5. Longest Palindromic Substring
Problem's Link
----------------------------------------------------------------------------
Mean:
给定一个字符串,输出这个字符串的最长回文子串.
analyse:
水题.
使用Manacher算法求Ma和Mp数组,根据这两个数组来构造最长回文子串即可.
Time complexity: O(N)
view code
/**
* -----------------------------------------------------------------
* Copyright (c) 2015 crazyacking.All rights reserved.
* -----------------------------------------------------------------
* Author: crazyacking
* Date : 2015-12-10-11.04
*/
#include <queue>
#include <cstdio>
#include <set>
#include <string>
#include <stack>
#include <cmath>
#include <climits>
#include <map>
#include <cstdlib>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long( LL);
typedef unsigned long long( ULL);
const double eps( 1e-8);
/*
Given a string S, find the longest palindromic substring in S.
You may assume that the maximum length of S is 1000, and there exists one unique longest palindromic substring.
*/
class Solution
{
public :
/** O(n)内求出所有回文串
*原串 :abaaba
*Ma串 :.,a,b,a,a,b,a,
*Mp[i]:Ma串中,以字符Ma[i]为中心的最长回文子串的半径长度(包括Ma[i],也就是把回文串对折后的长度).
****经过对原串扩展处理后,将奇数串的情况也合并到了偶数的情况(不需要考虑奇数串)
*/
const static int MAXN = 1010;
char Ma [ MAXN * 2 ],s [ MAXN ];
int Mp [ MAXN * 2 ], Mplen;
void Manacher( string s)
{
memset( Ma , '\0' , sizeof Ma);
int len =s . length();
int le = 0;
Ma [ le ++ ] = '.';
Ma [ le ++ ] = ',';
for( int i = 0; i < len; ++ i)
{
Ma [ le ++ ] =s . at( i);
Ma [ le ++ ] = ',';
}
Mplen = le;
Ma [ le ] = 0;
int pnow = 0 , pid = 0;
for( int i = 1; i < le; ++ i)
{
if( pnow > i)
Mp [ i ] = min( Mp [ 2 * pid - i ], pnow - i);
else
Mp [ i ] = 1;
for(; Ma [ i - Mp [ i ]] == Ma [ i + Mp [ i ]]; ++ Mp [ i ]);
if( i + Mp [ i ] > pnow)
{
pnow = i + Mp [ i ];
pid = i;
}
}
}
string longestPalindrome( string s)
{
int idx = 0;
int MaxPalindomLength = 1;
Manacher(s);
for( int i = 0; i < Mplen; ++ i)
{
if( Mp [ i ] > MaxPalindomLength)
MaxPalindomLength = Mp [ i ], idx = i;
}
-- MaxPalindomLength;
int startPos = idx - MaxPalindomLength + 1;
char str [ MAXN ];
int strLen = 0;
for( int i = startPos; strLen < MaxPalindomLength; i += 2)
str [ strLen ++ ] = Ma [ i ];
str [ strLen ] = '\0';
return string( str);
}
};
int main()
{
Solution solution;
string s;
while( cin >>s)
{
cout << solution . longestPalindrome(s) << endl;
}
return 0;
}
* -----------------------------------------------------------------
* Copyright (c) 2015 crazyacking.All rights reserved.
* -----------------------------------------------------------------
* Author: crazyacking
* Date : 2015-12-10-11.04
*/
#include <queue>
#include <cstdio>
#include <set>
#include <string>
#include <stack>
#include <cmath>
#include <climits>
#include <map>
#include <cstdlib>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long( LL);
typedef unsigned long long( ULL);
const double eps( 1e-8);
/*
Given a string S, find the longest palindromic substring in S.
You may assume that the maximum length of S is 1000, and there exists one unique longest palindromic substring.
*/
class Solution
{
public :
/** O(n)内求出所有回文串
*原串 :abaaba
*Ma串 :.,a,b,a,a,b,a,
*Mp[i]:Ma串中,以字符Ma[i]为中心的最长回文子串的半径长度(包括Ma[i],也就是把回文串对折后的长度).
****经过对原串扩展处理后,将奇数串的情况也合并到了偶数的情况(不需要考虑奇数串)
*/
const static int MAXN = 1010;
char Ma [ MAXN * 2 ],s [ MAXN ];
int Mp [ MAXN * 2 ], Mplen;
void Manacher( string s)
{
memset( Ma , '\0' , sizeof Ma);
int len =s . length();
int le = 0;
Ma [ le ++ ] = '.';
Ma [ le ++ ] = ',';
for( int i = 0; i < len; ++ i)
{
Ma [ le ++ ] =s . at( i);
Ma [ le ++ ] = ',';
}
Mplen = le;
Ma [ le ] = 0;
int pnow = 0 , pid = 0;
for( int i = 1; i < le; ++ i)
{
if( pnow > i)
Mp [ i ] = min( Mp [ 2 * pid - i ], pnow - i);
else
Mp [ i ] = 1;
for(; Ma [ i - Mp [ i ]] == Ma [ i + Mp [ i ]]; ++ Mp [ i ]);
if( i + Mp [ i ] > pnow)
{
pnow = i + Mp [ i ];
pid = i;
}
}
}
string longestPalindrome( string s)
{
int idx = 0;
int MaxPalindomLength = 1;
Manacher(s);
for( int i = 0; i < Mplen; ++ i)
{
if( Mp [ i ] > MaxPalindomLength)
MaxPalindomLength = Mp [ i ], idx = i;
}
-- MaxPalindomLength;
int startPos = idx - MaxPalindomLength + 1;
char str [ MAXN ];
int strLen = 0;
for( int i = startPos; strLen < MaxPalindomLength; i += 2)
str [ strLen ++ ] = Ma [ i ];
str [ strLen ] = '\0';
return string( str);
}
};
int main()
{
Solution solution;
string s;
while( cin >>s)
{
cout << solution . longestPalindrome(s) << endl;
}
return 0;
}