多重背包

 

 

Description

The cows are going to space!  They plan to achieve orbit by building a sort of space elevator: a giant tower of blocks.  They have K (1 <= K <= 400) different types of blocks with which to build the tower.  Each block of type i has height h_i (1 <= h_i <= 100) and is available in quantity c_i (1 <= c_i <= 10).  Due to possible damage caused by cosmic rays, no part of a block of type i can exceed a maximum altitude a_i (1 <= a_i <= 40000).
Help the cows build the tallest space elevator possible by stacking blocks on top of each other according to the rules.

Input

* Line 1: A single integer, K
* Lines 2..K+1: Each line contains three space-separated integers: h_i, a_i, and c_i. Line i+1 describes block type i.

Output

* Line 1: A single integer H, the maximum height of a tower that can be built

Sample Input

3
7 40 3
5 23 8
2 52 6

Sample Output

48

Hint

OUTPUT DETAILS:
From the bottom: 3 blocks of type 2, below 3 of type 1, below 6 of type 3.  Stacking 4 blocks of type 2 and 3 of type 1 is not legal, since the top of the last type 1 block would exceed height 40.

#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
struct Node
{
    int h,c;
    int lim;
}node[401];
int dp[50000];
int H;
void ZeroOnePack(int cost,int weight,int lim)
{
    for(int i=lim;i>=cost;i--)
       dp[i]=max(dp[i],dp[i-cost]+weight);
}

void CompletePack(int cost,int weight,int lim)
{
    for(int i=cost;i<=lim;i++)
      dp[i]=max(dp[i],dp[i-cost]+weight);
}

void MultiplePack(int cost,int weight,int amount,int lim)
{
    if(cost*amount>=lim)
        CompletePack(cost,weight,lim);//完全背包问题
    else
    {
        for(int k=1;k<amount;)
        {
            ZeroOnePack(k*cost,k*weight,lim);//0-1背包问题
            amount-=k;
            k=k*2;//二进制思想
        }
        ZeroOnePack(amount*cost,amount*weight,lim);
    }
}

int cmp(Node a,Node b)
{
    return a.lim<b.lim;
}
int main()
{
    int n;

    while(cin>>n)
    {
        H=0;
        for(int i=0;i<n;i++)
        {
            cin>>node[i].h>>node[i].lim>>node[i].c;
        
            if(node[i].lim>H)
                H=node[i].lim;//H用来记录最大高度
        }
        for(int i=0;i<=H;i++)
            dp[i]=0;
        sort(node,node+n,cmp);//排序后变成一般的多重背包问题

        for(int i=0;i<n;i++)
          MultiplePack(node[i].h,node[i].h,node[i].c,node[i].lim);
        int ans=0;

        for(int i=0;i<=H;i++)ans=max(ans,dp[i]);//这个过程一定要
          cout<<ans<<endl;
    }
    return 0;
}