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Problem 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.
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：
给出一个字符串，问让此字符串变成一个回文串最少要加多少个字符
思路：
将此字符串倒序所得的字符串与本身进行lcs，用n减去所求的最长公共子序列的长度就是答案
代码：
import java.util.*;
class P1513{static String str;static char[] str1;static char[] str2;static int n;static int[][] dp;public static void main(String[] args){Scanner sc=new Scanner(System.in);while(sc.hasNext()){n=sc.nextInt();str2=new char[n];str1=new char[n];str=sc.next();str1=str.toCharArray();for(int i=0;i<n;i++){str2[i]=str1[n-i-1];}lcs();System.out.println(n-dp[n%2][n]);}}public static void lcs(){int i,j;dp=new int[n+1][n+1];for(i=1;i<=n;i++){for(j=1;j<=n;j++){int x=i%2;int y=1-x;if(str1[i-1]==str2[j-1]){dp[x][j]=dp[y][j-1]+1;}else{dp[x][j]=Math.max(dp[y][j], dp[x][j-1]);}}}}
}
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