Maximise length of smallest group by dividing Binary String into K groups of same bit

Given a binary string S of length N. Distribute 0s and 1s of the string into K groups such that:

• Each group consists atleast a character.
• No group contains both 1 and 0.
• All 1s and 0s of the string are distributed among all the groups.

The task is to distribute all the characters in such a way that minimum number of characters in any group is maximized and print that number of characters (i.e. minimum number of characters in any group among the K groups).

Examples:

Input: S = “01011”, K=5
Output: 1
Explanation: the K groups would be – {0}, {0}, {1}, {1}, {1}

Input: S = “11110000000111111”, K=4
Output: 3

Approach: The problem can be easily solved by greedy technique. 

We will iteratively take each case into consideration i.e. 

• for each i, from 1 to K-1,
  • we will assign i groups to store all the zeroes and
  • K-i groups to store all the ones.
• At each iteration, we will keep taking maximum of the current answer.

The following approach can be followed to arrive at the answer:

• Calculate the number of 0s and 1s in the string.
• Initialize answer by 0.
• If K>N (where N is length of string), return 0, as in this case it is not possible to make K groups such that each of them contains atleast one character.
• Iterate from i=1 to i=K-1. At each iteration, assign i groups to store all the zeroes and K-i groups to store all the ones.
• Find number of zeroes in each of the i groups by dividing total number of 0s by the number of groups assigned to store the 0s (suppose some zeroes are left, as they may not be distributed equally to all the groups, then they can be put into any one group. It doesn’t matter, as we need the group with minimum characters). Similarly, find number of 1s in each group.
• Find minimum of both (i.e. 0s in a group and 1s in a group) and store in a variable, say min_count.
• Find maximum of all min_count in each iteration and return that.

Below is the code based on above approach:

C++

// C++ code for Divide the binary string
// into K groups  such that minimum number
// of characters in  any group is maximized

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

// Function to find the maximized minimum
// number of characters in a group,
// when given string is divided into
// K groups
int divideString(string S, int K)
{
    // calculating length of given string
    int N = S.length();

    int zero = 0, one = 0;

    // Calculating number of 0s and 1s
    // in given string
    for (int i = 0; i < N; i++) {
        if (S[i] == '0') {
            zero++;
        }
        else {
            one++;
        }
    }

    // initializing answer by 0
    int answer = 0;

    // if K>size of string, then it is not
    // possible to make K groups such that
    // each of them contains atleast 1 character
    if (K > N) {
        return 0;
    }

    for (int i = 1; i < K; i++) {
        // let there be i groups with
        // all elements 0
        int zero_groups = i;
        int one_groups = K - i;
        // so, there will be K-i groups with
        // all elements 1

        int count0 = zero / zero_groups;
        // number of 0s in
        // each zero_groups
        int count1 = one / one_groups;
        // number of 1s in
        // each one_groups

        int min_count = min(count0, count1);
        // since we have to find the
        // count of characters in group
        // with minimum characters

        answer = max(answer, min_count);
        // since we have to
        // maximize the answer
    }

    // returning answer
    return answer;
}

// Driver Code
int main()
{
    string S = "11110000000111111";
    int K = 4;
    int ans = divideString(S, K);
    cout << ans;
}

Java

// Java program of the above approach
import java.io.*;

class GFG {

  // Function to find the maximized minimum
  // number of characters in a group,
  // when given string is divided into
  // K groups
  static int divideString(String S, int K)
  {
    // calculating length of given string
    int N = S.length();

    int zero = 0, one = 0;

    // Calculating number of 0s and 1s
    // in given string
    for (int i = 0; i < N; i++) {
      if (S.charAt(i) == '0') {
        zero++;
      }
      else {
        one++;
      }
    }

    // initializing answer by 0
    int answer = 0;

    // if K>size of string, then it is not
    // possible to make K groups such that
    // each of them contains atleast 1 character
    if (K > N) {
      return 0;
    }

    for (int i = 1; i < K; i++) {
      // let there be i groups with
      // all elements 0
      int zero_groups = i;
      int one_groups = K - i;
      // so, there will be K-i groups with
      // all elements 1

      int count0 = zero / zero_groups;
      // number of 0s in
      // each zero_groups
      int count1 = one / one_groups;
      // number of 1s in
      // each one_groups

      int min_count = Math.min(count0, count1);
      // since we have to find the
      // count of characters in group
      // with minimum characters

      answer = Math.max(answer, min_count);
      // since we have to
      // maximize the answer
    }

    // returning answer
    return answer;
  }

  // Driver Code
  public static void main (String[] args) {
    String S = "11110000000111111";
    int K = 4;
    int ans = divideString(S, K);
    System.out.println(ans);
  }
}

// This code is contributed by hrithikgarg03188.

Python3

'''Python code for Divide the binary string
into K groups  such that minimum number
of characters in  any group is maximized
'''

# Function to find the maximized minimum
# number of characters in a group,
# when given string is divided into
# K groups
def divideString(S, K):

     # calculating length of given string
    N = len(S)
    zero, one = 0, 0

    # Calculating number of 0s and 1s in given string
    for i in range(0, N):
        if S[i] == '0':
            zero += 1
        else:
            one += 1

    # initializing answer by 0
    answer = 0

    # if K>size of string, then it is not
    # possible to make K groups such that
    # each of them contains atleast 1 character
    if K > N:
        return 0

    # let there be i groups with all elements 0
    for i in range(1, K):
        zero_groups = i
        one_groups = K - i

        # so, there will be K-i groups with all elements 1
        count0 = zero//zero_groups

        # number of 0s in each zero_groups
        count1 = one//one_groups

        # number of 1s in each one_groups
        min_count = min(count0, count1)

        # since we have to find the count of
        # characters in group with minimum characters
        answer = max(answer, min_count)

        # since we have to maximize the answer
    return answer
S = '11110000000111111'
K = 4
ans = divideString(S, K)
print(ans)

'''This code is contributed by Rajat Kumar (GLA University).'''

C#

// C# program of the above approach
using System;
using System.Collections.Generic;

public class GFG{

  // Function to find the maximized minimum
  // number of characters in a group,
  // when given string is divided into
  // K groups
  static int divideString(string S, int K)
  {
    // calculating length of given string
    int N = S.Length;

    int zero = 0, one = 0;

    // Calculating number of 0s and 1s
    // in given string
    for (int i = 0; i < N; i++) {
      if (S[i] == '0') {
        zero++;
      }
      else {
        one++;
      }
    }

    // initializing answer by 0
    int answer = 0;

    // if K>size of string, then it is not
    // possible to make K groups such that
    // each of them contains atleast 1 character
    if (K > N) {
      return 0;
    }

    for (int i = 1; i < K; i++) {
      // let there be i groups with
      // all elements 0
      int zero_groups = i;
      int one_groups = K - i;
      // so, there will be K-i groups with
      // all elements 1

      int count0 = zero / zero_groups;
      // number of 0s in
      // each zero_groups
      int count1 = one / one_groups;
      // number of 1s in
      // each one_groups

      int min_count = Math.Min(count0, count1);
      // since we have to find the
      // count of characters in group
      // with minimum characters

      answer = Math.Max(answer, min_count);
      // since we have to
      // maximize the answer
    }

    // returning answer
    return answer;
  }

  // Driver Code
  public static void Main(String[] args)
  {
    string S = "11110000000111111";
    int K = 4;
    int ans = divideString(S, K);
    Console.Write(ans);

  }
}

// This code is contributed by sanjoy_62.

Javascript

<script>
    // JavaScript code for Divide the binary string
    // into K groups such that minimum number
    // of characters in any group is maximized

    // Function to find the maximized minimum
    // number of characters in a group,
    // when given string is divided into
    // K groups
    const divideString = (S, K) => {
        // calculating length of given string
        let N = S.length;

        let zero = 0, one = 0;

        // Calculating number of 0s and 1s
        // in given string
        for (let i = 0; i < N; i++) {
            if (S[i] == '0') {
                zero++;
            }
            else {
                one++;
            }
        }

        // initializing answer by 0
        let answer = 0;

        // if K>size of string, then it is not
        // possible to make K groups such that
        // each of them contains atleast 1 character
        if (K > N) {
            return 0;
        }

        for (let i = 1; i < K; i++) {
            // let there be i groups with
            // all elements 0
            let zero_groups = i;
            let one_groups = K - i;
            // so, there will be K-i groups with
            // all elements 1

            let count0 = parseInt(zero / zero_groups);
            // number of 0s in
            // each zero_groups
            let count1 = parseInt(one / one_groups);
            // number of 1s in
            // each one_groups

            let min_count = Math.min(count0, count1);
            // since we have to find the
            // count of characters in group
            // with minimum characters

            answer = Math.max(answer, min_count);
            // since we have to
            // maximize the answer
        }

        // returning answer
        return answer;
    }

    // Driver Code

    let S = "11110000000111111";
    let K = 4;
    let ans = divideString(S, K);
    document.write(ans);

// This code is contributed by rakeshsahni

</script>

Output

3

Time Complexity: O(N)
Auxiliary Space: O(1)

Another Approach:

1. Count the number of ‘1’ and ‘0’ characters in the input string “S”.
2. Determine the maximum count among the ‘1’s and ‘0’s.
3. Calculate the minimum number of characters in any group by dividing the maximum count by “K” and rounding up to the nearest integer.
4. Return the minimum number of characters as the output.

Below is the implementation of the above approach:

C++

#include <iostream>
#include <vector>
#include <algorithm>

int distributeCharacters(std::string S, int K) {
    // Count the number of '1' and '0' characters in the string
    int count_1 = std::count(S.begin(), S.end(), '1');
    int count_0 = std::count(S.begin(), S.end(), '0');

    // Find the maximum count among '1' and '0' characters
    int max_characters = std::max(count_1, count_0);

    // Calculate the minimum number of characters in any group
    int min_characters = std::max(1, (max_characters + K - 1) / K);

    // Return the minimum number of characters
    return min_characters;
}

int main() {
    std::string S = "11110000000111111";
    int K = 4;

    // Call the distributeCharacters function and store the result
    int result = distributeCharacters(S, K);

    // Print the result
    std::cout << result << std::endl;

    return 0;
}

Output

3

Time Complexity: The time complexity is O(N).

Auxiliary Space: The space complexity is O(1).