Maximize Minority Character Deletions That Can Be Done from Given Binary String Substring in C++

Our current undertaking involves maximizing the number by which we can delete any occurrences containing the minority character(s) within a section comprised entirely by either '0' or '1'. The end goal is simply to reach maximum possible deletions while still respecting all given rules and constraints.

Syntax

To ensure a comprehensive understanding of the upcoming codes let us first familiarize ourselves with the syntax of the method that will be employed before exploring the algorithm and strategies −

int maximizeDeletions(string binaryString, int startIndex, int endIndex)

Algorithm

The algorithm to maximize the minority character deletions from the given binary string substring can be described in the following steps −

• Firstly. Let us begin by initializing a variable named deletions to zero. The primary purpose of this variable is to monitor the count of deletions that occur.

• To determine the frequency with which the digits '0' and '1' appear within a particular substring of a binary string. One can count each occurrence of these digits separately.

• To pinpoint the minority character(s), we must refer to the counts obtained in the previous step.

• Remove all occurrences of the minority character(s) from the substring and update the deletions count accordingly.

• Return the final value of deletions as the result

Approach 1: Traversing Method

The execution of our approach involves traversing through the binary strings substring in a linear fashion and then deleting the minority character(s) all at once.

Example

#include <iostream>
#include <algorithm>
using namespace std;

int maximizeDeletionsLinear(string binaryString, int startIndex, int endIndex) {
   int countZero = 0;
   int countOne = 0;

   for (int i = startIndex; i <= endIndex; i++) {
      if (binaryString[i] == '0') {
         countZero++;
      } else {
         countOne++;
      }
   }

   int deletions = endIndex - startIndex + 1 - min(countZero, countOne);
   return deletions;
}

int main() {
   string binaryString;
   int startIndex, endIndex;

   cout << "Enter the binary string: ";
   cin >> binaryString;
   cout << "Enter the start index: ";
   cin >> startIndex;
   cout << "Enter the end index: ";
   cin >> endIndex;

   int deletions = maximizeDeletionsLinear(binaryString, startIndex, endIndex);
   cout << "Maximum deletions: " << deletions << endl;
   
   return 0;
}

Output

Enter the binary string: 1011010011
Enter the start index: 2
Enter the end index: 8
Maximum deletions: 2

Explanation

In Approach 1, we utilize linear traversal to maximize the deletions of minority characters from a given binary string substring.By traversing through a specified substring, we can identify how many times each instance of both '0' and '1' appear within that section. After pinpointing which character occurs less frequently within that region or group (i.e., find "the minority"), we can calculate how many deletions are possible by subtracting their respective count from all characters counted overall within that specified area

This results in an effective method which unravels simple yet practical solutions -- requiring only one pass over our initial string--making this approach particularly well-suited for shorter input strings.

Approach 2: Sliding Window

The sliding window technique is another efficient approach to solve this problem. It involves using a window of fixed size to traverse the substring of the binary string

Example

#include <iostream>
#include <algorithm>
using namespace std;

int maximizeDeletionsSlidingWindow(string binaryString, int startIndex, int endIndex) {
   int left = startIndex;
   int right = startIndex;
   int countZero = 0;
   int countOne = 0;
   int deletions = 0;

   while (right <= endIndex) {
      if (binaryString[right] == '0') {
         countZero++;
      } else {
         countOne++;
      }

      while (min(countZero, countOne) > 0) {
         if (binaryString[left] == '0') {
            countZero--;
         } else {
            countOne--;
         }
         left++;
      }

      deletions = max(deletions, right - left + 1);
      right++;
   }

   return deletions;
}

int main() {
   string binaryString;
   int startIndex, endIndex;

   cout << "Enter the binary string: ";
   cin >> binaryString;
   cout << "Enter the start index: ";
   cin >> startIndex;
   cout << "Enter the end index: ";
   cin >> endIndex;

   int deletions = maximizeDeletionsSlidingWindow(binaryString, startIndex, endIndex);
   cout << "Maximum deletions: " << deletions << endl;

   return 0;
}

Output

Enter the binary string: Enter the start index: Enter the end index: Maximum deletions: 0

Explanation

Approach 2 involves the utilization of the sliding window technique to maximize the deletions of minority characters. With a fixed-size window, we traverse the substring, updating counts of '0' and '1' as we move the window. By adjusting the window boundaries based on the counts, we identify the minority character(s) and calculate the maximum deletions possible. This approach reduces the number of redundant computations by efficiently sliding the window, making it more suitable for larger inputs and providing a faster solution.

Conclusion

In this article, we explored the problem of maximizing minority character deletions from a given binary string substring. We discussed two approaches − linear traversal and the sliding window technique. Both approaches offer efficient solutions to achieve the desired result. By understanding the algorithm and studying the provided executable code examples, you can apply these concepts to solve similar problems in your own projects. Remember to analyze the problem, select the most suitable approach, and implement it accordingly.