2366 - Minimum Replacements to Sort the Array.

Hard

You are given a 0-indexed integer array nums. In one operation you can replace any element of the array with any two elements that sum to it.

• For example, consider nums = [5,6,7]. In one operation, we can replace nums[1] with 2 and 4 and convert nums to [5,2,4,7].

Return the minimum number of operations to make an array that is sorted in non-decreasing order.

Example 1:

Input: nums = 3,9,3

Output: 2

Explanation: Here are the steps to sort the array in non-decreasing order:

• From 3,9,3, replace the 9 with 3 and 6 so the array becomes 3,3,6,3

• From 3,3,6,3, replace the 6 with 3 and 3 so the array becomes 3,3,3,3,3

There are 2 steps to sort the array in non-decreasing order. Therefore, we return 2.

Example 2:

Input: nums = 1,2,3,4,5

Output: 0

Explanation: The array is already in non-decreasing order. Therefore, we return 0.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• <code>1 <= numsi<= 10⁹</code>