# 2366 Minimum Replacements to Sort the Array

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:

• `1 <= nums.length <= 105`
• `1 <= nums[i] <= 109`
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 `````` ``````class Solution: def minimumReplacement(self, nums: List[int]) -> int: n = len(nums) res = 0 prev = nums[n - 1] for i in range(n - 2, -1, -1): num = nums[i] k = ceil(num / prev) # (k - 1) is the min of times we have to split res += k - 1 # (num // k) is the max from splitting (k - 1) times prev = num // k return res``````