POJ 2393:Yogurt Factory

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

4 588 20089 40097 30091 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.

How to solve?

        Think about the yogurt needed in each week: it have to be either produced in the current week or several weeks ago. In other word, the price of yogurt in a week could be used to "update" the succeeding several weeks. So you may think that it is a double loop.

        Actually, it's not . A single loop is enough. The price of each week is only responsible for updating the next week, for the updated price , which is represented by a temporary integer variable ,could continue to update the price of its adjacent next week.

          Here is the Accepted code [1]:

#include<iostream>#include<fstream>#include<cstdio>#include<cstring>#include<cstdlib>#include<cmath>#include<algorithm>#include<complex>#include<set>#include<map>#include<list>#include<vector>#include<deque>using namespace std;typedef long long ll;const int INF=0x3f3f3f3f;const int Mod=1e9+7;const double eps=1e-7;int main(){int N,S;scanf("%d%d",&N,&S);int *C,*Y;C=(int*)malloc((N+1)*sizeof(int));Y=(int*)malloc((N+1)*sizeof(int));C[0]=Y[0]=0;for(int i=1;i<=N;i++){scanf("%d%d",C+i,Y+i);}ll ans=0;int tmp=INF;for(int i=1;i<=N;i++){tmp+=S;tmp=min(tmp,C[i]);ans+=tmp*Y[i];}cout<<ans<<endl;return 0;}

Reference:

#9231912 UnderSilence's solution for [POJ-2393]