The Burden of Order: A Melancholic Descent into Algorithmic Redemption
IntuitionIn a world governed by entropy, man seeks order — such is the nature of this undertaking. The list, disheveled and chaotic, yearns to find peace in a n
# Intuition
In a world governed by entropy, man seeks order — such is the nature of this undertaking. The list, disheveled and chaotic, yearns to find peace in a non-decreasing sequence, much like a tormented soul yearning for redemption. One must, with grim determination and unwavering patience, sacrifice pairs — plucking them from the ranks like condemned men — merging them into something new, something possibly less destructive. Yet not all pairs are equal; one must choose wisely, for the one with the least sum is perhaps the least wicked, the most humble in its contribution to disorder.

# Approach
The method is neither fast nor merciful. It is deliberate — a slow, brooding march toward harmony. We begin by observing, by inspecting the array for its afflictions. We do not rush. We look for the weakest link: the adjacent pair whose sum is minimal, for such a pair, by its very insignificance, can be torn apart and merged into one without disturbing the fragile fabric too much.

And so the steps follow, like chapters in a dark novel:
1. Begin with no operations — innocence.
2. While the list remains in turmoil, while it still declines where it should rise:
   - Search the depths of the list, with the care of a man leafing through old letters, to find the adjacent pair with the smallest sum.
   - Merge them, not unlike how sorrow and hope may merge into bitter understanding.
   - Remove one, absorb it into the other.
   - Count this act, tally the sin.
3. When the sequence becomes one of order, when the noise fades and ascension reigns — we halt, and return the number of such transgressions.

# Complexity
- Time complexity:  
  $$O(n^2)$$  
  Like revisiting the same regretful memory again and again — each pass, each scan — all until peace is finally reached.

- Space complexity:  
  $$O(1)$$  
  For in the end, we carry no burdens but those already within us. All is done in-place, within the soul of the list.

# Code
```python3
from typing import List

class Solution:
    def minimumPairRemoval(self, nums: List[int]) -> int:
        operations = 0
        while not self.isNonDecreasing(nums):
            # As though choosing which regret to face first
            min_sum = float('inf')
            min_index = -1
            for i in range(len(nums) - 1):
                current_sum = nums[i] + nums[i + 1]
                if current_sum < min_sum:
                    min_sum = current_sum
                    min_index = i
            # Sacrifice the pair, merge them into one
            nums[min_index] = nums[min_index] + nums[min_index + 1]
            nums.pop(min_index + 1)
            operations += 1
        return operations

    def isNonDecreasing(self, nums: List[int]) -> bool:
        for i in range(1, len(nums)):
            if nums[i] < nums[i - 1]:
                return False
        return True
```
['Python3']