, int K) { int N = s.Length; int res = 0; int countOfOne = 0; int []freq = new int[N+1]; // initialize index having zero // sum as 1 freq[0] = 1; // loop over binary characters // of string for (int i = 0; i < N; i++) { // update countOfOne variable // with value of ith character countOfOne += (s[i] - '0'); // if value reaches more than // K, then update result if (countOfOne >= K) { // add frequency of indices, // having sum (current sum - K), // to the result res += freq[countOfOne - K]; } // update frequency of one's count freq[countOfOne]++; } return res; } // Driver code to test above methods static public void Main () { string s = "10010"; int K = 1; Console.WriteLine( countOfSubstringWithKOnes(s, K)); } } // This code is contributed by vt_m.

## PHP

<?php // PHP program to find count // of substring containing // exactly K ones // method returns total number // of substring having K ones function countOfSubstringWithKOnes($s, $K) { $N = strlen($s); $res = 0; $countOfOne = 0; $freq = array(); for ($i = 0; $i <= $N; $i++) $freq[$i] = 0; // initialize index // having zero sum as 1 $freq[0] = 1; // loop over binary // characters of string for ($i = 0; $i < $N; $i++) { // update countOfOne // variable with value // of ith character $countOfOne += ($s[$i] - '0'); // if value reaches more // than K, then update result if ($countOfOne >= $K) { // add frequency of indices, // having sum (current sum - K), // to the result $res = $res + $freq[$countOfOne - $K]; } // update frequency // of one's count $freq[$countOfOne]++; } return $res; } // Driver code $s = "10010"; $K = 1; echo countOfSubstringWithKOnes($s, $K) ,"\n"; // This code is contributed by m_kit ?>

## Javascript

<script> // Javascript program to find count of // substring containing exactly K ones // Method returns total number of // substring having K ones function countOfSubstringWithKOnes(s, K) { let N = s.length; let res = 0; let countOfOne = 0; let freq = new Array(N + 1); freq.fill(0); // Initialize index having zero // sum as 1 freq[0] = 1; // Loop over binary characters // of string for(let i = 0; i < N; i++) { // Update countOfOne variable // with value of ith character countOfOne += (s[i] - '0'); // If value reaches more than // K, then update result if (countOfOne >= K) { // Add frequency of indices, // having sum (current sum - K), // to the result res += freq[countOfOne - K]; } // Update frequency of one's count freq[countOfOne]++; } return res; } // Driver code let s = "10010"; let K = 1; document.write(countOfSubstringWithKOnes(s, K)); // This code is contributed by suresh07 </script>

**Output:**

9

This article is contributed by **Utkarsh Trivedi**. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.