最小化所需的翻转次数，使 0 的子串的长度不超过 K

给定一个长度为N的二进制字符串str和一个整数K ，其中K在范围 (1 ≤ K ≤ N) 内，任务是找到所需的最小翻转次数(从0 s 转换为1 ，反之亦然)对给定的字符串执行，使得结果字符串不包含K 个或多个零。

例子：

Input: str = “11100000011”, K = 3 
Output: 2 
Explanation: 
Flipping 6^th and 7^th characters modifies the string to “11100110011”. 
Therefore, no substring of 0s are present in the string having length 3 or more.

Input: str = “110011”, K = 1 
Output: 2 
Flip 3rd and 4th characters then str = “111111” which does not contain 1 or more zeros together.

朴素的方法：最简单的方法是生成给定字符串的所有可能的子字符串，并且对于每个子字符串，检查它是否仅由 0 组成。如果发现为真，则检查其长度是否超过 K。如果发现为真，则计算该子串所需的翻转次数。最后，打印获得的翻转次数。

时间复杂度： O(2 ^N )
辅助空间： O(N)

有效的方法：要使结果字符串中连续零的计数小于K ，请选择仅由长度≥ K 的零组成的子串。所以问题简化为找到每个子串中的最小翻转。最终结果将是所有这些子段的最小翻转的总和。以下是步骤：

1. 将结果初始化为0和连续零的计数(比如cnt_zeros ) 到0 。
2. 遍历字符串并遇到‘0’增量cnt_zeros 1 。
3. 如果cnt_zeros变得等于K则增加结果并将cnt_zeros设置为0 。
4. 当‘1’出现时，将cnt_zeros设置为0 ，因为连续零的计数应该变为0 。

下面是上述方法的实现：

C++

// C++ program to implement
// the above approach
#include 
using namespace std;
 
// Function to return minimum
// number of flips required
int min_flips(string& str, int k)
{
    // Base Case
    if (str.size() == 0)
        return 0;
 
    // Stores the count of
    // minimum number of flips
    int ans = 0;
 
    // Stores the count of zeros
    // in current substring
    int cnt_zeros = 0;
 
    for (char ch : str) {
 
        // If current character is 0
        if (ch == '0') {
 
            // Continue ongoing
            // substring
            ++cnt_zeros;
        }
        else {
 
            // Start a new substring
            cnt_zeros = 0;
        }
 
        // If k consecutive
        // zeroes are obtained
        if (cnt_zeros == k) {
            ++ans;
 
            // End segment
            cnt_zeros = 0;
        }
    }
 
    // Return the result
    return ans;
}
 
// Driver Code
int main()
{
    string str = "11100000011";
    int k = 3;
 
    // Function call
    cout << min_flips(str, k);
    return 0;
}

Java

// Java program to implement
// the above approach
class GFG{
 
// Function to return minimum
// number of flips required
static int min_flips(String str, int k)
{
     
    // Base Case
    if (str.length() == 0)
        return 0;
 
    // Stores the count of
    // minimum number of flips
    int ans = 0;
 
    // Stores the count of zeros
    // in current subString
    int cnt_zeros = 0;
 
    for(char ch : str.toCharArray())
    {
         
        // If current character is 0
        if (ch == '0')
        {
             
            // Continue ongoing
            // subString
            ++cnt_zeros;
        }
        else
        {
             
            // Start a new subString
            cnt_zeros = 0;
        }
 
        // If k consecutive
        // zeroes are obtained
        if (cnt_zeros == k)
        {
            ++ans;
             
            // End segment
            cnt_zeros = 0;
        }
    }
 
    // Return the result
    return ans;
}
 
// Driver Code
public static void main(String[] args)
{
    String str = "11100000011";
    int k = 3;
 
    // Function call
    System.out.print(min_flips(str, k));
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 program to implement
# the above approach
 
# Function to return minimum
# number of flips required
def min_flips(strr, k):
     
    # Base Case
    if (len(strr) == 0):
        return 0
 
    # Stores the count of
    # minimum number of flips
    ans = 0
 
    # Stores the count of zeros
    # in current sub
    cnt_zeros = 0
 
    for ch in strr:
 
        # If current character is 0
        if (ch == '0'):
 
            # Continue ongoing
            # sub
            cnt_zeros += 1
        else:
 
            # Start a new sub
            cnt_zeros = 0
 
        # If k consecutive
        # zeroes are obtained
        if (cnt_zeros == k):
            ans += 1
 
            # End segment
            cnt_zeros = 0
 
    # Return the result
    return ans
 
# Driver Code
if __name__ == '__main__':
     
    strr = "11100000011"
    k = 3
 
    # Function call
    print(min_flips(strr, k))
 
# This code is contributed by mohit kumar 29

C#

// C# program to implement
// the above approach
using System;
 
class GFG{
 
// Function to return minimum
// number of flips required
static int min_flips(String str, int k)
{
     
    // Base Case
    if (str.Length == 0)
        return 0;
 
    // Stores the count of
    // minimum number of flips
    int ans = 0;
 
    // Stores the count of zeros
    // in current subString
    int cnt_zeros = 0;
 
    foreach(char ch in str.ToCharArray())
    {
         
        // If current character is 0
        if (ch == '0')
        {
             
            // Continue ongoing
            // subString
            ++cnt_zeros;
        }
        else
        {
             
            // Start a new subString
            cnt_zeros = 0;
        }
 
        // If k consecutive
        // zeroes are obtained
        if (cnt_zeros == k)
        {
            ++ans;
             
            // End segment
            cnt_zeros = 0;
        }
    }
 
    // Return the result
    return ans;
}
 
// Driver Code
public static void Main(String[] args)
{
    String str = "11100000011";
    int k = 3;
 
    // Function call
    Console.Write(min_flips(str, k));
}
}
 
// This code is contributed by 29AjayKumar

Javascript

// javascript program for the
// above approach
 
// Function to return minimum
// number of flips required
function min_flips(str, k)
{
       
    // Base Case
    if (str.length == 0)
        return 0;
   
    // Stores the count of
    // minimum number of flips
    let ans = 0;
   
    // Stores the count of zeros
    // in current subString
    let cnt_zeros = 0;
   
    for(let ch in str.split(''))
    {
           
        // If current character is 0
        if (str[ch] == '0')
        {
               
            // Continue ongoing
            // subString
            ++cnt_zeros;
        }
        else
        {
               
            // Start a new subString
            cnt_zeros = 0;
        }
   
        // If k consecutive
        // zeroes are obtained
        if (cnt_zeros == k)
        {
            ++ans;
               
            // End segment
            cnt_zeros = 0;
        }
    }
   
    // Return the result
    return ans;
}
  
// Driver Code
 
    let str = "11100000011";
    let k = 3;
   
    // Function call
    document.write(min_flips(str, k));
  
 // This code is contributed by decode2207.

输出：

2

时间复杂度： O(N)
辅助空间： O(1)

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