洛谷 P2925 [USACO08DEC]干草出售Hay For Sale

题目描述

Farmer John suffered a terrible loss when giant Australian cockroaches ate the entirety of his hay inventory, leaving him with nothing to feed the cows. He hitched up his wagon with capacity C (1 <= C <= 50,000) cubic units and sauntered over to Farmer Don’s to get some hay before the cows miss a meal.

Farmer Don had a wide variety of H (1 <= H <= 5,000) hay bales for sale, each with its own volume (1 <= V_i <= C). Bales of hay, you know, are somewhat flexible and can be jammed into the oddest of spaces in a wagon.

FJ carefully evaluates the volumes so that he can figure out the largest amount of hay he can purchase for his cows.

Given the volume constraint and a list of bales to buy, what is the greatest volume of hay FJ can purchase? He can’t purchase partial bales, of course. Each input line (after the first) lists a single bale FJ can buy.

约翰遭受了重大的损失：蟑螂吃掉了他所有的干草，留下一群饥饿的牛．他乘着容量为C(1≤C≤50000)个单位的马车，去顿因家买一些干草． 顿因有H(1≤H≤5000)包干草，每一包都有它的体积Vi(l≤Vi≤C).约翰只能整包购买，

他最多可以运回多少体积的干草呢？

输入输出格式

输入格式：

Line 1: Two space-separated integers: C and H

Lines 2..H+1: Each line describes the volume of a single bale: V_i

输出格式：

Line 1: A single integer which is the greatest volume of hay FJ can purchase given the list of bales for sale and constraints.

输入输出样例

输入样例#1：

7 3

2

6

5

输出样例#1：

7

说明

The wagon holds 7 volumetric units; three bales are offered for sale with volumes of 2, 6, and 5 units, respectively.

Buying the two smaller bales fills the wagon.

【分析】

01背包

【代码】

//洛谷 P2925 [USACO08DEC]干草出售Hay For Sale
#include<stack>
#include<queue>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define fo(i,j,k) for(i=j;i<=k;i++)
using namespace std;
int n,m,v[5005];
bool dp[50005];
int main()
{
int i,j;
scanf("%d%d",&m,&n);
fo(i,1,n) scanf("%d",&v[i]);
dp[0]=1;
fo(i,1,n)
for(j=m;j>=v[i];j--)
dp[j]=dp[j]|dp[j-v[i]];
for(j=m;j>=1;j--) if(dp[j]) break;
printf("%d\n",j);
return 0;
}