Minimum number of flips to make a Binary String increasing

Given a binary string S, the task is to find the minimum number of characters the needed to be flipped to make the given binary string increasing.

Example:

Input: S = "00110"
Output: 1
Explanation: Flip S[4] = '0' to '1' of the string modifies the given string to "00111". Therefore, the minimum number of flips required is 1.

Input: S = "010110"
Output: 2

Approach: The given problem can be solved by using a Greedy Algorithm based on the observations that the resultant monotonically increasing string after any number of flips will be of the form ('0'*p + '1'*q), where p and q are the count of 0s and 1s respectively in the modified string. The idea is to traverse the given string S and for each index, i modify the substring S[0, i) to 0s and substring S[i, N) to 1s and find the minimum flips required accordingly. Follow the steps below to solve the problem:

• Find the count of 0s in the given binary string S and store it in a variable countZero.
• Initialize variable, say minFlips as (N - cntZero) that stores the minimum number of flips required.
• Initialize variable, say cntOne as 0 that stores the count of 1s in the string while traversing the string.
• Traverse the given string S and perform the following steps:
  • If the character S[i] is 0, then decrement the value of countZero by 1.
  • Otherwise, update the value of minFlips as the minimum of minFlips and (countZero + countOne) and increment the value of countOne by 1.
• After completing the above steps, print the value of minFlips as the result.

Below is the implementation of the above approach.

// C++ program for the above approach;

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

// Function to find the minimum number of
// flips required to make string increasing
int minimumFlips(string s)
{

  // Length of s
  int n = s.size();

  // Total number of zero in s
  int cnt0 = count(s.begin(), s.end(), '0');

  // Stores count of 1s till ith index
  int cnt1 = 0;

  // stores the minimum count of flip
  int res = n - cnt0;

  // Traverse the given string
  for (int i = 0; i < n; i++) {
    if (s[i] == '0') {
      cnt0 -= 1;
    }

    // Update the value of res
    // and count of 1s
    else if (s[i] == '1') {
      res = min(res, cnt1 + cnt0);
      cnt1++;
    }
  }

  // Return the minimum number
  // of flips
  return res;
}

// Driver code 
int main()
{

  // Given string
  string S = "000110";

  // function call
  cout << minimumFlips(S);
  return 0;
}

// This code is contributed by parthmanchanda81

// Java program for the above approach;
import java.util.*;

class GFG
{

    // Function to find the minimum number of
    // flips required to make String increasing
    static int minimumFlips(String s) {

        // Length of s
        int n = s.length();

        // Total number of zero in s
        int cnt0 = count(s, '0');

        // Stores count of 1s till ith index
        int cnt1 = 0;

        // stores the minimum count of flip
        int res = n - cnt0;

        // Traverse the given String
        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == '0') {
                cnt0 -= 1;
            }

            // Update the value of res
            // and count of 1s
            else if (s.charAt(i) == '1') {
                res = Math.min(res, cnt1 + cnt0);
                cnt1++;
            }
        }

        // Return the minimum number
        // of flips
        return res;
    }

    private static int count(String s, char c) {
        int ans = 0;
        for (char i : s.toCharArray())
            if (c == i)
                ans++;
        return ans;
    }

    // Driver code
    public static void main(String[] args) {

        // Given String
        String S = "000110";

        // function call
        System.out.print(minimumFlips(S));
    }
}

// This code is contributed by Princi Singh

# Python program for the above approach

# Function to find the minimum number of
# flips required to make string increasing
def minimumFlips(s):

    # Length of s
    n = len(s)

    # Total number of zero in s
    cnt0 = s.count('0')

    # Stores count of 1s till ith index
    cnt1 = 0

    # Stores the minimum count of flips
    res = n - cnt0

    # Traverse the given string S
    for i in range(n):

        if s[i] == '0':
            cnt0 -= 1

        elif s[i] == '1':

            # Update the value of res
            # and count of 1s
            res = min(res, cnt1 + cnt0)
            cnt1 += 1

    # Return the minimum number
    # of flips
    return res


# Driver Code
S = '000110'

# Function Call
print(minimumFlips(S))

using System;

public class GFG {
    // Function to find the minimum number of
    // flips required to make String increasing
    static int minimumFlips(String s)
    {

        // Length of s
        int n = s.Length;

        // Total number of zero in s
        int cnt0 = count(s, '0');

        // Stores count of 1s till ith index
        int cnt1 = 0;

        // stores the minimum count of flip
        int res = n - cnt0;

        // Traverse the given String
        for (int i = 0; i < n; i++) {
            if (s[i] == '0') {
                cnt0 -= 1;
            }

            // Update the value of res
            // and count of 1s
            else if (s[i] == '1') {
                res = Math.Min(res, cnt1 + cnt0);
                cnt1++;
            }
        }

        // Return the minimum number
        // of flips
        return res;
    }

    private static int count(String s, char c)
    {
        int ans = 0;
        for (int j = 0; j < s.Length; j++) {
            char i = s[j];
            if (c == i)
                ans++;
        }
        return ans;
    }

    // Driver code
    static public void Main()
    {
        // Given String
        String S = "000110";

        // function call
        Console.Write(minimumFlips(S));
    }
}

// This code is contributed by maddler.

<script>

        // JavaScript program for the above approach;

        // Function to find the minimum number of
        // flips required to make string increasing
        function minimumFlips(s) {

            // Length of s
            let n = s.length;

            // Total number of zero in s
            let i;
            let cnt0 = 0;
            for (i = 0; i < n; i++) {
                if (s[i] == '0')
                    cnt0++;

            }

            // Stores count of 1s till ith index
            let cnt1 = 0

            // Stores the minimum count of flips
            let res = n - cnt0

            // Traverse the given string S
            for (i = 0; i < n; i++)
                if (s[i] == '0') {
                    cnt0 -= 1
                }

                else if (s[i] == '1') {

                    // Update the value of res
                    // and count of 1s
                    res = Math.min(res, cnt1 + cnt0)
                    cnt1 += 1
                }

            // Return the minimum number
            // of flips
            return res
        }

        // Driver Code
        S = '000110'

        // Function Call
        document.write(minimumFlips(S))

// This code is contributed by Potta Lokesh
    </script>

1

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