[JPMorganChase] NAMR ETSE – Campus Hiring 2025 Start – 11 Dec OA

Title: "Array Reduction Cost Calculation"

Problem Description
Given an array arr of n integers, a sequence of n-1 operations must be performed on the array.

Operation Details

  1. Remove the minimum and maximum elements from the current array and add their sum back to the array.
  2. The cost of an operation is calculated as: cost = ceil((minimum_element + maximum_element) / (maximum_element - minimum_element + 1)) where ceil represents the ceiling function (round up to the nearest integer).

Goal
Find the total cost to reduce the array to a single element.


Example
Given arr = [2, 3, 4, 5, 7]:

The possible sequence of operations is:

  1. Choose 2 and 7: cost = ceil((2 + 7) / (7 - 2 + 1)) = ceil(9 / 6) = 2 Remove 2 and 7, append 9.
    Updated arr = [3, 4, 5, 9].
    total_cost = 2.
  2. Choose 3 and 9: cost = ceil((3 + 9) / (9 - 3 + 1)) = ceil(12 / 7) = 2 Remove 3 and 9, append 12.
    Updated arr = [4, 5, 12].
    total_cost = 2 + 2 = 4.
  3. Choose 4 and 12: cost = ceil((4 + 12) / (12 - 4 + 1)) = ceil(16 / 9) = 2 Remove 4 and 12, append 16.
    Updated arr = [5, 16].
    total_cost = 4 + 2 = 6.
  4. Choose 5 and 16: cost = ceil((5 + 16) / (16 - 5 + 1)) = ceil(21 / 12) = 2 Remove 5 and 16, append 21.
    Updated arr = [21].
    total_cost = 6 + 2 = 8.

Output
Return the total cost: 8.


Function Description
Complete the function findTotalCost in the editor below.

findTotalCost has the following parameter(s):

  • arr (list[int]): An array of integers.

Returns:

  • int: The total cost to reduce the array to a single element.

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