poj 1159 dp Palindrome

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

5Ab3bd

Sample Output

2

#include <iostream>#include <cstdio>#include <cstdlib>#include <cstring>using namespace std;#define maxn 5005char s[maxn];int n;int dp[maxn][maxn];int main(){    scanf("%d", &n);    scanf("%s", s);    for (int i = n -1; i >=0; i--)    {        dp[i][i] =0;        for (int j = i +1; j < n; j++)            if (s[i] == s[j])                dp[i][j] = dp[i +1][j -1];            else                dp[i][j] = min(dp[i +1][j], dp[i][j -1]) +1;    }    printf("%d\n", dp[0][n-1]);    return 0;}

dp[i][j]表示从i到j这段子串若变为回文串最少添加的字符数

当i与j位置字符相同时，即不插入；

当i与j位置字符不同时，要么在i位置的前一个插入1个与j相同的字符，要么在j的前一个位置上插入一个与i字符相同的字符