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