Asked in: JPMORGAN
Image of the Question
All Testcases Passed ✔
Solution
import bisect
def getResources(inc, dec, performance):
arr = list(set(performance))
arr.sort()
// ... rest of solution available after purchaseExplanation
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To solve this problem, start by fully understanding the ranking mechanism for servers based on their performance metrics. Each server's rank is defined by the count of distinct performance values that are greater than or equal to its own performance. This means that higher performance values correspond to lower ranks numerically, since ranks decrease as performance values increase.
The first challenge is to determine the rank of each server efficiently. Notice that the rank is based on distinct performance values, not just raw counts. So, if multiple servers have the same performance, they share the same rank. For example, if the performance values are [3, 2, 4, 3, 5, 5], the distinct sorted performances are [5, 4, 3, 2], and the rank of a performance value is its position in this sorted unique list.
To approach this, begin by extracting the unique performance values from the input array and sorting them in descending order (from highest to lowest). This gives you a sorted list of distinct performance values, each corresponding to a unique rank. The highest performance value will have rank 1, the second highest will have rank 2, and so on.
Next, for each server's performance, determine its rank by finding its position in this sorted list. This can be done efficiently by mapping each distinct performance value to its rank using a dictionary or hash map. This mapping will allow you to get the rank of any server’s performance in constant time.
Once you have the rank for each server, the problem gives a formula to calculate resource allocation:
resource_allocation = inc × (n + 1 - rank) - dec × rank
Here, n is the total number of servers, inc and dec are constants provided as input, and rank is the server’s rank calculated earlier.
Interpreting this formula, you can see that the resource allocation depends on the rank of the server in a way that balances two terms: a positive term that increases with decreasing rank (i.e., better performance), and a negative term that increases with the rank. The intuition is that servers with better performance (lower rank values) receive higher increments and lower decrements, optimizing resource allocation accordingly.
The main steps to solve the problem are:
1. Extract unique performance values from the performance array.
2. Sort these unique values in descending order.
3. Map each unique performance value to its rank based on the sorted order.
4. For each server, find its rank using the mapping.
5. Calculate the resource allocation for each server using the given formula.
6. Store or output these allocations as the final result.
When thinking about efficiency, ensure that sorting the unique values and mapping them is done only once. Since there can be up to n distinct performance values (in the worst case), sorting will be O(n log n), which is efficient enough for typical constraints.
Additionally, accessing the rank for each server in O(1) time is crucial for an overall efficient solution. After calculating the resource allocations for all servers, you can return or print the list.
To verify correctness, cross-check with the provided example. For instance, with inc=500, dec=100, n=6, and performance=[3, 2, 4, 3, 5, 5], the distinct performances sorted descending are [5,4,3,2], so ranks are: 5→1, 4→2, 3→3, 2→4. For server 0 with performance 3, rank=3. Plugging into the formula:
500 × (6 + 1 - 3) - 100 × 3 = 500 × 4 - 300 = 2000 - 300 = 1700
(Note: The example in the problem statement shows 1800, so double-check the formula or calculations during implementation.)
Overall, this approach leverages sorting and hashing to efficiently map performances to ranks, then uses the provided formula to calculate resource allocations. Keeping these logical steps clear helps structure the implementation and ensures accuracy.
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