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   Problem Statement  

 Problem Statement for TheProgrammingContestDivOne

Problem Statement

    Farmer John and Fox Brus are participating in a programming contest as a team.



The duration of the contest is T minutes and they are given N tasks. Solutions can be submitted at any time during the contest, including exactly T minutes after the start of the contest. If they solve the i-th task immediately after the start of the contest, they get maxPoints[i] points and it decreases by pointsPerMinute[i] points per minute. In other words, if they solve the i-th task t minutes after the start of the contest, they will get maxPoints[i] - t * pointsPerMinute[i] points. It takes them requiredTime[i] minutes to solve the i-th task.



Return the maximal points they can get.
 

Definition

    
Class:TheProgrammingContestDivOne
Method:find
Parameters:int, int[], int[], int[]
Returns:int
Method signature:int find(int T, int[] maxPoints, int[] pointsPerMinute, int[] requiredTime)
(be sure your method is public)
    
 

Constraints

-T will be between 1 and 100,000, inclusive.
-maxPoints will contain between 1 and 50 elements, inclusive.
-maxPoints, pointsPerMinute and requiredTime will contain the same number of elements.
-Each element of maxPoints will be between 1 and 100,000, inclusive.
-Each element of pointsPerMinute will be between 1 and 100,000, inclusive.
-Each element of requiredTime will be between 1 and 100,000, inclusive.
 

Examples

0)
    
74
{502}
{2}
{47}
Returns: 408
They can solve the task 47 minutes after the start of the contest. They will get 502 - 2 * 47 = 408 points.
1)
    
40000
{100000, 100000}
{1, 100000}
{50000, 30000}
Returns: 0
They don't have time to solve the first task. If they solve the second task, they will get negative points (100000 - 100000 * 30000 = -2999900000 points), so they shouldn't solve it.
2)
    
75
{250, 500, 1000}
{2, 4, 8}
{25, 25, 25}
Returns: 1200
  • First, they can solve the third task 25 minutes after the start of the contest. They get 1000 - 8 * 25 = 800 points.
  • Second, they can solve the second task 50 minutes after the start of the contest. They get 500 - 4 * 50 = 300 points.
  • Third, they can solve the first task 75 minutes after the start of the contest. They get 250 - 2 * 75 = 100 points.
In total, they can get 800 + 300 + 100 = 1200 points.
3)
    
30
{100, 100, 100000}
{1, 1, 100}
{15, 15, 30}
Returns: 97000
The best strategy is solving only the third task.

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This problem was used for:
       Single Round Match 502 Round 1 - Division I, Level Two