Light OJ 1422 Halloween Costumes(区间DP）

Problem 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 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：

给你n天需要穿的衣服的样式，每次可以套着穿衣服，脱掉的衣服就不能再用了（可以再穿，但算cost），问至少要带多少条衣服才能参加所有宴会。

思路：

很明显为区间dp，dp[i][j]表示i~j天所需的最小数量。

考虑第j天穿不穿，如果穿的话那么 dp[i][j]=dp[i][j-1]+1;

如果不穿的话，那么需要有一个 k (i<=k<j)，第j天和第k天穿的衣服相同，将k+1~j-1衣服套着穿后全部脱掉，那么

dp[i][j]=dp[i][k]+dp[k+1][j-1]；
 

代码：

#include <cstdio>
#include <algorithm>
#include <cmath>
using namespace std;
const int MAXN = 100+7;
int n,m;
int num[MAXN];
int dp[MAXN][MAXN];
int main()
{
    int t;
    scanf("%d",&t);
    int ca = 0;
    while(t--)
    {
        scanf("%d",&n);
        for(int i = 1 ; i <= n ; ++i)scanf("%d",&num[i]);
        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(num[k] == num[i])dp[i][j] = min(dp[i][j],dp[i+1][k-1] + dp[k][j]);
            }
        }
        printf("Case %d: %d\n",++ca,dp[1][n]);
    }
}

  作者：utobe67
来源：CSDN
转自原文：https://blog.csdn.net/tobewhatyouwanttobe/article/details/36420755