Score Inflation_usaco3.1.2_dp

最新推荐文章于 2023-07-06 19:54:23 发布

原创最新推荐文章于 2023-07-06 19:54:23 发布 · 562 阅读

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#dp #c++ #usaco #完全背包

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本文介绍了一个USACO竞赛中的典型问题：如何在限定时间内通过选择不同难度级别的题目来最大化得分。文章提供了一种解决方案，即使用完全背包算法进行优化，并给出了具体的C++实现代码。

DESCRIPTION

The more points students score in our contests, the happier we here at the USACO are. We try to design our contests so that people can score as many points as possible, and would like your assistance.

We have several categories from which problems can be chosen, where a “category” is an unlimited set of contest problems which all require the same amount of time to solve and deserve the same number of points for a correct solution. Your task is write a program which tells the USACO staff how many problems from each category to include in a contest so as to maximize the total number of points in the chosen problems while keeping the total solution time within the length of the contest.

The input includes the length of the contest, M (1 <= M <= 10,000) (don’t worry, you won’t have to compete in the longer contests until training camp) and N, the number of problem categories, where 1 <= N <= 10,000.

Each of the subsequent N lines contains two integers describing a category: the first integer tells the number of points a problem from that category is worth (1 <= points <= 10000); the second tells the number of minutes a problem from that category takes to solve (1 <= minutes <= 10000).

Your program should determine the number of problems we should take from each category to make the highest-scoring contest solvable within the length of the contest. Remember, the number from any category can be any nonnegative integer (0, one, or many). Calculate the maximum number of possible points.

PROGRAM NAME: inflate

INPUT FORMAT

Line 1: M, N – contest minutes and number of problem classes
Lines 2-N+1: Two integers: the points and minutes for each class

OUTPUT FORMAT

A single line with the maximum number of points possible given the constraints.

ANALYSIS

完全背包的模板，套一套就好了
我也不是很懂刷这种题目的意义;-p

CODE

/*
ID:wjp13241
PROG:inflate
LANG:C++
*/
#include <stdio.h>
using namespace std;
int f[10101];
int w[10101],v[10101];
int max(int x,int y)
{
    return x>y?x:y;
}
int main()
{
    freopen("inflate.in","r",stdin);
    freopen("inflate.out","w",stdout);
    int n,m;
    scanf("%d%d",&n,&m);
    for (int i=1;i<=m;i++)
        scanf("%d%d",&v[i],&w[i]);
    for (int i=1;i<=m;i++)
        for (int j=w[i];j<=n;j++)
            f[j]=max(f[j],f[j-w[i]]+v[i]);
    printf("%d\n",f[n]);
    return 0;
}