Convert A Binary String To Another String By Flipping Prefixes A Minimum Number Of Times In C++ Tp

In this tutorial, we will explore the process of transforming a binary string into a different string by minimizing the number of flips required for the prefixes in C++.

Problem Statement:

X and Y are two unique binary sequences provided to us. These sequences are of equal length and designated as Num. The objective is to transform the first sequence into the second one by inverting its prefixes. The process involves counting the overall instances of flipping prefixes, where flipping denotes changing '0' to '1'.

Example:

Input:

X = "101"

Y = "011"

Output:

Explanation:

Step 1:

• ✅ Choose the initial segment of size 1 from the given string X = ("101").
• ✅ By changing the segment with a value of "1" to "0", the string transforms into "001".
• ✅ Choose the initial 2 characters from the transformed string, which is the fresh string ("001").
• ✅ Switching the starting "0" to "1" will change the string to "011".

Therefore, the total amount of steps needed to transform the string is 2.

Approach:

• ✅ Observation: Flipping every letter in the prefix (from the beginning to that bit) will ensure the change when we need to alter a specific bit in the string. It is not required to flip the string in its whole many times because doing so will return it to its initial state.
• ✅ Method: We traverse through the strings from the end to the start. We compare the characters in the two strings at each place. If they differ, we revise our response to reflect the requirement to flip the prefix from the beginning to this place. In order to indicate whether the prefix is flipped or not, we utilize a variable rather than directly flipping the text. Once flipped, the characters are altered. It returns to its original form after being flipped twice.
• ✅ Execution: We go through the strings backwards, which verifies characters because we go from the end to the beginning. The "flipped" variable is toggled and the response is updated if the characters are different. The final result, which is the least number of prefix flips required to change one string into another, is returned.
• ✅ Optimization: Compared to brute force methods, this approach is more efficient because it avoids the needless flipping of full strings numerous times. It makes sure that every bit is only flipped once when needed, which reduces the amount of operations needed.
• ✅ Flipping every letter in the prefix (from the beginning to that bit) will ensure the change when we need to alter a specific bit in the string.
• ✅ It is not required to flip the string in its whole many times because doing so will return it to its initial state.
• ✅ We traverse through the strings from the end to the start.
• ✅ We compare the characters in the two strings at each place.
• ✅ If they differ, we revise our response to reflect the requirement to flip the prefix from the beginning to this place.
• ✅ In order to indicate whether the prefix is flipped or not, we utilize a variable rather than directly flipping the text. Once flipped, the characters are altered. It returns to its original form after being flipped twice.
• ✅ We go through the strings backwards, which verifies characters because we go from the end to the beginning.
• ✅ The "flipped" variable is toggled and the response is updated if the characters are different.
• ✅ The final result, which is the least number of prefix flips required to change one string into another, is returned.
• ✅ Compared to brute force methods, this approach is more efficient because it avoids the needless flipping of full strings numerous times.
• ✅ It makes sure that every bit is only flipped once when needed, which reduces the amount of operations needed.

Example:

Let's consider a C++ program that converts one binary string to another by minimally flipping prefixes.

#include <iostream>
#include <string>
using namespace std;
// Function to count the minimum number of flips needed to convert
// one binary string to another by flipping prefixes
int minFlips(string s1, string s2) {
    int num = s1.length();
    int flips = 0;
    
for (int i = 0; i < num; i++) 
{ 
if (s1[i] != s2[i]) 
{ 
flips++; 
while (i < num && s1[i] != s2[i]) 
{ 
i++;      
      }
        }
    }
    return flips;
}
// Function to convert binary string to another by flipping prefixes
string convertBinaryString(string s1, string s2) {
    int num = s1.length();
    string result = "";
    // Iterate through the strings and flip prefixes as needed
    for (int i = 0; i < num; i++)
{
 if (s1[i] != s2[i]) { result += '1'; 
// Flip the prefix 
while (i < num && s1[i] != s2[i])
 {                
i++;
            }
        } else {
            result += '0';
        }
    }
    return result;
}
int main() {
    string s1, s2;
    cout << "Enter the first binary string: ";
    cin >> s1;
    cout << "Enter the second binary string: ";
    cin >> s2;   
    int minFlipsNeed= minFlips(s1, s2);
    cout << "Min number of flips needed to convert string to another is: " << minFlipsNeed << endl;
    string convertedString = convertBinaryString(s1, s2);
    cout << "Converted binary string: " << convertedString << endl;
    return 0;
}

Output:

Complexity Analysis:

Time Complexity:

The time complexity of the aforementioned code for transforming a binary string into another by flipping prefixes as few times as possible is O(n).

Space Complexity:

The space efficiency of the aforementioned program for transforming a binary string into another by minimizing the flips of prefixes is O(n).

Conclusion:

In summary, we can deduce that we have developed a program that minimally flips prefixes to transform one Binary String into another. The approach involves iterating through the string from the end to the beginning and flipping the prefix whenever a mismatched character is encountered.