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
- Remove the minimum and maximum elements from the current array and add their sum back to the array.
- The cost of an operation is calculated as:
cost = ceil((minimum_element + maximum_element) / (maximum_element - minimum_element + 1))whereceilrepresents 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:
- Choose 2 and 7:
cost = ceil((2 + 7) / (7 - 2 + 1)) = ceil(9 / 6) = 2Remove 2 and 7, append 9.
Updatedarr = [3, 4, 5, 9].total_cost = 2. - Choose 3 and 9:
cost = ceil((3 + 9) / (9 - 3 + 1)) = ceil(12 / 7) = 2Remove 3 and 9, append 12.
Updatedarr = [4, 5, 12].total_cost = 2 + 2 = 4. - Choose 4 and 12:
cost = ceil((4 + 12) / (12 - 4 + 1)) = ceil(16 / 9) = 2Remove 4 and 12, append 16.
Updatedarr = [5, 16].total_cost = 4 + 2 = 6. - Choose 5 and 16:
cost = ceil((5 + 16) / (16 - 5 + 1)) = ceil(21 / 12) = 2Remove 5 and 16, append 21.
Updatedarr = [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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