算法设计（最长可能的回文）

本文概述

建议：在继续解决方案之前, 请先在{IDE}上尝试使用你的方法。
Java
Python3
C#

给定一个字符串, 任务是返回其可能的最长分块回文的长度。它表示在不是由字符串字符形成的情况下, 由子字符串形成的回文。为了更好地理解示例
【算法设计（最长可能的回文）】例子：

Input : ghiabcdefhelloadamhelloabcdefghi Output : 7(ghi)(abcdef)(hello)(adam)(hello)(abcdef)(ghi)Input : merchantOutput : 1(merchant)Input : antaprezatepzapreantaOutput : 11(a)(nt)(a)(pre)(za)(tpe)(za)(pre)(a)(nt)(a)Input : lsbinOutput : 3(geeks)(for)(geeks)

推荐：请尝试以下方法{IDE}首先, 在继续解决方案之前。整个想法是从左侧和右侧递归地创建块。

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如你所见, 我们可以匹配左侧块中的子字符串, 并将其与确切的右侧块进行匹配。一旦找到匹配项, 我们将递归计算剩余字符串中可能的最长分块回文的长度。一旦不留下任何字符串或找不到更多有效的分块部分, 我们便结束递归。
Java

/* Java program to find the length of longest palindromic chunk */ import java.util.*; import java.lang.*; import java.io.*; class LongestPalindromicChunk { // Here s is the string whose LCP is needed // ln is length of string evaluated till now // and str is original string private static int LPCRec(String curr_str, int count, int len, String str) { // if there is noting at all!! if (curr_str == null || curr_str.isEmpty()) return ( 0 ); // if a single letter is left out if (curr_str.length() < = 1 ) { if (count != 0 & & str.length() - len < = 1 ) return (count + 1 ); else return ( 1 ); }// for each length of substring chunk in string int n = curr_str.length(); for ( int i = 0 ; i < n/ 2 ; i++) { // if left side chunk and right side chunk // are same if (curr_str.substring( 0 , i + 1 ). equals(curr_str.substring(n- 1 -i, n))) { // Call LCP for the part between the // chunks and add 2 to the result. // Length of string evaluated till // now is increased by (i+1)*2 return LPCRec(curr_str.substring(i+ 1 , n- 1 -i), count + 2 , len + (i+ 1 )* 2 , str); } }return count + 1 ; }// Wrapper over LPCRec() public static int LPC(String str) { return LPCRec(str, 0 , 0 , str); }// driver function public static void main(String[] args) { System.out.println( "V : " + LPC( "V" )); System.out.println( "VOLVO : " + LPC( "VOLVO" )); System.out.println( "VOLVOV : " + LPC( "VOLVOV" )); System.out.println( "ghiabcdefhelloadamhelloabcdefghi : " + LPC( "ghiabcdefhelloadamhelloabcdefghi" )); System.out.println( "ghiabcdefhelloadamhelloabcdefghik : " + LPC( "ghiabcdefhelloadamhelloabcdefghik" )); System.out.println( "antaprezatepzapreanta : " + LPC( "antaprezatepzapreanta" )); } }

Python3

# Python3 program to find length of # longest palindromic chunk# Here curr_str is the string whose # LCP is needed leng is length of # string evaluated till now and s # is original string def LPCRec(curr_str, count, leng, s):# If there is nothing at all!! if not curr_str: return 0# If a single letter is left out if len (curr_str) < = 1 : if count ! = 0 and len (s) - leng < = 1 : return (count + 1 ) else : return 1# For each length of substring # chunk in string n = len (curr_str) for i in range (n / / 2 ): # If left side chunk and right # side chunk are same if (curr_str[ 0 : i + 1 ] = = curr_str[n - 1 - i : n]): # Call LCP for the part between the # chunks and add 2 to the result. # Length of string evaluated till # now is increased by (i+1)*2 return LPCRec(curr_str[i + 1 : n - 1 - i], count + 2 , leng + (i + 1 ) * 2 , s)return count + 1# Wrapper over LPCRec() def LPC(s): return LPCRec(s, 0 , 0 , s)# Driver code print ( "V :" , LPC( "V" )) print ( "VOLVO :" , LPC( "VOLVO" )) print ( "VOLVOV :" , LPC( "VOLVOV" )) print ( "ghiabcdefhelloadamhelloabcdefghi :" , LPC( "ghiabcdefhelloadamhelloabcdefghi" ))print ( "ghiabcdefhelloadamhelloabcdefghik :" , LPC( "ghiabcdefhelloadamhelloabcdefghik" ))print ( "antaprezatepzapreanta :" , LPC( "antaprezatepzapreanta" ))# This code is contributed by Prateek Gupta

// C# program to find length of // longest palindromic chunk using System; class GFG { // Here s is the string whose LCP // is needed ln is length of string // evaluated till now and str is // original string private static int LPCRec( string curr_str, int count, int len, string str) { // if there is noting at all!! if ( string .ReferenceEquals(curr_str, null ) || curr_str.Length == 0) { return (0); }// if a single letter is left out if (curr_str.Length < = 1) { if (count != 0 & & str.Length - len < = 1) { return (count + 1); } else { return (1); } }// for each length of substring // chunk in string int n = curr_str.Length; for ( int i = 0; i < n / 2; i++) { // if left side chunk and right side chunk // are same if (curr_str.Substring(0, i + 1).Equals( curr_str.Substring(n - 1 - i, n - (n - 1 - i)))) { // Call LCP for the part between the // chunks and add 2 to the result. // Length of string evaluated till // now is increased by (i+1)*2 return LPCRec(curr_str.Substring(i + 1, (n - 1 - i) - (i + 1)), count + 2, len + (i + 1) * 2, str); } }return count + 1; }// Wrapper over LPCRec() public static int LPC( string str) { return LPCRec(str, 0, 0, str); }// Driver Code public static void Main( string [] args) { Console.WriteLine( "V : " + LPC( "V" )); Console.WriteLine( "VOLVO : " + LPC( "VOLVO" )); Console.WriteLine( "VOLVOV : " + LPC( "VOLVOV" )); Console.WriteLine( "ghiabcdefhelloadamhelloabcdefghi : " + LPC( "ghiabcdefhelloadamhelloabcdefghi" )); Console.WriteLine( "ghiabcdefhelloadamhelloabcdefghik : " + LPC( "ghiabcdefhelloadamhelloabcdefghik" )); Console.WriteLine( "antaprezatepzapreanta : " + LPC( "antaprezatepzapreanta" )); } }// This code is contributed by Shrikant13

输出如下：

V : 1VOLVO : 3VOLVOV : 5ghiabcdefhelloadamhelloabcdefghi : 7ghiabcdefhelloadamhelloabcdefghik : 1antaprezatepzapreanta : 11

以下是带有上述问题的备注的C ++实现。

#include < iostream> #include < climits> #include < unordered_map> using namespace std; unordered_map< string, int > mem; int process(string& s, int l, int r) { int ans = 1; if (l > r) return 0; // check if we've already solved this if (mem.find(s.substr(l, r-l+1)) != mem.end()) return mem[s.substr(l, r-l+1)]; for ( int len = 1; len < = (r-l+1)/2; len++) { if (s.substr(l, len) == s.substr(r-len+1, len)) ans = max(ans, 2 + process(s, l+len, r-len)); } // remember result for future mem[s.substr(l, r-l+1)] = ans; return ans; }int LPC(string s) { return process(s, 0, s.length()-1); }int main() { cout < < LPC( "aaaaabaababbaabaaababababababababbbbaaaaa" ) < < endl; return 0; }

资源：职业杯
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