C - Half and Half
Time limit : 2sec / Memory limit : 256MB
Score : 300 points
Problem Statement
"Pizza At", a fast food chain, offers three kinds of pizza: "A-pizza", "B-pizza" and "AB-pizza". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively.
Nakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.
Constraints
- 1≤A,B,C≤5000
- 1≤X , Y≤105
- All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C X Y
Output
Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas.
Sample Input 1
1500 2000 1600 3 2
Sample Output 1
7900
It is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.
Sample Input 2
1500 2000 1900 3 2
Sample Output 2
8500
It is optimal to directly buy three A-pizzas and two B-pizzas.
Sample Input 3
1500 2000 500 90000 100000
Sample Output 3
100000000
It is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine.
After reading the question, I feel that it should be very good, and the last example should be the pit of this question.
I used the dp method.
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
//C question
using namespace std;
int dp[100010];
int main()
{
int A,B,C ,X,Y,n,m,ans;int flag=0;
scanf("%d %d %d %d %d",&A,&B,&C,&X,&Y);
if(X>Y){
n =Y;flag=1;
m=X;
}
if(X<Y){
n=X;flag=2;
m=Y;
}
if(X==Y){
n=X;
}
for(int i= 1;i<=n;i++){
dp[i]=min(dp[i-1]+A+B,dp[i-1]+2*C);
}//If there are two pizza requirements If they are not the same, first find the minimum amount of money in the same part
if(flag!=0){//Compare the extra part separately to see which strategy has less money
if(flag==1){
for(int j=n+1;j<=m;j++){
dp[j]=min(dp[j-1]+A,dp[j-1]+2*C);
}
ans=dp[m];
}
if(flag==2){
for(int j=n+1;j<=m;j++){
dp[j]=min(dp[j-1]+B,dp[j-1]+2*C);
}
ans=dp[m];
}
}
else ans=dp[n];
printf("%d\n",ans);
return 0;
}