POJ3616 Milking Time —— DP

题目链接：http://poj.org/problem?id=3616

Milking Time

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 10819		Accepted: 4556

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

 

 

 

题解：

经典的类LIS题型（最长上升子序列）。

类似的题：HDU1160

 

 

代码如下：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <string>
#include <set>
#define ms(a,b) memset((a),(b),sizeof((a)))
using namespace std;
typedef long long LL;
const double EPS = 1e-8;
const int INF = 2e9;
const LL LNF = 2e18;
const int MAXN = 1e3+10;

struct node
{
    int st, en, val;
    bool operator<(const node &x)const{
        return st<x.st;
    }
}a[MAXN];
int dp[MAXN];
int N, M, R;

int main()
{
    while(scanf("%d%d%d", &N, &M, &R)!=EOF)
    {
        for(int i = 1; i<=M; i++)
            scanf("%d%d%d", &a[i].st, &a[i].en, &a[i].val);

        sort(a+1, a+1+M);
        memset(dp, 0, sizeof(dp));
        for(int i = 1; i<=M; i++)
        for(int j = 0; j<i; j++)
            if(j==0 || a[i].st>=a[j].en+R )
                dp[i] = max(dp[i], dp[j] + a[i].val);

        int ans = -INF;
        for(int i = 1; i<=M; i++)
            ans = max(ans, dp[i]);
        printf("%d
", ans);
    }
}