2366. Minimum Replacements to Sort the Array

Problem

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 <= 10^5

• 1 <= nums[i] <= 10^9

Solution

class Solution {
    public long minimumReplacement(int[] nums) {
        int limit = nums[nums.length - 1];
        long ans = 0;
        for (int i = nums.length - 2; i >= 0; i--) {
            int replacements = nums[i] / limit - 1;
            if (nums[i] % limit != 0) {
                replacements++;
            }
            ans += replacements;
            limit = nums[i] / (replacements + 1);
        }
        return ans;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).