Steps to Make Array Non-decreasing

Problem Description

You are given a 0-indexed integer array nums. In one step, remove all elements nums[i] where nums[i - 1] > nums[i] for all 0 < i < nums.length. Return the number of steps performed until nums becomes a non-decreasing array.

Key Insights

• The operation removes elements that disrupt the non-decreasing order of the array.
• The process continues until no more elements can be removed.
• Each step reduces the size of the array, leading to a potential faster convergence to a non-decreasing state.
• The solution can leverage the concept of tracking the number of elements removed in each iteration.

Space and Time Complexity

Time Complexity: O(n * m), where n is the length of the array and m is the number of steps until the array becomes non-decreasing.
Space Complexity: O(1), since we are modifying the array in place and not using any additional data structures.

Solution

To solve this problem, we can use a loop to repeatedly check the array for elements that violate the non-decreasing condition. In each iteration, we create a new array that only contains the elements that are not removed. We count how many times we perform this operation until the array becomes non-decreasing.

1. Iterate through the array and find elements that need to be removed.
2. Build a new array without the removed elements.
3. Count each iteration until no elements are removed.

Code Solutions