【杭电oj1513】Palindrome

爱被打了一巴掌 2022-09-25 04:27 173阅读 0赞

# Palindrome #

**Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)  
Total Submission(s): 5202 Accepted Submission(s): 1780**

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.

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

Source

[IOI 2000 ][IOI 2000]

Recommend

linle | We have carefully selected several similar problems for you: [1505][] [1506][] [1074][] [1003][] [1510][]

本题用到滚动数组，否则可能超内存。

需要添加的字符个数=总字符数-正序与倒序字符串的最长公共子序列的长度。

#include<cstdio>
    #include<cmath>
    #include<cstring>
    #include<algorithm>
    using namespace std;
    const int N = 5001; 
    char a[N],b[N];
    int dp[2][N];
    int main() {
    	int n,i,j;
    	while(scanf("%d",&n)!=EOF) {
    		memset(dp,0,sizeof(dp));
    		scanf("%s",a);
    		for(i=0; i<n; i++)
    			b[i]=a[n-1-i];
    		for(i=1; i<=n; i++)
    			for(j=1; j<=n; j++)
    				if(a[i-1]==b[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",n-dp[n%2][n]);
    	}
    	return 0;
    }

[题目地址：http://acm.hdu.edu.cn/showproblem.php?pid=1513][http_acm.hdu.edu.cn_showproblem.php_pid_1513]

[IOI 2000]: http://acm.hdu.edu.cn/search.php?field=problem&key=IOI+2000&source=1&searchmode=source
[1505]: http://acm.hdu.edu.cn/showproblem.php?pid=1505
[1506]: http://acm.hdu.edu.cn/showproblem.php?pid=1506
[1074]: http://acm.hdu.edu.cn/showproblem.php?pid=1074
[1003]: http://acm.hdu.edu.cn/showproblem.php?pid=1003
[1510]: http://acm.hdu.edu.cn/showproblem.php?pid=1510
[http_acm.hdu.edu.cn_showproblem.php_pid_1513]: http://acm.hdu.edu.cn/showproblem.php?pid=1513