MKBUDGET  Making A Budget
A company uses temporary employees (“temps”) to handle its varying workloads. By doing so, it avoids having to pay for benefits normally provided to its permanent employees. However, the company must pay an employment agency a fixed fee for each temp they hire, as well as paying the temp a fixed amount of severance pay when they are terminated – in addition, of course, to the monthly salary each temp receives. The company has a good understanding of when it needs temporary workers, and how many such workers it will require each month. Depending on the fee paid to the employment agency, the temporary worker’s salary, and the severance pay, it may make sense to retain an unneeded worker for one or more months if it’s known that they will be needed again in the future.
Let’s consider an example. Suppose we know that in March the company will need 10 temps, in April they’ll need 9, and in May they’ll need 11. Suppose a temp earns $500 per month, that the employment agency receives $400 for each temp hired, and $600 is paid as severance to each temp that is terminated. If the company employs just the minimum number of temps required, then their payments will be as follows (we ignore the cost of terminating all employees at the end of the last month):
The total cost to the company is $20,400. But suppose they did not terminate the unneeded temp at the end of March, but just let that person remain employed. They would then save $400 in employment agency fees (since they’d need to hire just one additional temp for May), $600 in severance pay, and only have to pay the temp worker $500, for an overall savings of $500.
In this problem you are given, as input, the number of months for which the company is to plan its temp worker budget, the cost of hiring and firing a temp worker, the temp worker’s monthly salary, and the required minimum number of workers needed each month. You are to determine the minimum cost to the company to have at least the required minimum number of workers on hand each month. Assume there are no temporary workers on hand before the first month, and that the cost of terminating the workers at the end of the last month is not to be included in the cost. You may assume that the planning interval will be no longer than 24 months, and the hiring cost, severance pay, and monthly salary for each temp worker is greater than zero.
Input
There will be multiple cases to consider. The input for each case begins with an integer N, the number of months for which planning is required (never larger than 24). This is followed by three integers giving the cost of hiring a worker, the worker’s monthly salary, and the severance pay for a terminated worker. Finally there will appear N integers giving the required minimum number of workers needed in each month. The last case will be followed by a zero.
Output
For each input case, display the case number (1, 2, …) and the minimum cost to the company. Use the format shown in the examples below.
Example
Input: 3 400 500 600 10 9 11 8 400 600 600 11 9 10 14 9 9 13 15 0 Output: Case 1, cost = $19900 Case 2, cost = $66600
Added by:  Camilo Andrés Varela León 
Date:  20071007 
Time limit:  0.188s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel Pentium G860 3GHz) 
Languages:  All except: ERL JS NODEJS PERL 6 SCM chicken VB.net 
Resource:  North Central North America Regional Programming Contest  2003 
hide comments
Lai Manh Tuan:
20150408 05:16:23
Just got AC but do we really need the upper bound of the number of employees each month ? Why doesn't the PS specify it ? 

Sachin Malhotra:
20150129 08:38:25
To recurse is TLE, to memoize is AC ;) 

srikar:
20141024 16:28:09
Last edit: 20141024 16:28:43 

bony2023:
20140923 19:53:18
Recursion is divine. ;) 

[deleted]:
20140730 17:16:50
PLEASE specify the limits for the question. The company's final amount can exceed 1000000 otherwise it will show WA and no. of workers can be less than 30. Last edit: 20140730 17:18:27 

IKKA:
20140726 16:47:49
use long long 

:
20140716 18:27:51
I made mistake between captalized 'Case' with 'case' and had to sub 5 times :3 this is crazy @@!


paras meena:
20140604 14:34:53
0.00 =D 

Martin Radev:
20140428 16:52:39
Hmm, I assumed at first that the number of employees is 1024, but got a TLE. Then I switched to 300 and it passed it. My solution is O(n^2) (with a lower constant factor though). What is your running time? 

parbays:
20140104 16:15:50
I got it AC, but din find it making use of dp states...avg algorithmic prob. 