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Solution: Minimum Replacements to Sort the Array

Explore how to transform an unsorted array into a non-decreasing sequence with the fewest replacements. Understand the greedy approach of processing elements from right to left and splitting larger numbers strategically to maintain order and minimize operations. This lesson helps develop skills to solve optimization problems efficiently in coding interviews.

Statement

You are given a 0-indexed integer array nums. You are allowed to perform the following operation any number of times:

  • Select any element in the array and replace it with two positive integers whose sum is equal to the selected element.

For example, if the array is nums = [5, 6, 7], you can choose the element 6 and replace it with 2 and 4, resulting in a new array [5, 2, 4, 7].

Your goal is to make the array sorted in non-decreasing order using the minimum number of operations.

Return the minimum number of operations required to achieve this.

Constraints:

  • 11 \leq nums.length 103\leq 10^3 ...