Space Elevator POJ 2392(多重背包dp)

原题

题目链接

题目分析

多重背包题,在放入的时候需要按a的大小排序.定义dp[i][j]为前i个积木凑成j高度,第i个物品最多剩下多少,然后j从0遍历到a[i],dp初始化为-1,dp[0][0]=0.更新方式跟多重背包完全一样,if(dp[i-1][j]!=-1) dp[i][j]=c[i];else if(j>=h[i]&&dp[i][j-h[i]]>0) dp[i][j]=dp[i][j-h[i]]-1;由更新方向可知可以状压,把第一维压掉,第二维j从小到大遍历即可.最后从dp数组中找一个最大的j即为答案.

代码

#include <iostream>
#include <algorithm>
#include <utility>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <map>
#include <set>

using namespace std;
typedef long long LL;
const int INF_INT=0x3f3f3f3f;
const LL INF_LL=0x3f3f3f3f3f3f3f3f;

struct N
{
    int h,a,c;
}block[500];

bool cmp(N x,N y)
{
    return x.a<y.a;
}

int dp[50000];

int main()
{
//    freopen("black.in","r",stdin);
//    freopen("black.out","w",stdout);
    int k;
    cin>>k;
    for(int i=1;i<=k;i++) cin>>block[i].h>>block[i].a>>block[i].c;
    sort(block+1,block+1+k,cmp);
//    for(int i=1;i<=k;i++) printf("block %d h=%d a=%d c=%d\n",i,block[i].h,block[i].a,block[i].c);
    for(int j=0;j<=block[k].a;j++) dp[j]=-1;
    for(int i=1;i<=k;i++)
    {
        dp[0]=block[i].c;
        for(int j=1;j<=block[i].a;j++)
        {
            if(dp[j]!=-1) dp[j]=block[i].c;
            else if(j>=block[i].h&&dp[j-block[i].h]>0) dp[j]=dp[j-block[i].h]-1;
        }
//        for(int j=0;j<=block[].a;j++) printf("dp %d %d=%d\n",i,j,dp[j]);
    }
    int ans=block[k].a;
    while(dp[ans]==-1) ans--;
    cout<<ans<<endl;
    return 0;
}