AMAZON Coding Question – Solved

As an operations engineer at Amazon, you are responsible for organizing the distribution of n different items in the warehouse. The size of each product is provided in an array `productSize`, where productSize[i] represents the size of the i-th product. You construct a new array called `variation`, where each element `variation[i]` is the difference between the largest and smallest product sizes among the first i products. Mathematically, this is defined as: variation[i] = max(productSize[0], productSize[1], ..., productSize[i]) - min(productSize[0], productSize[1], ..., productSize[i]) Your goal is to arrange the products in a way that minimizes the total variation, i.e., the sum of variation[0] + variation[1] + ... + variation[n-1]. Determine the minimum possible value of this sum after you have reordered the products. Example: n = 3 productSize = [3, 1, 2] By reordering the products as productSize = [2, 3, 1]: - variation[0] = max(2) - min(2) = 2 - 2 = 0. - variation[1] = max(2, 3) - min(2, 3) = 3 - 2 = 1. - variation[2] = max(2, 3, 1) - min(2, 3, 1) = 3 - 1 = 2. The sum is variation[0] + variation[1] + variation[2] = 0 + 1 + 2 = 3. This is the minimum possible total variation after rearranging. Function Description: Complete the function `minimizeVariation` in the editor below. `minimizeVariation` has the following parameter(s): - int productSize[n]: The size of each product. Returns: - int: The minimum possible total variation after rearranging the array productSize. Constraints: - 1 ≤ n ≤ 2000 - 1 ≤ productSize[i] ≤ 10^9 Sample Input 0: productSize = [4, 5, 4, 6, 2, 6, 1, 1] Sample Output 0: 16 Explanation: By reordering the products as productSize = [1, 1, 2, 4, 4, 5, 6]: - variation[0] = max(1) - min(1) = 1 - 1 = 0. - variation[1] = max(1, 1) - min(1, 1) = 1 - 1 = 0. - variation[2] = max(1, 1, 2) - min(1, 1, 2) = 2 - 1 = 1. - variation[3] = max(1, 1, 2, 4) - min(1, 1, 2, 4) = 4 - 1 = 3. - variation[4] = max(1, 1, 2, 4, 4) - min(1, 1, 2, 4, 4) = 4 - 1 = 3. - variation[5] = max(1, 1, 2, 4, 4, 5) - min(1, 1, 2, 4, 4, 5) = 5 - 1 = 4. - variation[6] = max(1, 1, 2, 4, 4, 5, 6) - min(1, 1, 2, 4, 4, 5, 6) = 6 - 1 = 5. The minimum total variation is variation[0] + variation[1] + variation[2] + variation[3] + variation[4] + variation[5] + variation[6] = 0 + 0 + 1 + 3 + 3 + 4 + 5 = 16.