1740: [Usaco2005 mar]Yogurt factory 奶酪工厂

2022-07-12 11:05:48

1740: [Usaco2005 mar]Yogurt factory 奶酪工厂

Time Limit: 5 Sec Memory Limit: 64 MB
Submit: 119 Solved: 100
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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.

牛们收购了一个奶酪工厂,接下来的N个星期里，牛奶价格和劳力价格不断起伏．第i周，生产一个单位奶酪需要Ci(1≤Ci≤5000)便士．工厂有一个货栈，保存一单位奶酪，每周需要S(1≤S≤100)便士，这个费用不会变化．货栈十分强大，可以存无限量的奶酪，而且保证它们不变质．工厂接到订单，在第i周需要交付Yi(0≤Yi≤104)单位的奶酪给委托人．第i周刚生产的奶酪，以及之前的存货，都可以作为产品交付．请帮牛们计算这段时间里完成任务的最小代价．

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.

第1行输入两个整数N和S．接下来N行输入Ci和Yi．

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.

输出最少的代价．注意，可能超过32位长整型．

Sample Input

4 5
88 200
89 400
97 300
91 500

Sample Output

126900

第1周生产200单位奶酪并全部交付；第2周生产700单位，交付400单位，有300单位；第3周交
付300单位存货．第4周生产并交付500单位．

HINT

Source

Gold

题解：很经典的递推题（根本算不上DP，甚至有几分贪心的味道在里面），第五次见到了，不多说了，直接上代码（HansBug：难以想象这种题居然上usaco金组= =）

 /**************************************************************

     Problem:

     User: HansBug

     Language: Pascal

     Result: Accepted

     Time: ms

     Memory: kb

 ****************************************************************/

 var

    i,j,k,l,m,n:longint;

    ans:int64;

 function min(x,y:longint):longint;

          begin

               if x<y then min:=x else min:=y;

          end;

 begin

      readln(n,m);

      l:=maxlongint-m;

      for i:= to n do

          begin

               readln(j,k);

               l:=min(l+m,j);

               ans:=ans+int64(l)*int64(k);

          end;

      writeln(ans);

      readln;

 end.

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