将给定的二进制字符串转换为另一个所需的最小子字符串翻转次数

给定两个二进制字符串A和B ，任务是找到从 A 的第一个字符开始的子字符串需要翻转的最小次数，即将1 s 转换为0 s 和0 s 到1 s，以将A转换为乙。

例子：

Input: A = “0010”, B = “1011”
Output; 3
Explanation:
Step 1: Flip the entire string A. Therefore, A becomes “1101” .
Step 2: Flip the substring {A[0], A[2]}. Therefore, A becomes “0011” .
Step 3: Flip A[0]. Therefore, A becomes “1011” which is equal to B.
Therefore, the minimum number of operations required is 3.

Input: A = “1010101”, B = “0011100”
Output: 5
Explanation:
Step 1: Flip the entiThehrefore, A becomes “0101010″
Step 2: Flip substring {A[0], A[5]}. Therefore, A becomes “1010100″
Step 3: Flip the substring {A[0], A[3]}. Therefore, A becomes “0101100″
Step 4: Flip the substring {A[0], A[2]}. Therefore, A becomes “1011100″
Step 5: Flip A[0]. Therefore, A becomes “0011100” which is equal to B.
Therefore, the minimum number of operations required is 5.

的方法：我们的想法是初始化，保持最后索引在该字符在A是从在B点的字符不同的变量。然后将 A从第一个索引到最后一个索引取反。重复直到两个字符串相等。请按照以下步骤解决问题：

• 初始化一个变量last_index ，该变量保存A和B 中字符不同的最后一个索引。
• 从第1 个索引到last_index 否定字符串A并增加步数。
• 重复上述步骤，直到字符串A变得等于字符串B 。
• 执行操作后，在两个字符串相同后打印步数。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function that finds the minimum
// number of operations required such
// that string A and B are the same
void findMinimumOperations(string a,
                           string b)
{
 
    // Stores the count of steps
    int step = 0;
 
    // Stores the last index whose
    // bits are not same
    int last_index;
 
    // Iterate until both string
    // are unequal
    while (a != b) {
 
        // Check till end of string to
        // find righmost unequals bit
        for (int i = 0;
             i < a.length(); i++) {
 
            // Update the last index
            if (a[i] != b[i]) {
                last_index = i;
            }
        }
 
        // Flipping characters up
        // to the last index
        for (int i = 0;
             i <= last_index; i++) {
 
            // Flip the bit
            a[i] = (a[i] == '0') ? '1' : '0';
        }
 
        // Increasing steps by one
        step++;
    }
 
    // Print the count of steps
    cout << step;
}
 
// Driver Code
int main()
{
    // Given strings A and B
    string A = "101010", B = "110011";
 
    // Function Call
    findMinimumOperations(A, B);
 
    return 0;
}

Java

// Java program for the
// above approach
import java.util.*;
class GFG{
 
// Function that finds the minimum
// number of operations required such
// that String A and B are the same
static void findMinimumOperations(char[] a,
                                  char[] b)
{
  // Stores the count of steps
  int step = 0;
 
  // Stores the last index whose
  // bits are not same
  int last_index = 0;
 
  // Iterate until both String
  // are unequal
  while (!Arrays.equals(a, b))
  {
    // Check till end of String to
    // find righmost unequals bit
    for (int i = 0;
             i < a.length; i++)
    {
      // Update the last index
      if (a[i] != b[i])
      {
        last_index = i;
      }
    }
 
    // Flipping characters up
    // to the last index
    for (int i = 0;
             i <= last_index; i++)
    {
 
      // Flip the bit
      a[i] = (a[i] == '0') ?
              '1' : '0';
    }
    // Increasing steps by one
    step++;
  }
 
  // Print the count of steps
  System.out.print(step);
}
 
// Driver Code
public static void main(String[] args)
{
    // Given Strings A and B
    String A = "101010",
           B = "110011";
 
    // Function Call
    findMinimumOperations(A.toCharArray(),
                          B.toCharArray());
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 program for the above approach
 
# Function that finds the minimum
# number of operations required such
# that string A and B are the same
def findMinimumOperations(a, b):
     
    # Stores the count of steps
    step = 0
 
    # Stores the last index whose
    # bits are not same
    last_index = 0
 
    # Iterate until both string
    # are unequal
    while (a != b):
        a = [i for i in a]
         
        # Check till end of string to
        # find righmost unequals bit
        for i in range(len(a)):
             
            # Update the last index
            if (a[i] != b[i]):
                last_index = i
 
        # Flipping characters up
        # to the last index
        for i in range(last_index + 1):
             
            # Flip the bit
            if (a[i] == '0'):
                a[i] = '1'
            else:
                a[i] = '0'
                 
        a = "".join(a)       
 
        # Increasing steps by one
        step += 1
 
    # Print the count of steps
    print(step)
 
# Driver Code
if __name__ == '__main__':
     
    # Given strings A and B
    A = "101010"
    B = "110011"
 
    # Function Call
    findMinimumOperations(A, B)
 
# This code is contributed by mohit kumar 29

C#

// C# program for the
// above approach
using System;
 
class GFG{
 
// Function that finds the minimum
// number of operations required such
// that string A and B are the same
static void findMinimumOperations(string a,
                                  string b)
{
   
  // Stores the count of steps
  int step = 0;
 
  // Stores the last index whose
  // bits are not same
  int last_index = 0;
 
  // Iterate until both string
  // are unequal
  while (a.Equals(b) == false)
  {
     
    // Check till end of string to
    // find righmost unequals bit
    for(int i = 0; i < a.Length; i++)
    {
       
      // Update the last index
      if (a[i] != b[i])
      {
        last_index = i;
      }
    }
 
    // Flipping characters up
    // to the last index
    char[] ch = a.ToCharArray();
    for(int i = 0;
            i <= last_index; i++)
    {
       
      // Flip the bit
      if (ch[i] == '0')
      {
        ch[i] = '1';
      }
      else
      {
        ch[i] = '0';
      }
    }
    a = new string(ch);
     
    // Increasing steps by one
    step++;
  }
 
  // Print the count of steps
  Console.WriteLine(step);
}
 
// Driver Code
public static void Main()
{
   
  // Given strings A and B
  string A = "101010";
  string B = "110011";
 
  // Function Call
  findMinimumOperations(A,B);
}
}
 
// This code is contributed by SURENDRA_GANGWAR

Javascript

 
// JavaScript program for the
// above approach
 
// Function that finds the minimum
// number of operations required such
// that string A and B are the same
function findMinimumOperations(a, b)
{
     
    // Stores the count of steps
    var step = 0;
     
    // Stores the last index whose
    // bits are not same
    var last_index = 0;
     
    // Iterate until both string
    // are unequal
    while (a !== b)
    {
         
        // Check till end of string to
        // find righmost unequals bit
        for (var i = 0; i < a.length; i++)
        {
             
            // Update the last index
            if (a[i] !== b[i])
            {
                last_index = i;
            }
        }
     
        // Flipping characters up
        // to the last index
        var ch = a.split("");
        for(var i = 0; i <= last_index; i++)
        {
             
            // Flip the bit
            if (ch[i] === "0")
            {
                ch[i] = "1";
            }
            else
            {
                ch[i] = "0";
            }
        }
        a = ch.join("");
         
        // Increasing steps by one
        step++;
    }
     
    // Print the count of steps
    document.write(step);
}
 
// Driver Code
 
// Given strings A and B
var A = "101010";
var B = "110011";
 
// Function Call
findMinimumOperations(A, B);
 
// This code is contributed by rdtank
 

输出：

4

时间复杂度： O(N ² )
辅助空间： O(1)

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