POJ-3616_Milking Time

Milking Time

Time Limit: 1000MS Memory Limit: 65536K

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_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 N hours

Sample Input

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

Sample Output

43

题意：给予M时间区间且每个区间可以挤多少牛奶，每工作一个时间段需要休息R个小时，问在N个小时最多可以得到多少牛奶。
题解：一个上升序列问题的变形。

#include <algorithm>
#include <iostream>
#include <stdio.h>
#include <cstdlib>
#include <cstring>
#include <cmath>

using namespace std;

const int maxn = 1050;

struct node
{
    int be,en,w;
}s[maxn];
int dp[maxn];

bool cmp(node a,node b)
{
    if(a.be==b.be)
        return a.en<b.en;
    return a.be < b.be;
}

int main()
{
    int n,m,i,j,r,Max,mmax;
    scanf("%d%d%d",&r,&m,&n);
    for(i=0;i<m;i++)
        scanf("%d%d%d",&s[i].be,&s[i].en,&s[i].w);
    sort(s,s+m,cmp);
    Max = 0;
    for(i=0;i<m;i++)
    {
        mmax = 0;
        for(j=0;j<i;j++)
        {
            if(s[j].en+n<=s[i].be&&mmax<dp[j])
                mmax = dp[j];
        };
        dp[i] = mmax + s[i].w;
        Max = max(Max,dp[i]);
    }
    printf("%d\n",Max);
    return 0;
}