LightOJ - 1422 Halloween Costumes （区间DP）

Description

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 i^th integer
c_i(1 ≤ c_i ≤ 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：给你n天分别要穿的衣服，可以套着穿，但是一旦脱下来就不能再穿了，问这n天最少要准备几件衣服。

思路：区间dp[i][j]表示从第i天到第j天的最少准备几件，那么对于第i天要么是穿了就脱了，要么是判断之后的某天是否有重复的，那么问题就变成了区间问题了

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 110;

int type[maxn], n;
int dp[maxn][maxn];

int main() {
	int t, cas = 1;
	scanf("%d\n", &t);
	while (t--) {
		scanf("%d", &n);
		for (int i = 1; i <= n; i++)
			scanf("%d", &type[i]);
		memset(dp, 0, sizeof(dp));
		for (int i = 1; i <= n; i++)
			for (int j = i; j <= n; j++)
				dp[i][j] = j-i+1;

		for (int i = n-1; i >= 1; i--)
			for (int j = i+1; j <= n; j++) {
				dp[i][j] = dp[i+1][j] + 1;
				for (int k = i; k <= j; k++)
					if (type[i] == type[k])
						dp[i][j] = min(dp[i][j], dp[i+1][k-1]+dp[k][j]);
			}

		printf("Case %d: %d\n", cas++, dp[1][n]);
	}
	return 0;
}