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  • 洛谷P2854 [USACO06DEC]牛的过山车Cow Roller Coaster

    P2854 [USACO06DEC]牛的过山车Cow Roller Coaster

    题目描述

    The cows are building a roller coaster! They want your help to design as fun a roller coaster as possible, while keeping to the budget.

    The roller coaster will be built on a long linear stretch of land of length L (1 ≤ L ≤ 1,000). The roller coaster comprises a collection of some of the N (1 ≤ N ≤ 10,000) different interchangable components. Each component i has a fixed length Wi (1 ≤ Wi ≤ L). Due to varying terrain, each component i can be only built starting at location Xi (0 ≤ Xi ≤ L - Wi). The cows want to string together various roller coaster components starting at 0 and ending at L so that the end of each component (except the last) is the start of the next component.

    Each component i has a "fun rating" Fi (1 ≤ Fi ≤ 1,000,000) and a cost Ci (1 ≤ Ci ≤ 1000). The total fun of the roller coster is the sum of the fun from each component used; the total cost is likewise the sum of the costs of each component used. The cows' total budget is B (1 ≤ B ≤ 1000). Help the cows determine the most fun roller coaster that they can build with their budget.

    奶牛们正打算造一条过山车轨道.她们希望你帮忙,找出最有趣,但又符合预算 的方案. 过山车的轨道由若干钢轨首尾相连,由x=0处一直延伸到X=L(1≤L≤1000)处.现有N(1≤N≤10000)根钢轨,每根钢轨的起点 Xi(0≤Xi≤L- Wi),长度wi(l≤Wi≤L),有趣指数Fi(1≤Fi≤1000000),成本Ci(l≤Ci≤1000)均己知.请确定一 种最优方案,使得选用的钢轨的有趣指数之和最大,同时成本之和不超过B(1≤B≤1000).

    输入输出格式

    输入格式:

    Line 1: Three space-separated integers: L, N and B.

    Lines 2..N+1: Line i+1 contains four space-separated integers, respectively: Xi, Wi, Fi, and Ci.

    输出格式:

    Line 1: A single integer that is the maximum fun value that a roller-coaster can have while staying within the budget and meeting all the other constraints. If it is not possible to build a roller-coaster within budget, output -1.

    输入输出样例

    输入样例#1:
    5 6 10
    0 2 20 6
    2 3 5 6
    0 1 2 1
    1 1 1 3
    1 2 5 4
    3 2 10 2
    输出样例#1:
    17

    说明

    Taking the 3rd, 5th and 6th components gives a connected roller-coaster with fun value 17 and cost 7. Taking the first two components would give a more fun roller-coaster (25) but would be over budget.

    /*
        看到本题不难想到二维费用的背包f[i][j]=max{f[i-a[i].len][j-a[i].w]+a[i].v},但是题目要求所有铁轨首尾相连,所以需要对a[]按起点排个序,剩下的就和上面的方程很像了
    */
    #include<iostream>
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    using namespace std;
    int L,N,B,f[1010][1010],ans=-1;
    struct node{
        int s,t,w,v;
    }a[10010];
    bool cmp(node x,node y){return x.s<y.s;}
    int main(){
        memset(f,-1,sizeof(f));
        f[0][0]=0;
        scanf("%d%d%d",&L,&N,&B);
        for(int i=1;i<=N;i++){
            scanf("%d%d%d%d",&a[i].s,&a[i].t,&a[i].v,&a[i].w);
            a[i].t+=a[i].s;
        }
        sort(a+1,a+N+1,cmp);
        for(int i=1;i<=N;i++){
            for(int j=B;j>=a[i].w;j--){
                if(f[a[i].s][j-a[i].w]>=0){
                    f[a[i].t][j]=max(f[a[i].t][j],f[a[i].s][j-a[i].w]+a[i].v);
                }
            }
        }
        for(int i=1;i<=B;i++)ans=max(ans,f[L][i]);
        printf("%d",ans);
    }
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  • 原文地址:https://www.cnblogs.com/thmyl/p/7568978.html
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