What is the minimum number of exchanges required so that a given substring contains exactly K 1's?

Finding the minimum number of swaps required for a substring to contain exactly K ones is a common problem in computer science and programming. In this article, we will delve into this problem and provide a C solution for it. This question has applications in various fields, including string manipulation, data structure optimization, and coding challenges in interviews.

Problem Statement

Given a binary string and a number K, the task is to find the minimum number of swaps required to ensure that each substring of the string has exactly K 1's.

method

To solve this problem, we can use the two-pointer method and sliding window technology. The basic idea is to maintain a window of size K and calculate the number of exchanges required for all 1s in the window.

Example

This is a C function that implements the above method -

#include<bits/stdc++.h>
using namespace std;

int minSwaps(string s, int K) {
   int n = s.length();
   vector<int> onesPrefix(n, 0);
   if(s[0] == '1') onesPrefix[0] = 1;
   
   for(int i = 1; i < n; i++) {
      onesPrefix[i] = onesPrefix[i-1];
      if(s[i] == '1') onesPrefix[i]++;
   }
   
   int ans = INT_MAX;
   for(int i = 0; i <= n - K; i++) {
      int j = i + K - 1;
      int ones = onesPrefix[j] - ((i == 0) ? 0 : onesPrefix[i - 1]);
      ans = min(ans, K - ones);
   }
   
   return ans;
}

int main() {
   string s = "10010110";
   int K = 3;
   cout << "Minimum number of swaps = " << minSwaps(s, K) << endl;
   return 0;
}

Output

Minimum number of swaps = 1

Test case description

Assume the string is "10010110", K = 3.

In the initial binary string "10010110", we want each substring of size 3 to have exactly 3 1's. For example, the substring "100" requires 2 exchanges to become "111". Similarly, the substring "001" also requires 2 exchanges. By iterating over the string, we find that the minimum number of swaps required for the substring "101" is 1.

in conclusion

This question is a great example of how to combine algorithms, data structures, and an understanding of the C language to solve complex problems. Understanding and implementing such questions can be very beneficial for software engineers, especially in coding interviews and competitive programming.

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