Maximize the number of minority characters that can be removed from a given binary string substring, implemented 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

An algorithm that maximizes the removal of a small number of characters in a given binary string substring can be described by the following steps:

• First, let's start by initializing a variable called deletions to zero. The main purpose of this variable is to monitor the count of delete operations that occur.

• Determine how often the digits '0' and '1' occur in a specific substring of a binary string. Each occurrence of these numbers can be calculated separately.

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

• Removes all characters with a small number of occurrences from the substring and updates the deletion count accordingly.

• Return the deleted final value as the result

Method 1: Traversal 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.

The Chinese translation of

Example

is:

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 method 1, we utilize linear traversal to maximize the number of minority characters removed from a given binary string substring. By iterating over the specified substring, we can determine the number of occurrences of '0' and '1' for each instance within that section. After identifying the less frequent characters within that region or group (i.e. finding the "minority"), we can calculate the number of possible deletions by subtracting their respective counts from the counts of all characters within that specified region.

This leads to an efficient method that reveals a simple but practical solution - requiring only a single pass over our initial string - which makes this method particularly suitable for shorter input strings.

Method 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

The Chinese translation of

Example

is:

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

Method 2 involves utilizing sliding window techniques to maximize deletion of a small number of characters. Using a fixed size window, we iterate over the substring, updating the count of '0's and '1's as the window moves. By adjusting the window bounds based on the count, we identify a small number of characters and calculate the maximum number of possible deletions. This approach reduces the number of redundant calculations by efficiently sliding the window, making it more suitable for larger inputs and providing faster solutions.

in conclusion

In this article, we explore the problem of how to maximize the removal of a small number of characters from a given binary string substring. We discussed two approaches - linear traversal and sliding window technique. Both methods provide efficient solutions to achieve the desired results. By understanding the algorithms and studying the executable code examples provided, you can apply these concepts to solve similar problems in your own projects. Remember to analyze the problem, choose the most appropriate approach, and implement it accordingly.

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