2366. Minimum Replacements to Sort the Array

Description

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

 

Solutions

Solution: Greedy

• Time complexity: O(n)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number[]} nums
 * @return {number}
 */
const minimumReplacement = function (nums) {
  const n = nums.length;
  let prev = nums[n - 1];
  let result = 0;

  for (let index = n - 2; index >= 0; index--) {
    const num = nums[index];
    const operations = Math.floor((num - 1) / prev);

    result += operations;
    prev = Math.floor(num / (operations + 1));
  }

  return result;
};