BZOJ1649: [Usaco2006 dec]cow Roller Coaster Backpack DP

1649: [Usaco2006 dec]cow Roller CoasterTime Limit:5 Sec Memory limit:64 MB submit:584 solved:302 [Submit][status][discuss] Description

The cows is building a roller coaster! They want your help to design as fun a roller coaster as possible and while keeping to the budget. The roller coaster'll be built to 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 <=) different interchangable components. Each component I have a fixed length WI (1 <= wi <= L). Due to varying terrains, each component I can is 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, the end of each C Omponent (except) is the start of the next component. Each component I have 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 was 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. The cows are going to build a roller coaster track. They want you to help find the most interesting, yet budget-compliant option. The track of the    roller coaster is connected to the end of a number of rails and extends from x=0 to X=l (1≤l≤1000). Existing N (1≤n≤10000) root rails, beginning Xi (0≤XI≤L-&NBSP;WI) of each rail, length Wi (l≤wi≤l), interesting index Fi (1≤fi≤1000000), cost Ci (l≤ci≤1000) are known. Please determine an optimal scheme that makes the most interesting index of the selected rails and the sum of the costs not exceeding B (1≤b≤1000).Input

* 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. Line 1th enters L,n,b, next N lines, four integers per line xi,wi,fi,ci. Output

* Line 1: A single integer, that's the maximum fun value, a roller-coaster can has while staying within the budget an D meeting All of the other constraints. If It is not possible to build a roller-coaster within budget, output-1.

Sample Input 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


Sample Output 17
Select 3rd, 5th and 6th rail : first Sort by starting point, the same starting point according to the length of the rails f[i][j], the front length of the railway with J can be paved for the cost of the maximum value of the interesting index

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
#define LL Long long
using namespace std;
struct Node{int s,c,w,f;} A[10005];
int l,n,mx;
ll f[1005][1005];
BOOL CMP (Node A,node b)
{
	if (A.S==B.S) return a.w<b.w;
	Return a.s<b.s;
}
int main ()
{
    scanf ("%d%d%d", &l,&n,&mx);
    for (int i=1;i<=n;i++) scanf ("%d%d%d%d", &a[i].s,&a[i].w,&a[i].f,&a[i].c);
    Sort (a+1,a+n+1,cmp);
    memset (F,-1,sizeof (f));
    f[0][0]=0;
    for (int i=1;i<=n;i++)
    {
    	int e=a[i].s+a[i].w;
    	for (int j=mx;j>=a[i].c;j--)
		if (f[a[i].s][j-a[i].c]>=0)
		F[e][j]=max (f[e][j],f[a[i].s][j-a[i].c]+ A[I].F);
    }
    ll Ans=-1;
    for (int i=0;i<=mx;i++) Ans=max (Ans,f[l][i]);
    printf ("%lld\n", ans);
}
The first I position spends the maximum fun value that J can get