所有字符至少出现 K 次的最大子串 | 2套

给定一个字符串str和一个整数K，任务是找到最长的子字符串的长度S，使得S中的每一个字符出现至少K倍。

例子：

Input: str = “aabbba”, K = 3
Output: 6
Explanation:
In substring aabbba, each character repeats at least k times and its length is 6.

Input: str = “ababacb”, K = 3
Output: 0
Explanation:
There is no substring where each character repeats at least k times.

朴素的方法：我们在上一篇文章中讨论了朴素的方法。

方法：在这篇文章中，我们将讨论使用分而治之技术和递归的方法。以下是步骤：

1. 将给定字符串的每个字符的频率存储在大小为26的频率数组中。
2. 初始化两个变量，从0开始，以字符串str的长度结束。
3. 遍历从开始字符串结束和计数的时间的每个字符重复数，并将其存储在数组中。
4. 如果任何字符的重复次数少于 K 次，则将字符串分成两半。如果 i 是我们发现字符串[i]重复次数少于K 次的字符串的索引，那么我们将字符串从start 到 i和i + 1 到 end分成两半。
5. 递归调用上述步骤中的两半，即分别从start到i和i+1到end ，重复步骤2和3，并通过上述递归调用返回两个值的最大值reutnr。
6. 如果start和end之间的所有字符至少重复K次，那么答案是end – start 。

   下面是上述方法的实现：

   C++

   // C++ program for the above approach 
   #include  
   using namespace std; 
     
   // Function to find the longest substring 
   int longestSubstring(int start, int end, 
                       string s, int k) 
   { 
       int left, right; 
     
       // Array for counting the number of 
       // times each character repeats 
       // count the number of times each 
       // character repeats from start to end 
       int count[26] = { 0 }; 
     
       // Store the frequency from s[start...end] 
       for (int i = start; i < end; i++) { 
           count[s[i] - 'a'] += 1; 
       } 
     
       // Iterate from [start, end] 
       for (int i = start; i < end; i++) { 
     
           if (count[s[i] - 'a'] < k) { 
     
               // Recursive call for left subpart 
               left = longestSubstring(start, 
                                       i, 
                                       s, 
                                       k); 
     
               // Recursive call for right subpart 
               right = longestSubstring(i + 1, 
                                       end, 
                                       s, 
                                       k); 
     
               // Return maximum of left & right 
               return max(left, right); 
           } 
       } 
     
       // If all the characters are repeated 
       // at least k times 
       return end - start; 
   } 
     
   // Driver Code 
   int main() 
   { 
       // Given String str 
       string str = "aabbba"; 
       int k = 3; 
     
       // Function Call 
       cout << longestSubstring(0, str.length(), 
                               str, k) 
           << endl; 
       return 0; 
   }

   Java

   // Java program for the above approach 
   import java.util.*; 
     
   class GFG{ 
     
   // Function to find the longest subString 
   static int longestSubString(int start, int end, 
                               String s, int k) 
   { 
       int left, right; 
     
       // Array for counting the number of 
       // times each character repeats 
       // count the number of times each 
       // character repeats from start to end 
       int count[] = new int[26]; 
     
       // Store the frequency from s[start...end] 
       for(int i = start; i < end; i++) 
       { 
           count[s.charAt(i) - 'a'] += 1; 
       } 
     
       // Iterate from [start, end] 
       for(int i = start; i < end; i++) 
       { 
           if (count[s.charAt(i) - 'a'] < k) 
           { 
                 
               // Recursive call for left subpart 
               left = longestSubString(start, i, 
                                       s, k); 
     
               // Recursive call for right subpart 
               right = longestSubString(i + 1, end, 
                                       s, k); 
     
               // Return maximum of left & right 
               return Math.max(left, right); 
           } 
       } 
     
       // If all the characters are repeated 
       // at least k times 
       return end - start; 
   } 
     
   // Driver Code 
   public static void main(String[] args) 
   { 
     
       // Given String str 
       String str = "aabbba"; 
       int k = 3; 
     
       // Function Call 
       System.out.print(longestSubString(0, str.length(), 
                                           str, k) + "\n"); 
   } 
   } 
     
   // This code is contributed by Amit Katiyar

   Python3

   # Python3 program for the above approach 
     
   # Function to find the longest substring 
   def longestSubString(start, end, s, k): 
         
       # List for counting the number of 
       # times each character repeats 
       # count the number of times each 
       # chracter repeats from start to end 
       count = [0 for i in range(26)] 
         
       # Store the frequency from s[start...end] 
       for i in range(start, end): 
           count[ord(s[i]) - ord('a')] += 1
         
       # Iterate from [start, end] 
       for i in range(start, end): 
           if(count[ ord(s[i]) - ord('a')] < k): 
                 
               # Recursive call for left subpart 
               left = longestSubString(start, i, 
                                           s, k) 
                                         
               # Recursive call for right subpart 
               right = longestSubString(i + 1, end, 
                                           s, k) 
                                         
               # Return maximum of left & right 
               return max(left, right) 
         
       # If all the characters are repeated 
       # at least k times 
       return end - start 
         
   # Driver Code 
     
   # Given String str 
   str = "aabbba"
   k = 3
     
   # Function call 
   print(longestSubString(0, len(str), str, k)) 
     
   # This code is contributed by dadimadhav

   C#

   // C# program for the above approach
   using System;
     
   class GFG{
     
   // Function to find the longest subString
   static int longestSubString(int start, int end,
                                string s, int k)
   {
       int left, right;
     
       // Array for counting the number of
       // times each character repeats
       // count the number of times each
       // character repeats from start to end
       int []count = new int[26];
     
       // Store the frequency from s[start...end]
       for(int i = start; i < end; i++)
       {
           count[s[i] - 'a'] += 1;
       }
     
       // Iterate from [start, end]
       for(int i = start; i < end; i++)
       {
           if (count[s[i] - 'a'] < k) 
           {
                 
               // Recursive call for left subpart
               left = longestSubString(start, i,
                                       s, k);
     
               // Recursive call for right subpart
               right = longestSubString(i + 1, end,
                                        s, k);
     
               // Return maximum of left & right
               return Math.Max(left, right);
           }
       }
     
       // If all the characters are repeated
       // at least k times
       return end - start;
   }
     
   // Driver Code
   public static void Main(string[] args)
   {
         
       // Given String str
       string str = "aabbba";
       int k = 3;
     
       // Function call
       Console.Write(longestSubString(0, str.Length,
                                         str, k) + "\n");
   }
   }
     
   // This code is contributed by rutvik_56

   输出：

   6
   

   时间复杂度： O(N*log ₂ N)

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