最长回文子串的长度：递归

给定一个字符串S ，任务是找到长度最长的回文子串

例子：

Input: S = “aaaabbaa”
Output: 6
Explanation:
Sub-string “aabbaa” is the longest palindromic sub-string.

Input: S = “banana”
Output: 5
Explanation:
Sub-string “anana” is the longest palindromic sub-string.

方法：想法是使用递归将问题分解为更小的子问题。为了将问题分解为两个较小的子问题，比较字符串的开始和结束字符，并递归调用中间子字符串的函数。下面是递归的图示：

• 基本情况：此问题的基本情况是字符串的起始索引大于或等于结束索引。

  if (start > end)
      return count
  if (start == end)
      return count + 1
  

• 递归案例：比较字符串的开始和结束索引字符：
  • 当开始和结束字符相等时，通过排除开始和结束字符递归调用子字符串

    recursive_func(string, start+1, end-1)
    

  • 当开始和结束字符不相等时，通过一次排除一个开始和结束字符递归调用子字符串。

    recursive_func(string, start+1, end)
    recursive_func(string, start, end-1)
    

• 返回语句：在每次递归调用时，通过包括和排除开始和结束字符返回可能的最大计数。

下面是上述方法的实现：

C++

// C++ implementation to find the 
// length of longest palindromic
// sub-string using Recursion
  
#include 
using namespace std;
  
// Function to find maximum
// of the two variables
int max(int x, int y)
{
    return (x > y) ? x : y;
}
  
// Function to find the longest
// palindromic substring : Recursion
int longestPalindromic(string str, 
             int i, int j, int count)
{
      
    // Base condition when the start
    // index is greater than end index
    if (i > j)
        return count;
      
    // Base condition when both the 
    // start and end index are equal
    if (i == j)
        return (count + 1);
          
    // Condition when corner characters
    // are equal in the string
    if (str[i] == str[j]) {
          
        // Recursive call to find the
        // longest Palindromic string
        // by excluding the corner characters
        count = longestPalindromic(str, i + 1, 
                  j - 1, count + 2);
        return max(count, 
        max(longestPalindromic(str, i + 1, j, 0), 
         longestPalindromic(str, i, j - 1, 0)));
    }
      
    // Recursive call to find the 
    // longest Palindromic string
    // by including one corner 
    // character at a time
    return max(
       longestPalindromic(str, i + 1, j, 0), 
       longestPalindromic(str, i, j - 1, 0));
}
  
// Function to find the longest 
// palindromic sub-string
int longest_palindromic_substr(string str)
{
    // Utility function call
    return longestPalindromic(str, 0, 
                 str.length() - 1, 0);
}
  
// Driver Code
int main()
{
    string str = "aaaabbaa";
      
    // Function Call
    cout << longest_palindromic_substr(str);
    return 0;
}

Java

// Java implementation to find the 
// length of longest palindromic
// sub-String using Recursion
class GFG{
   
// Function to find maximum
// of the two variables
static int max(int x, int y)
{
    return (x > y) ? x : y;
}
   
// Function to find the longest
// palindromic subString : Recursion
static int longestPalindromic(String str, 
             int i, int j, int count)
{
       
    // Base condition when the start
    // index is greater than end index
    if (i > j)
        return count;
       
    // Base condition when both the 
    // start and end index are equal
    if (i == j)
        return (count + 1);
           
    // Condition when corner characters
    // are equal in the String
    if (str.charAt(i) == str.charAt(j)) {
           
        // Recursive call to find the
        // longest Palindromic String
        // by excluding the corner characters
        count = longestPalindromic(str, i + 1, 
                  j - 1, count + 2);
        return max(count, 
        max(longestPalindromic(str, i + 1, j, 0), 
         longestPalindromic(str, i, j - 1, 0)));
    }
       
    // Recursive call to find the 
    // longest Palindromic String
    // by including one corner 
    // character at a time
    return Math.max(
       longestPalindromic(str, i + 1, j, 0), 
       longestPalindromic(str, i, j - 1, 0));
}
   
// Function to find the longest 
// palindromic sub-String
static int longest_palindromic_substr(String str)
{
    // Utility function call
    return longestPalindromic(str, 0, 
                 str.length() - 1, 0);
}
   
// Driver Code
public static void main(String[] args)
{
    String str = "aaaabbaa";
       
    // Function Call
    System.out.print(longest_palindromic_substr(str));
}
}
  
// This code is contributed by Rajput-Ji

Python3

# Python3 implementation to find the 
# length of longest palindromic
# sub-string using Recursion
  
# Function to find maximum 
# of the two variables 
def maxi(x, y) :
    if x > y :
        return x
    else :
        return y
  
# Function to find the longest 
# palindromic substring : Recursion 
def longestPalindromic(strn, i, j, count): 
      
    # Base condition when the start 
    # index is greater than end index 
    if i > j : 
        return count 
      
    # Base condition when both the 
    # start and end index are equal 
    if i == j : 
        return (count + 1)
          
    # Condition when corner characters 
    # are equal in the string 
    if strn[i] == strn[j] : 
          
        # Recursive call to find the 
        # longest Palindromic string 
        # by excluding the corner characters 
        count = longestPalindromic(strn, i + 1, j - 1, count + 2) 
        return maxi(count, maxi(longestPalindromic(strn, i + 1, j, 0), 
                    longestPalindromic(strn, i, j - 1, 0))) 
      
    # Recursive call to find the 
    # longest Palindromic string 
    # by including one corner 
    # character at a time 
    return maxi( longestPalindromic(strn, i + 1, j, 0), 
                longestPalindromic(strn, i, j - 1, 0)) 
  
# Function to find the longest 
# palindromic sub-string 
def longest_palindromic_substr(strn):
  
    # Utility function call
    k = len(strn) - 1
    return longestPalindromic(strn, 0, k, 0)
  
strn = "aaaabbaa"
  
# Function Call 
print( longest_palindromic_substr(strn) )
      
# This code is contributed by chsadik99

C#

// C# implementation to find the 
// length of longest palindromic
// sub-String using Recursion
using System;
  
class GFG{
    
// Function to find maximum
// of the two variables
static int max(int x, int y)
{
    return (x > y) ? x : y;
}
    
// Function to find the longest
// palindromic subString : Recursion
static int longestPalindromic(String str, 
             int i, int j, int count)
{
        
    // Base condition when the start
    // index is greater than end index
    if (i > j)
        return count;
        
    // Base condition when both the 
    // start and end index are equal
    if (i == j)
        return (count + 1);
            
    // Condition when corner characters
    // are equal in the String
    if (str[i] == str[j]) {
            
        // Recursive call to find the
        // longest Palindromic String
        // by excluding the corner characters
        count = longestPalindromic(str, i + 1, 
                  j - 1, count + 2);
        return max(count, 
        max(longestPalindromic(str, i + 1, j, 0), 
         longestPalindromic(str, i, j - 1, 0)));
    }
        
    // Recursive call to find the 
    // longest Palindromic String
    // by including one corner 
    // character at a time
    return Math.Max(
       longestPalindromic(str, i + 1, j, 0), 
       longestPalindromic(str, i, j - 1, 0));
}
    
// Function to find the longest 
// palindromic sub-String
static int longest_palindromic_substr(String str)
{
    // Utility function call
    return longestPalindromic(str, 0, 
                 str.Length - 1, 0);
}
    
// Driver Code
public static void Main(String[] args)
{
    String str = "aaaabbaa";
        
    // Function Call
    Console.Write(longest_palindromic_substr(str));
}
}
  
// This code is contributed by 29AjayKumar

输出：

6

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