HDU 3466 Proud Merchants

Posted 2020-10-04 一蓑烟雨任生平

Proud Merchants

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/65536 K (Java/Others)
Total Submission(s): 6981    Accepted Submission(s): 2916

Problem Description

Recently, iSea went to an ancient country. For such a long time, it was the most wealthy and powerful kingdom in the world. As a result, the people in this country are still very proud even if their nation hasn’t been so wealthy any more.
The merchants were the most typical, each of them only sold exactly one item, the price was Pi, but they would refuse to make a trade with you if your money were less than Qi, and iSea evaluated every item a value Vi.
If he had M units of money, what’s the maximum value iSea could get?

Input

There are several test cases in the input.

Each test case begin with two integers N, M (1 ≤ N ≤ 500, 1 ≤ M ≤ 5000), indicating the items’ number and the initial money.
Then N lines follow, each line contains three numbers Pi, Qi and Vi (1 ≤ Pi ≤ Qi ≤ 100, 1 ≤ Vi ≤ 1000), their meaning is in the description.

The input terminates by end of file marker.

Output

For each test case, output one integer, indicating maximum value iSea could get.

Sample Input

2 10 10 15 10 5 10 5 3 10 5 10 5 3 5 6 2 7 3

 

Sample Output

5 11

 

Author

iSea @ WHU

 

Source

2010 ACM-ICPC Multi-University Training Contest（3）——Host by WHU

 

Recommend

zhouzeyong   |   We have carefully selected several similar problems for you:  3460 3463 3468 3467 3465 

思路：

与顺序有关的01背包。初看之下似乎和普通背包差不多，判容量大于q时才装。但是这会出大问题，如果一个物品p = 5,q = 7,一个物品p = 5,q = 9，如果先算第一个,那么当次只有7,8...m可以进行状态转移，装第二个物品的时候9,10..m进行转移，第二个物品转移就可以借用第一个物品的那些个状态，而第二个物品先转移，第一个再转移则不能。当然，还有价格有关，当限制一样价格不同时顺序就影响结果。一种组合的排序策略--限制又小价格又贵的先选，也就是q-p小的先选。为什么这样呢？A：p1,q1 B: p2,q2，先选A，则至少需要p1+q2的容量，而先选B则至少需要p2+q1，如果p1+q2>p2+q1，那么要选两个的话的就要先选A再选B，公式可换成q1-p1 < q2-p2，就按这样的方法排序最后的顺序就是最优的顺序。

该题要确保P[i]-Q[i]小的先被”挑选“，差值越小使用它的价值越大(做出的牺牲越小).

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int n,m,f[5050];
struct nond{
    int p,q,v;
}num[550];
int cmp(nond a,nond b){
    return a.q-a.p<b.q-b.p;
}
int main(){
    while(scanf("%d%d",&n,&m)!=EOF){
        for(int i=1;i<=n;i++)
            scanf("%d%d%d",&num[i].p,&num[i].q,&num[i].v);
        sort(num+1,num+1+n,cmp);
        memset(f,0,sizeof(f));
        for(int i=1;i<=n;i++)
            for(int j=m;j>=num[i].q;j--)
                f[j]=max(f[j],f[j-num[i].p]+num[i].v);
        printf("%d\n",f[m]);
    }
}