Minimum Replacements to Sort the Array — LeetCode 2366 Python Solution

The 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.

Example

Input

nums = [3,9,3]

Output

2

Explanation

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

Python solution

class Solution:
    def minimumReplacement(self, nums: List[int]) -> int:
        ans = 0
        n = len(nums)
        mx = nums[-1]
        for i in range(n - 2, -1, -1):
            if nums[i] <= mx:
                mx = nums[i]
                continue
            k = (nums[i] + mx - 1) // mx
            ans += k - 1
            mx = nums[i] // k
        return ans

Complexity

Pattern: Greedy

Take the locally best option every time — when you can prove that never costs you later. LeetCode 2366. Minimum Replacements to Sort the Array is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Greedy.

The greedy guide has the Python template for the pattern and the 346 LeetCode problems that use it.

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