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Minimize cost to make all characters of a Binary String equal to ‘1’ by reversing or flipping characters of substrings

  • Difficulty Level : Expert
  • Last Updated : 22 Jun, 2021

Given a binary string S, and two integers A, which denotes the cost of reversing a substring, and B, which denotes the cost of flipping all characters of a substring, the task is to find the minimum cost to reduce the string S to 1s only.

Examples:

Input: S = “01100”, A = 1, B = 5
Output: 6
Explanation: 
One possible way to make all characters equal to ‘1’ is as follows:

  1. Reverse the substring {S[0], S[2]}. Cost = A (= 1), The string modifies to “11000”.
  2. Flip the characters of substring {S[2], S[4]}. Cost of B (= 5). The string modifies to “11111”.

Therefore, the total cost = 5+1 = 6 (which is the minimum cost possible)

Input: S = “1111111”, A = 2, B = 3
Output: 0



Approach: The given problem can be solved based on the following observations: 

  • Assuming there are P disjoint groups of continuous ‘0’s,
  • If A is less than B, then it is optimal to convert P groups into ‘1’ group of continuous ‘0’s by performing the first type of operation for a cost of (P – 1) * A and then converting all the ‘0’s to ‘1’s for a cost of B.
  • Otherwise, it is optimal to perform the second operation on each group separately, for a cost of B * P.

Follow the steps below to solve the problem:

  • Initialize a variable say P with 0 value to store the count of disjoint groups of continuous 0s.
  • Also, initialize a variable say count as 0 to store the temporary count of the number of 0s in a group.
  • Iterate over the character of the string S and do the following:
    • If the current character is ‘0‘ then increment the count by 1.
    • Otherwise, if the count is greater than 0 then increment P by 1 and then assign 0 to count.
  • If the count is greater than 0 then increment P by 1.
  • Print the minimum cost obtained as (P-1)*A+B.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate minimum cost to
// convert all the characters of S to '1'
void MinimumCost(string S, int A, int B)
{
    // Stores the result
    int count = 0;
 
    // Stores the number of groups
    // that have 0 as characters
    int group = 0;
 
    // Traverse the string S
    for (int i = 0; i < S.size(); i++) {
 
        // If current character is '0'
        if (S[i] == '0') {
            count += 1;
        }
        else {
            // If count is greater
            // than 0
            if (count > 0) {
                group += 1;
            }
 
            // Set the count to 0
            count = 0;
        }
    }
 
    // If the last few consecutive
    // characters are '0'
    if (count > 0)
        group += 1;
 
    // If string contains
    // all characters as '1'
    if (group == 0) {
        cout << 0 << endl;
    }
    else {
        // Minimum Cost
        cout << min(A, B) * (group - 1) + B;
    }
}
 
// Driver Code
int main()
{
 
    // Given Input
    int A = 1;
    int B = 5;
    string S = "01100";
 
    // Function Call
    MinimumCost(S, A, B);
    return 0;
}

Java




// Java program for the above approach
class GFG{
 
// Function to calculate minimum cost to
// convert all the characters of S to '1'
static void MinimumCost(String S, int A, int B)
{
     
    // Stores the result
    int count = 0;
 
    // Stores the number of groups
    // that have 0 as characters
    int group = 0;
 
    // Traverse the string S
    for(int i = 0; i < S.length(); i++)
    {
         
        // If current character is '0'
        if (S.charAt(i) == '0')
        {
            count += 1;
        }
        else
        {
             
            // If count is greater
            // than 0
            if (count > 0)
            {
                group += 1;
            }
             
            // Set the count to 0
            count = 0;
        }
    }
 
    // If the last few consecutive
    // characters are '0'
    if (count > 0)
        group += 1;
 
    // If string contains
    // all characters as '1'
    if (group == 0)
    {
        System.out.println(0);
    }
    else
    {
         
        // Minimum Cost
        System.out.print(Math.min(A, B) *
                        (group - 1) + B);
    }
}
 
// Driver Code
public static void main(String args[])
{
     
    // Given Input
    int A = 1;
    int B = 5;
    String S = "01100";
     
    // Function Call
    MinimumCost(S, A, B);
}
}
 
// This code is contributed by SoumikMondal

Python3




# Python3 program for the above approach
 
# Function to calculate minimum cost to
# convert all the characters of S to '1'
def MinimumCost(S, A, B):
    # Stores the result
    count = 0
 
    # Stores the number of groups
    # that have 0 as characters
    group = 0
 
    # Traverse the S
    for i in range(len(S)):
        # If current character is '0'
        if (S[i] == '0'):
            count += 1
        else:
            # If count is greater
            # than 0
            if (count > 0):
                group += 1
            # Set the count to 0
            count = 0
 
    # If the last few consecutive
    # characters are '0'
    if (count > 0):
        group += 1
 
    # If contains
    # all characters as '1'
    if (group == 0):
        print(0)
    else:
        # Minimum Cost
        print(min(A, B) * (group - 1) + B)
 
# Driver Code
if __name__ == '__main__':
 
    # Given Input
    A = 1
    B = 5
    S = "01100"
 
    # Function Call
    MinimumCost(S, A, B)
 
     # This code is contributed by mohit kumar 29.

C#




// C# program for the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Function to calculate minimum cost to
// convert all the characters of S to '1'
static void MinimumCost(string S, int A, int B)
{
     
    // Stores the result
    int count = 0;
 
    // Stores the number of groups
    // that have 0 as characters
    int group = 0;
 
    // Traverse the string S
    for(int i = 0; i < S.Length; i++)
    {
         
        // If current character is '0'
        if (S[i] == '0')
        {
            count += 1;
        }
        else
        {
             
            // If count is greater
            // than 0
            if (count > 0)
            {
                group += 1;
            }
 
            // Set the count to 0
            count = 0;
        }
    }
 
    // If the last few consecutive
    // characters are '0'
    if (count > 0)
        group += 1;
 
    // If string contains
    // all characters as '1'
    if (group == 0)
    {
        Console.WriteLine(0);
    }
    else
    {
         
        // Minimum Cost
        Console.Write(Math.Min(A, B) *
                      (group - 1) + B);
    }
}
 
// Driver Code
public static void Main()
{
     
    // Given Input
    int A = 1;
    int B = 5;
    string S = "01100";
 
    // Function Call
    MinimumCost(S, A, B);
}
}
 
// This code is contributed by SURENDRA_GANGWAR

Javascript




<script>
// Javascript program for the above approach
 
// Function to calculate minimum cost to
// convert all the characters of S to '1'
function MinimumCost(S, A, B) {
    // Stores the result
    let count = 0;
 
    // Stores the number of groups
    // that have 0 as characters
    let group = 0;
 
    // Traverse the string S
    for (let i = 0; i < S.length; i++) {
 
        // If current character is '0'
        if (S[i] == '0') {
            count += 1;
        }
        else
        {
         
            // If count is greater
            // than 0
            if (count > 0) {
                group += 1;
            }
 
            // Set the count to 0
            count = 0;
        }
    }
 
    // If the last few consecutive
    // characters are '0'
    if (count > 0)
        group += 1;
 
    // If string contains
    // all characters as '1'
    if (group == 0) {
        document.write(0 + "<br>");
    }
    else {
        // Minimum Cost
        document.write(Math.min(A, B) * (group - 1) + B);
    }
}
 
// Driver Code
 
// Given Input
let A = 1;
let B = 5;
let S = "01100";
 
// Function Call
MinimumCost(S, A, B);
 
// This code is contributed by gfgking.
</script>
Output: 
6

 

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

 

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