Palindrome

题目：

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

题意：

输入一个字符串，问最少添加几个字符可以使原字符串成为回文字符串。

思路：

需要加的字符的个数=原来字符串的长度-原来字符串和逆字符串的最长公共子序列的长度。

但是此题中n<=5000，计算最长公共子序列的长度时用int dp[5000][5000]容易超内存，

所以定义dp数组时用short。

代码：

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
short dp[5005][5005];
int main()
{int n;while(~scanf("%d",&n)){getchar();memset(dp,0,sizeof(dp));char a[5005],b[5005];for(int i=1,j=n;i<=n;j--,i++){scanf("%c",&a[i]);b[j]=a[i];}for(int i=1;i<=n;i++){for(int j=1;j<=n;j++){if(a[i]==b[j])dp[i][j]=dp[i-1][j-1]+1;elsedp[i][j]=max(dp[i-1][j],dp[i][j-1]);}}printf("%d\n",n-dp[n][n]);}return 0;
}

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