POJ3616Milking Time题解动态规划DP

Milking Time

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 2159		Accepted: 890

Description

Bessie is such a hard-working cow. In fact, she is so focused on maximizing her productivity that she decides to schedule her next N (1 ≤ N ≤ 1,000,000) hours (conveniently labeled 0..N-1) so that she produces as much milk as possible.

Farmer John has a list of M (1 ≤ M ≤ 1,000) possibly overlapping intervals in which he is available for milking. Each interval i has a starting hour (0 ≤ starting_hour_i ≤ N), an ending hour (starting_hour_i < ending_hour_i ≤ N), and a corresponding efficiency (1 ≤ efficiency_i ≤ 1,000,000) which indicates how many gallons of milk that he can get out of Bessie in that interval. Farmer John starts and stops milking at the beginning of the starting hour and ending hour, respectively. When being milked, Bessie must be milked through an entire interval.

Even Bessie has her limitations, though. After being milked during any interval, she must rest R (1 ≤ R ≤ N) hours before she can start milking again. Given Farmer Johns list of intervals, determine the maximum amount of milk that Bessie can produce in the N hours.

Input

* Line 1: Three space-separated integers: N, M, and R
* Lines 2..M+1: Line i+1 describes FJ's ith milking interval withthree space-separated integers: starting_hour_i , ending_hour_i , and efficiency_i

Output

* Line 1: The maximum number of gallons of milk that Bessie can product in the N hours

Sample Input

12 4 2
1 2 8
10 12 19
3 6 24
7 10 31

Sample Output

43

Source

USACO 2007 November Silver

 

 

状态：

先按结束时间排序

d[i]表示第i个区间和前面的区间组成的最优值

状态转移方程：

d[i]=max(d[j])+w[i].v       (w[i].s>=w[j].e+r)

最终结果是max{d[i]}

刚开始直接写的d[m]一直WA

w[0].e=-r

代码：

#include<cstdio> #include<algorithm> using namespace std; int m,r,i,j,ans,d[1005]; struct node {int s,e,v;}w[1005]; bool cmp(node a,node b) {return a.e<b.e;} int main() { scanf("%*d%d%d",&m,&r); w[0].e=-r; for(i=1;i<=m;i++) scanf("%d%d%d",&w[i].s,&w[i].e,&w[i].v); sort(w+1,w+m+1,cmp); for(i=1;i<=m;i++) { for(j=0;j<i;j++) if(w[i].s>=w[j].e+r) d[i]=max(d[i],d[j]+w[i].v); ans=max(ans,d[i]); } printf("%d/n",ans); }