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LightOJ1422---Halloween Costumes (区间dp)

时间:2015-05-15 17:49:45      阅读:142      评论:0      收藏:0      [点我收藏+]

标签: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

Output for Sample Input

2

4

1 2 1 2

7

1 2 1 1 3 2 1

Case 1: 3

Case 2: 4

dp[i][j]表示参加第i个到第j个活动,所需要的最少的衣服数目
枚举中间的活动k,如果和第j个相同,那么第k个活动和第j个可以共用一件
dp[i][j]=dp[i][k]+dp[k+1][j?1]
如果不同
dp[i][j]=dp[i][k]+dp[k+1][j]

/*************************************************************************
    > File Name: B.cpp
    > Author: ALex
    > Mail: zchao1995@gmail.com 
    > Created Time: 2015年05月15日 星期五 15时09分49秒
 ************************************************************************/

#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <queue>
#include <stack>
#include <map>
#include <bitset>
#include <set>
#include <vector>

using namespace std;

const double pi = acos(-1.0);
const int inf = 0x3f3f3f3f;
const double eps = 1e-15;
typedef long long LL;
typedef pair <int, int> PLL;

int dp[110][110];
int arr[110];

int main() {
    int t;
    int icase = 1;
    scanf("%d", &t);
    while (t--) {
        int n;
        scanf("%d", &n);
        memset(dp, 0, sizeof(dp));
        for (int i = 1; i <= n; ++i) {
            scanf("%d", &arr[i]);
            dp[i][i] = 1;
        }
        for (int i = n - 1; i >= 1; --i) {
            for (int j = i + 1; j <= n; ++j) {
                dp[i][j] = dp[i][j - 1] + 1;
                for (int k = i; k <= j; ++k) {
                    int cost;
                    if (arr[k] == arr[j]) {
                        if (k + 1 > j - 1) {
                            dp[i][j] = min(dp[i][j], dp[i][k]);
                        }
                        else {
                            dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j - 1]);
                        }
                    }
                    else {
                        dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j]);
                    }
                }
            }
        }
        printf("Case %d: %d\n", icase++, dp[1][n]);
    }
    return 0;
}

LightOJ1422---Halloween Costumes (区间dp)

标签:dp

原文地址:http://blog.csdn.net/guard_mine/article/details/45746179

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