POJ_1159_Palindrome【dp】

/*Palindrome

Time Limit: 3000MS        Memory Limit: 65536K

Total Submissions: 62592        Accepted: 21811

Description

A palindrome is a symmetrical string, that is, a string read identically from left to right as well as from right to left. You are to write a program which, given a string, determines the minimal number of characters to be inserted into the string in order
to obtain a palindrome.

As an example, by inserting 2 characters, the string "Ab3bd" can be transformed into a palindrome ("dAb3bAd" or "Adb3bdA"). However, inserting fewer than 2 characters does not produce a palindrome.

Input

Your program is to read from standard input. The first line contains one integer: the length of the input string N, 3 <= N <= 5000. The second line contains one string with length N. The string is formed from uppercase letters from 'A' to 'Z', lowercase letters
from 'a' to 'z' and digits from '0' to '9'. Uppercase and lowercase letters are to be considered distinct.

Output

Your program is to write to standard output. The first line contains one integer, which is the desired minimal number.

Sample Input

5

Ab3bd

Sample Output

2

  题意，给你一个字符串，可在任意位置添加字符，最少再添加几个字符，可以使这个字符串成为回文字符串。

 

  思路：求原串与其逆串的最长公共子序列，然后用串长减去最长公共子序列的长度就是要添加的最少的字符数。

 

*/

#include <cstdio>
#include<iostream>
#include<cstring>
#include <algorithm>
using namespace std;
const int Max = 5005;
char str1[Max],str2[Max];
int dp[2][Max];
int main()
{
int n,i,j,k;
while(cin>>n)
{
scanf("%s",&str1[1]);
for(i=1;i<=n;i++)//str1的逆串
str2[i]=str1[n-i+1];
memset(dp,0,sizeof(dp));
i=0;
for(k=1;k<=n;k++)
{
i=1-i;//滚动数组
for(j=1;j<=n;j++)
{
if(str1[k]==str2[j])
dp[i][j] = dp[1-i][j-1] + 1;
else
dp[i][j] = max(dp[i][j-1], dp[1-i][j]);
}
}
cout<<n-dp[i]
<<endl;
}
return 0;
}