Minimize cost of flipping or swaps to make a Binary String balanced

Given a binary string S of size N(where N is even), the task is to find the minimum cost of making the given binary string balanced by flipping one of the adjacent different characters at the cost of 1 unit or swap the characters at indices i and j such that (i < j) at the cost of (j – i) unit. If it is impossible to make the string balanced, the print “-1”.

A binary string is balanced if it can be reduced to an empty string by deleting two consecutive alternating characters at once and then concatenating the remaining characters.

Examples:

Input: S = “110110”
Output: 1
Explanation: Following operations are performed:
Operation 1: As the adjacent characters at indices 0 and 1 are different, flipping S[0] modifies S to “010110”. Cost = 1.

After completing the above operations, the given string becomes balanced, as it can be reduced to an empty string by deleting two consecutive alternating characters.
Therefore, the total cost is 1.

Input: S = “11100”
Output: -1

Approach: The given problem can be solved based on the observations that the flipping of the adjacent different characters is more optimal than using the swapping of characters and the position of 0s and 1s in the string does not matter. Follow the steps below to solve the problem:

• If all the characters are equal, then it is impossible to make the string balanced. Therefore, print “-1”.
• Store the count of 1s and 0s in variables, say count1 and count0 respectively.
• Store the absolute difference of count1 and count0 in a variable K.
• Now, flip the K/2 characters to make the string balanced and print the value of K/2 as the result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the minimum cost
// to convert the given string into
// balanced string
void findMinimumCost(string s, int N)
{

    // Stores count of 1's and 0's in
    // the string
    int count_1 = 0, count_0 = 0;

    // Traverse the string
    for (int i = 0; i < N; i++) {
        if (s[i] == '1')

            // Increment count1
            count_1++;
        else

            // Increment count 0
            count_0++;
    }

    // Stores absolute difference of
    // counts of 0's and 1's
    int k = abs(count_0 - count_1);

    // If string consists of only
    // 0's and 1's
    if (count_1 == N || count_0 == N)
        cout << -1 << endl;

    // Print minimum cost
    else
        cout << k / 2 << endl;
}

// Driver Code
int main()
{
    string S = "110110";
    int N = S.length();
    findMinimumCost(S, N);

    return 0;
}

Java

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

class GFG{

// Function to find the minimum cost
// to convert the given string into
// balanced string
static void findMinimumCost(String s, int N)
{

    // Stores count of 1's and 0's in
    // the string
    int count_1 = 0, count_0 = 0;

    // Traverse the string
    for (int i = 0; i < N; i++) {
        if (s.charAt(i) == '1')

            // Increment count1
            count_1++;
        else

            // Increment count 0
            count_0++;
    }

    // Stores absolute difference of
    // counts of 0's and 1's
    int k = Math.abs(count_0 - count_1);

    // If string consists of only
    // 0's and 1's
    if (count_1 == N || count_0 == N)
        System.out.println( -1);

    // Print minimum cost
    else
        System.out.println( k / 2);
}

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

    String S = "110110";
    int N = S.length();
    findMinimumCost(S, N);
}
}
// This code is contributed by code_hunt.

Python3

# Python3 program for the above approach

# Function to find the minimum cost
# to convert the given into
# balanced string
def findMinimumCost(s, N):

    # Stores count of 1's and 0's in
    # the string
    count_1, count_0 = 0, 0

    # Traverse the string
    for i in range(N):
        if (s[i] == '1'):

            # Increment count1
            count_1 += 1
        else:

            # Increment count 0
            count_0 += 1

    # Stores absolute difference of
    # counts of 0's and 1's
    k = abs(count_0 - count_1)

    # If consists of only
    # 0's and 1's
    if (count_1 == N or count_0 == N):
        print(-1)

    # Print the minimum cost
    else:
        print(k // 2)

# Driver Code
if __name__ == '__main__':

    S = "110110"
    N = len(S)

    findMinimumCost(S, N)

# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;

class GFG{

// Function to find the minimum cost
// to convert the given string into
// balanced string
static void findMinimumCost(String s, int N)
{

    // Stores count of 1's and 0's in
    // the string
    int count_1 = 0, count_0 = 0;

    // Traverse the string
    for(int i = 0; i < N; i++)
    {
        if (s[i] == '1')

            // Increment count1
            count_1++;
        else

            // Increment count 0
            count_0++;
    }

    // Stores absolute difference of
    // counts of 0's and 1's
    int k = Math.Abs(count_0 - count_1);

    // If string consists of only
    // 0's and 1's
    if (count_1 == N || count_0 == N)
        Console.WriteLine(-1);

    // Print minimum cost
    else
        Console.WriteLine(k / 2);
}

// Driver Code
static public void Main()
{
    String S = "110110";
    int N = S.Length;

    findMinimumCost(S, N);
}
}

// This code is contributed by Dharanendra L V.

Javascript

<script>

// JavaScript program for the above approach

// Function to find the minimum cost
// to convert the given string into
// balanced string
function findMinimumCost(s, N)
{

    // Stores count of 1's and 0's in
    // the string
    let count_1 = 0, count_0 = 0;

    // Traverse the string
    for (let i = 0; i < N; i++) {
        if (s[i] == '1')

            // Increment count1
            count_1++;
        else

            // Increment count 0
            count_0++;
    }

    // Stores absolute difference of
    // counts of 0's and 1's
    let k = Math.abs(count_0 - count_1);

    // If string consists of only
    // 0's and 1's
    if (count_1 == N || count_0 == N)
        document.write( -1);

    // Print minimum cost
    else
        document.write( k / 2);
}

// Driver Code

    let S = "110110";
    let N = S.length;
    findMinimumCost(S, N);

</script>

Output:

1

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