Minimum number of alternate subsequences required to be removed to empty a Binary String

Last Updated : 22 Sep, 2021

Given a binary string S consisting of N characters, the task is to print the minimum number of operations required to remove all the characters from the given string S by removing a single character or removing any subsequence of alternate characters in each operation.

Examples:

Input: S = "010101"
Output: 1
Explanation:
Below are the operations performed:
Operation 1: Consider the subsequence S[0, 5] i.e., "010101" as it contains alternating characters. Therefore, removing this modifies the string to "".
Hence, the total number of operation required is 1.

Input: S = "00011"
Output: 3

Approach: The given problem can be solved by iterating over the string once and keep track of the maximum number of remaining 0s and 1s. Follow the steps below to solve the problem:

Initialize a variable, say ans to store the maximum number of 0s and 1s which are still left to be removed, a variable cnt0 to count the number of 0s, and a variable cnt1 to count the number of 1s.
Traverse the given string S from the beginning and perform the following steps:
- If the current character is 0, then increment the value of cnt0 by 1 and decrement the value of cnt1 by 1 if it is greater than 0.
- If the current character is 1, increment the value of cnt1 by 1 and decrement the value of cnt0 by 1 if it is greater than 0.
- Update the value of ans to the maximum of ans, cnt1, and cnt0.
After completing the above steps, print the value of ans as the minimum number of operations required to remove all the characters.

Below is the implementation of the approach:

C++

// C++ program for the above approach  #include <bits/stdc++.h> using namespace std;  // Function to find the minimum number // of operations to empty a binary string int minOpsToEmptyString(string s) {     // Stores the resultant number of     // operations     int ans = INT_MIN;      // Stores the number of 0s     int cn0 = 0;      // Stores the number of 1s     int cn1 = 0;      // Traverse the given string     for (int i = 0;          i < s.length(); i++) {          if (s[i] == '0') {              // To balance 0 with 1             // if possible             if (cn1 > 0)                 cn1--;              // Increment the value             // of cn0 by 1             cn0++;         }         else {              // To balance 1 with 0             // if possible             if (cn0 > 0)                 cn0--;              // Increment the value             // of cn1             cn1++;         }          // Update the maximum number         // of unused 0s and 1s         ans = max({ ans, cn0, cn1 });     }      // Print the resultant count     cout << ans; }  // Driver Code int main() {     string S = "010101";     minOpsToEmptyString(S);      return 0; }

Java

// Java program for the above approach import java.util.*;  class GFG{  // Function to find the minimum number // of operations to empty a binary string static void minOpsToEmptyString(String s) {          // Stores the resultant number of     // operations     int ans = Integer.MIN_VALUE;       // Stores the number of 0s     int cn0 = 0;       // Stores the number of 1s     int cn1 = 0;       // Traverse the given string     for(int i = 0; i < s.length(); i++)     {         if (s.charAt(i) == '0')         {                          // To balance 0 with 1             // if possible             if (cn1 > 0)                 cn1--;               // Increment the value             // of cn0 by 1             cn0++;         }         else          {                          // To balance 1 with 0             // if possible             if (cn0 > 0)                 cn0--;               // Increment the value             // of cn1             cn1++;         }           // Update the maximum number         // of unused 0s and 1s         ans = Math.max(ans, Math.max(cn0, cn1));     }       // Print the resultant count     System.out.print(ans); }   // Driver Code public static void main(String[] args) {     String S = "010101";     minOpsToEmptyString(S); } }  // This code is contributed by sanjoy_62

Python3

# Python3 program for the above approach  # Function to find the minimum number # of operations to empty a binary string def minOpsToEmptyString(s):        # Stores the resultant number of     # operations     ans = -10**9      # Stores the number of 0s     cn0 = 0      # Stores the number of 1s     cn1 = 0      # Traverse the given string     for i in range(len(s)):         if (s[i] == '0'):              # To balance 0 with 1             # if possible             if (cn1 > 0):                 cn1 -= 1              # Increment the value             # of cn0 by 1             cn0 += 1         else:              # To balance 1 with 0             # if possible             if (cn0 > 0):                 cn0 -= 1              # Increment the value             # of cn1             cn1 += 1          # Update the maximum number         # of unused 0s and 1s         ans = max([ans, cn0, cn1])      # Print resultant count     print (ans)  # Driver Code if __name__ == '__main__':     S = "010101"     minOpsToEmptyString(S)  # This code is contributed by mohit kumar 29.

// C# program for the above approach using System; using System.Collections.Generic;  class GFG{  // Function to find the minimum number // of operations to empty a binary string static void minOpsToEmptyString(string s) {          // Stores the resultant number of     // operations     int ans = 0;       // Stores the number of 0s     int cn0 = 0;       // Stores the number of 1s     int cn1 = 0;       // Traverse the given string     for(int i = 0; i < s.Length; i++)     {         if (s[i] == '0')         {                          // To balance 0 with 1             // if possible             if (cn1 > 0)                 cn1--;               // Increment the value             // of cn0 by 1             cn0++;         }         else          {                          // To balance 1 with 0             // if possible             if (cn0 > 0)                 cn0--;               // Increment the value             // of cn1             cn1++;         }           // Update the maximum number         // of unused 0s and 1s         ans = Math.Max(ans, Math.Max(cn0, cn1));     }       // Print the resultant count     Console.Write(ans); }  // Driver Code public static void Main() {     string S = "010101";     minOpsToEmptyString(S); } }  // This code is contributed by avijitmondal1998.

JavaScript

<script> // JavaScript program for the above approach // Function to find the minimum number // of operations to empty a binary string function minOpsToEmptyString(s) {          // Stores the resultant number of     // operations     var ans = Number.MIN_VALUE;       // Stores the number of 0s     var cn0 = 0;       // Stores the number of 1s     var cn1 = 0;       // Traverse the given string     for(var i = 0; i < s.length; i++)     {         if (s.charAt(i) == '0')         {                          // To balance 0 with 1             // if possible             if (cn1 > 0)                 cn1--;               // Increment the value             // of cn0 by 1             cn0++;         }         else          {                          // To balance 1 with 0             // if possible             if (cn0 > 0)                 cn0--;               // Increment the value             // of cn1             cn1++;         }           // Update the maximum number         // of unused 0s and 1s         ans = Math.max(ans, Math.max(cn0, cn1));     }       // Print the resultant count     document.write(ans); }   // Driver Code var S = "010101"; minOpsToEmptyString(S);   //This code is contributed by shivanisinghss2110   </script>

Output:

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

Smallest string which not a subsequence of the given string

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Minimum number of alternate subsequences required to be removed to empty a Binary String

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