学步园

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.

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.

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

5
Ab3bd

2

IOI 2000

问你加入多少字符使得字符串变成回文串

我们对字符串和他的逆序串求一个最长公共子序列，这样一来，LCS里的一定是回文的，而其他的一定不会回文，所以必须在相应位置插入那些字符使得他们对称，最后整个串才可以回文

#include <map>    
#include <set>    
#include <list>    
#include <stack>    
#include <queue>    
#include <vector>    
#include <cstdio>    
#include <cmath>    
#include <cstring>    
#include <iostream>    
#include <algorithm>    
    
using namespace std;

char str1[5010];
char str2[5010];
int dp[2][5010];

int main()
{
	int len;
	while (~scanf("%d", &len))
	{
		scanf("%s", str1);
		for (int i = 0; i < len; i++)
		{
			str2[i] = str1[len - i - 1];
		}
		str2[len] = '\0';
		memset (dp, 0, sizeof(dp) );
		for (int i = 1; i <= len; i++)
		{
			for (int j = 1; j <= len; j++)
			{
				if (str1[i - 1] == str2[j - 1])
				{
					dp[i % 2][j] = dp[(i - 1) % 2][j - 1] + 1;
				}
				else
				{
					dp[i % 2][j] = max(dp[(i - 1) % 2][j], dp[i % 2][j - 1]);
				}
			}
		}
		printf("%d\n", len - dp[len % 2][len]);
	}
}