Poj 2393 Yogurt factory【贪心】

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Yogurt factory

Time Limit:

1000MS

Memory Limit:

65536K

Total Submissions:

8497

Accepted:

4346

Description

The cows have purchased a yogurt factory that makes world-famous Yucky Yogurt. Over the next N (1 <= N <= 10,000) weeks, the price of milk and labor will fluctuate weekly such that it will cost the company C_i (1 <= C_i <= 5,000) cents to produce one unit of yogurt in week i. Yucky’s factory, being well-designed, can produce arbitrarily many units of yogurt each week.

Yucky Yogurt owns a warehouse that can store unused yogurt at a constant fee of S (1 <= S <= 100) cents per unit of yogurt per week. Fortuitously, yogurt does not spoil. Yucky Yogurt’s warehouse is enormous, so it can hold arbitrarily many units of yogurt.

Yucky wants to find a way to make weekly deliveries of Y_i (0 <= Y_i <= 10,000) units of yogurt to its clientele (Y_i is the delivery quantity in week i). Help Yucky minimize its costs over the entire N-week period. Yogurt produced in week i, as well as any yogurt already in storage, can be used to meet Yucky’s demand for that week.

Input

* Line 1: Two space-separated integers, N and S.

* Lines 2..N+1: Line i+1 contains two space-separated integers: C_i and Y_i.

Output

* Line 1: Line 1 contains a single integer: the minimum total cost to satisfy the yogurt schedule. Note that the total might be too large for a 32-bit integer.

Sample Input

4 5
88 200
89 400
97 300
91 500

Sample Output

126900

Hint

OUTPUT DETAILS:

In week 1, produce 200 units of yogurt and deliver all of it. In week 2, produce 700 units: deliver 400 units while storing 300 units. In week 3, deliver the 300 units that were stored. In week 4, produce and deliver 500 units.

题意:

有一个奶酪工厂,给出这个工厂每天加工每个奶酪需要的价格,以及每天的需求量,另外,奶酪也可以存放在仓库里(竟然放不坏!),给出每个奶酪存放一天需要的价格,问,这些生产任务全部完成,最少的花费是多少

题解:

刚开始做这道题的时候,感觉自己想的太多了,需要对每天都计算是当天生产最划算还是其他天生产最划算,连优先队列都用上了………

后来写着写着发现有更简便的方法了,完全可以在线性时间内完成运算!

贪心策略:

1,第一天的奶酪只能当天生产,这是无法贪心选取的,暂时假设以后的奶酪全在这一天生产

2,第二天的话,就要考虑是前一天生产存放到第二天还是第二天再生产呢?这就需要比较了,

如果当天生产比较省钱,那么就当天生产!而且假设以后的所有奶酪都在这天生产的!为何这样呢?


因为题目给出的奶酪存放的需要的价格完全一样!(细细想想看)


3,哪天生产更廉价,就哪天生产,这就要求对每天进行编号了。这样才能进行定量计算和查找最优解


另外注意,用64位的整数,个人一个马虎,WA 了一次,好在对自己的贪心思路比较自信,改了一下,果断提交,A掉!

/*
http://blog.csdn.net/liuke19950717
*/
#include<stdio.h>
#include<string.h>
using namespace std;
typedef long long ll;
struct node 
{
	ll p,num,id;//价格,数量,编号
}x[10005];
ll slove(ll n,ll s)
{
	ll ans=x[0].p*x[0].num,kase=0;	
	for(ll i=1;i<n;++i)
	{
		ll tp=x[kase].p+s*(i-x[kase].id),cur=x[i].p;//一个是之前生产的实际价格,一个是当天生产的价格
		if(tp<cur)//如果之前生产划算 
		{
			ans+=tp*x[i].num; 
		}
		else
		{
			ans+=cur*x[i].num;
			kase=i;
		}
	}
	return ans;
}
int main()
{
	ll n,s;
	while(~scanf("%lld%lld",&n,&s))
	{
		for(ll i=0;i<n;++i)
		{
			scanf("%lld%lld",&x[i].p,&x[i].num);
			x[i].id=i;
		}
		printf("%lld\n",slove(n,s));
	}
	return 0;
} 



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