POJ1157LITTLE SHOP OF FLOWERS【dp】

最新推荐文章于 2018-06-06 17:36:57 发布

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LITTLE SHOP OF FLOWERS

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 19642		Accepted: 9057

Description

You want to arrange the window of your flower shop in a most pleasant way. You have F bunches of flowers, each being of a different kind, and at least as many vases ordered in a row. The vases are glued onto the shelf and are numbered consecutively 1 through V, where V is the number of vases, from left to right so that the vase 1 is the leftmost, and the vase V is the rightmost vase. The bunches are moveable and are uniquely identified by integers between 1 and F. These id-numbers have a significance: They determine the required order of appearance of the flower bunches in the row of vases so that the bunch i must be in a vase to the left of the vase containing bunch j whenever i < j. Suppose, for example, you have bunch of azaleas (id-number=1), a bunch of begonias (id-number=2) and a bunch of carnations (id-number=3). Now, all the bunches must be put into the vases keeping their id-numbers in order. The bunch of azaleas must be in a vase to the left of begonias, and the bunch of begonias must be in a vase to the left of carnations. If there are more vases than bunches of flowers then the excess will be left empty. A vase can hold only one bunch of flowers.

Each vase has a distinct characteristic (just like flowers do). Hence, putting a bunch of flowers in a vase results in a certain aesthetic value, expressed by an integer. The aesthetic values are presented in a table as shown below. Leaving a vase empty has an aesthetic value of 0.

		V A S E S
		1	2	3	4	5
Bunches	1 (azaleas)	7	23	-5	-24	16
	2 (begonias)	5	21	-4	10	23
	3 (carnations)	-21	5	-4	-20	20

According to the table, azaleas, for example, would look great in vase 2, but they would look awful in vase 4.

To achieve the most pleasant effect you have to maximize the sum of aesthetic values for the arrangement while keeping the required ordering of the flowers. If more than one arrangement has the maximal sum value, any one of them will be acceptable. You have to produce exactly one arrangement.

Input

The first line contains two numbers: F, V.
The following F lines: Each of these lines contains V integers, so that A_ij is given as the j^th number on the (i+1)^st line of the input file.

1 <= F <= 100 where F is the number of the bunches of flowers. The bunches are numbered 1 through F.
F <= V <= 100 where V is the number of vases.
-50 <= Aij <= 50 where Aij is the aesthetic value obtained by putting the flower bunch i into the vase j.

Output

The first line will contain the sum of aesthetic values for your arrangement.

Sample Input

3 5
7 23 -5 -24 16
5 21 -4 10 23
-21 5 -4 -20 20

Sample Output

题意：F束鲜花插入V个花瓶中不同的花插入不同的花瓶中能获得不同的美观值要求把i花插入j瓶时比i花编号大的花只能插在比j大的花瓶中求美观值最大；

解题思路：动态规划dp[i][j]表示将i花插入j瓶能获得的最大美观值；

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<vector>
#define MAXN 1010
#define inf 0x3f3f3f3f
using namespace std;
int dp[MAXN][MAXN],map[MAXN][MAXN];
int MAX(int a,int b){
	return a>b?a:b;
}
int main()
{
	int F,V,i,j,k;
	while(scanf("%d%d",&F,&V)!=EOF){
		for(i=1;i<=F;++i){
			for(j=1;j<=V;++j){
				scanf("%d",&map[i][j]);
			}
		}
		for(i=1;i<=F;++i){
			for(j=1;j<=V;++j){
				dp[i][j]=-inf;
			}
		}
		for(j=1;j<=V;++j)
			dp[1][j]=map[1][j];
		for(i=2;i<=F;++i){
			for(j=1;j<=V;++j){
				for(k=1;k<j;++k){
					dp[i][j]=MAX(dp[i][j],dp[i-1][k]+map[i][j]);
				}
			}
		}
		int ans=-inf;
		for(i=1;i<=V;++i){
			ans=MAX(ans,dp[F][i]);
		}
		printf("%d\n",ans);
	}
	return 0;
}