Halloween Costumes LightOJ - 1422 （区间Dp）

Gappu has a very busy weekend ahead of him. Because, next weekend is Halloween, and he is planning to attend as many parties as he can. Since it's Halloween, these parties are all costume parties, Gappu always selects his costumes in such a way that it blends with his friends, that is, when he is attending the party, arranged by his comic-book-fan friends, he will go with the costume of Superman, but when the party is arranged contest-buddies, he would go with the costume of 'Chinese Postman'.

Since he is going to attend a number of parties on the Halloween night, and wear costumes accordingly, he will be changing his costumes a number of times. So, to make things a little easier, he may put on costumes one over another (that is he may wear the uniform for the postman, over the superman costume). Before each party he can take off some of the costumes, or wear a new one. That is, if he is wearing the Postman uniform over the Superman costume, and wants to go to a party in Superman costume, he can take off the Postman uniform, or he can wear a new Superman uniform. But, keep in mind that, Gappu doesn't like to wear dresses without cleaning them first, so, after taking off the Postman uniform, he cannot use that again in the Halloween night, if he needs the Postman costume again, he will have to use a new one. He can take off any number of costumes, and if he takes off k of the costumes, that will be the last k ones (e.g. if he wears costume A before costume B, to take off A, first he has to remove B).

Given the parties and the costumes, find the minimum number of costumes Gappu will need in the Halloween night.

Input

Input starts with an integer T (≤ 200), denoting the number of test cases.

Each case starts with a line containing an integer N (1 ≤ N ≤ 100) denoting the number of parties. Next line contains N integers, where the ith integer ci (1 ≤ ci ≤ 100) denotes the costume he will be wearing in party i. He will attend party 1 first, then party 2, and so on.

Output

For each case, print the case number and the minimum number of required costumes.

Sample Input

2

4

1 2 1 2

7

1 2 1 1 3 2 1

Sample Output

Case 1: 3

Case 2: 4

题意

有个人要去参加一些不同的聚会，不同聚会要穿不同衣服，给你参加聚会的顺序，问最小需要准备多少衣服

这个人可以在装着衣服时再穿一件，脱掉后再去参见之前类型的聚会，但脱掉之后不能再穿，再穿只能记一件新衣服

思路

区间DP，在碰到有个之前参见过得一个聚会时，他可以选择脱到之前那件，也可以选择穿一件新的，选择会对后面有影响。

我们可以选择逆推，先假设他穿了一件新衣服，在判断如果脱会不会更优。

#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <queue>
using namespace std;
int a[120],n;
int dp[120][120];
int main()
{
    int t;
    scanf("%d",&t);
    int ca = 1;
    while(t--)
    {
        scanf("%d",&n);
        for(int i = 1;i<=n ;i++) scanf("%d",&a[i]);
        memset(dp,0,sizeof(dp));
        for(int i = n;i>=1;i--)
        {
            for(int j  = i;j<=n;j++)
            {
                dp[i][j] = dp[i+1][j] + 1;
                for(int k = i+1;k<=j;k++)
                {
                    if(a[i] == a[k])
                    {
                        dp[i][j] = min(dp[i][j],dp[i+1][k]+dp[k+1][j]);
                    }
                }
            }
        }
        printf("Case %d: %d\n",ca++,dp[1][n]);
    }
    return 0;
}