【POJ - 3616】Milking Time （贪心+dp）

题干：

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_houri ≤ N), an ending hour (starting_houri < ending_houri ≤ N), and a corresponding efficiency (1 ≤ efficiencyi ≤ 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_houri , ending_houri , and efficiencyi

Output

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

Sample Input

Sample Output

题目大意：

贝茜是一个勤劳的牛。事实上，她如此专注于最大化她的生产力，于是她决定安排下一个N（1≤N≤1,000,000）小时（方便地标记为0..N-1），以便她生产尽可能多的牛奶。

农民约翰有一个M（1≤M≤1,000）可能重叠的间隔列表，他可以在那里进行挤奶。每个区间我有一个起始小时（0≤starting_houri≤N），一个结束小时（starting_houri <ending_houri≤N），以及相应的效率（1≤efficiencyi≤1,000,000），表示他可以从中获取多少加仑的牛奶。贝西在那段时间。 Farmer John分别在开始时间和结束时间开始时开始和停止挤奶。在挤奶时，Bessie必须在整个间隔内挤奶。

尽管贝茜有其局限性。在任何间隔期间挤奶后，她必须休息R（1≤R≤N）小时才能再次开始挤奶。鉴于Farmer Johns的间隔清单，确定Bessie在N小时内可以产生的最大牛奶量。

一句话题意：

给奶牛挤奶,共m次可以挤,给出每次开始挤奶的时间st,结束挤奶的时间ed,还有挤奶的量ef,每次挤完奶要休息r时间,问最大挤奶量.

解题报告：

对于每一次挤奶,结束时间+=休息时间.

先把m次挤奶按照开始时间排个序,用f[i]表示挤完第i个时间段的奶以后的最大挤奶量,那么有:

f[i]=max(f[i],f[j]+(第i次挤奶.ef)) (1<=j<i&&(第j次挤奶).ed<=(第i次挤奶).st).

附上一年前写的垃圾代码Orz

这题一个点，一般这种题都是考虑贪心，从时间轴上去贪心，但是这题是dp，从第 i 个段去考虑。

AC代码：

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<queue>
#include<map>
#include<vector>
#include<set>
#include<string>
#include<cmath>
#include<cstring>
#define F first
#define S second
#define ll long long
#define pb push_back
#define pm make_pair
using namespace std;
typedef pair<int,int> PII;
const int MAX = 2e5 + 5;
typedef struct Node{
	int start;
	int end;
	int value;
} node;
int dp[1005];
bool cmp (const node & a,const node & b) {
	return a.start<b.start;
}
int main()
{
	int n,m,r;
	node cow[1005];
	cin>>n>>m>>r;
	for(int i = 1 ; i<=m; i++) {
		scanf("%d%d%d",&cow[i].start,&cow[i].end,&cow[i].value);
		cow[i].end+=r;
	}	
	sort(cow+1,cow+m+1,cmp);
	for(int i = 1 ; i<=m; i++) {
		dp[i]=cow[i].value;
	}	
	for(int i = 1; i<=m; i++) {
		for(int j = 1; j<=i; j++) {
			if(cow[i].start>=cow[j].end) {
				dp[i]=max(dp[j]+cow[i].value,dp[i]);
			}
			
		}
	}
	printf("%d\n",*max_element(dp+1,dp+m+1));
	return 0 ;
 } 
/*
12 4 2
1 2 8
10 12 19
3 6 24
7 10 31

*/