lightoj 1422 - Halloween Costumes 【区间dp入门】

1422 - Halloween Costumes

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Time Limit: 2 second(s)

Memory Limit: 32 MB

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

 

题意：有n个party，每个party都有规定的服装。已知衣服可以套着穿，但是脱掉的衣服就不能再穿了。问参加所有的聚会至少要准备的衣服数。参加party的顺序为1 - 2 - 3 - ... - n。

思路：把每个party当做坐标点。dp[i][j]表示区间[i, j]需要准备的衣服数，状态转移方程

dp[i][j] = min(dp[i+1][j]+1, dp[i+1][k-1]+dp[k][j]) (i < k <= j && a[k] == a[i])。

a[i]表示第i个party规定的衣服类。

AC代码：

#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <vector>
#define INF 0x3f3f3f
#define eps 1e-8
#define MAXN (100+1)
#define MAXM (100000)
#define Ri(a) scanf("%d", &a)
#define Rl(a) scanf("%lld", &a)
#define Rf(a) scanf("%lf", &a)
#define Rs(a) scanf("%s", a)
#define Pi(a) printf("%d\n", (a))
#define Pf(a) printf("%.2lf\n", (a))
#define Pl(a) printf("%lld\n", (a))
#define Ps(a) printf("%s\n", (a))
#define W(a) while(a--)
#define CLR(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define LL long long
#define lson o<<1, l, mid
#define rson o<<1|1, mid+1, r
#define ll o<<1
#define rr o<<1|1
using namespace std;
int a[MAXN];
int dp[MAXN][MAXN];
int main()
{
int t, kcase = 1;
Ri(t);
W(t)
{
int n; Ri(n);
for(int i = 1; i <= n; i++)
Ri(a[i]);
CLR(dp, 0);
for(int i = n; i >= 1; i--)
{
for(int j = i; j <= n; j++)
{
if(i == j)
dp[i][j] = 1;
else

dp[i][j] = dp[i+1][j] + 1;
for(int k = i+1; k <= j; k++)
{
if(a[k] == a[i])
dp[i][j] = min(dp[i][j], dp[i+1][k-1]+dp[k][j]);
}
}
}
printf("Case %d: %d\n", kcase++, dp[1]
);
}
return 0;
}