BZOJ 1740: [Usaco2005 mar]Yogurt factory 奶酪工厂 贪心 + 问题转化
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.
题解:
太经典了.
不难贪心证明,每次只可能用同一价格的存储方式.
我们只需维护一个 $minv$ ,表示价格最小值.
到下一周时,用 $minv[cur-1]$ 与 $cur_cost$ 作比较,并更新 $minv[i]$ 即可.
甚至都不用数组,几个变量即可搞定.
#include<bits/stdc++.h>
#define setIO(s) freopen(s".in","r",stdin)
#define ll long long
using namespace std;
int main()
{
// setIO("input");
int n;
ll s,c,y,cur=0,ans=0;
scanf("%d%lld",&n,&s);
scanf("%lld%lld",&c,&y);
ans+=c*y, cur=c;
for(int i=2;i<=n;++i)
{
scanf("%lld%lld",&c,&y);
cur=min(cur+s,c);
ans+=cur*y;
}
printf("%lld\n",ans);
return 0;
}
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