<p>Given an integer array <code>nums</code>, your goal is to make all elements in <code>nums</code> equal. To complete one operation, follow these steps:</p>

<ol>
	<li>Find the <strong>largest</strong> value in <code>nums</code>. Let its index be <code>i</code> (<strong>0-indexed</strong>) and its value be <code>largest</code>. If there are multiple elements with the largest value, pick the smallest <code>i</code>.</li>
	<li>Find the <strong>next largest</strong> value in <code>nums</code> <strong>strictly smaller</strong> than <code>largest</code>. Let its value be <code>nextLargest</code>.</li>
	<li>Reduce <code>nums[i]</code> to <code>nextLargest</code>.</li>
</ol>

<p>Return <em>the number of operations to make all elements in </em><code>nums</code><em> equal</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,1,3]
<strong>Output:</strong> 3
<strong>Explanation:</strong>&nbsp;It takes 3 operations to make all elements in nums equal:
1. largest = 5 at index 0. nextLargest = 3. Reduce nums[0] to 3. nums = [<u>3</u>,1,3].
2. largest = 3 at index 0. nextLargest = 1. Reduce nums[0] to 1. nums = [<u>1</u>,1,3].
3. largest = 3 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1,<u>1</u>].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong>&nbsp;All elements in nums are already equal.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,2,2,3]
<strong>Output:</strong> 4
<strong>Explanation:</strong>&nbsp;It takes 4 operations to make all elements in nums equal:
1. largest = 3 at index 4. nextLargest = 2. Reduce nums[4] to 2. nums = [1,1,2,2,<u>2</u>].
2. largest = 2 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1,<u>1</u>,2,2].
3. largest = 2 at index 3. nextLargest = 1. Reduce nums[3] to 1. nums = [1,1,1,<u>1</u>,2].
4. largest = 2 at index 4. nextLargest = 1. Reduce nums[4] to 1. nums = [1,1,1,1,<u>1</u>].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 5 * 10<sup>4</sup></code></li>
</ul>

from typing import List
from collections import Counter

class Solution:
    def reductionOperations(self, nums: List[int]) -> int:
        # Step 1: Get unique sorted values
        unique_values = sorted(set(nums), reverse=True)
        
        # If there is only one unique value, no operations are needed
        if len(unique_values) == 1:
            return 0
        
        # Step 2: Create a frequency counter for the numbers
        freq = Counter(nums)
        
        # Initialize operation count
        operations = 0
        
        # Step 3: Iterate from the largest to the smallest unique value
        for i in range(len(unique_values) - 1):
            largest = unique_values[i]
            next_largest = unique_values[i + 1]
            
            # Number of elements that are currently 'largest'
            count_largest = freq[largest]
            
            # Update operations needed
            operations += count_largest
            
            # Reduce the count of the largest value and add it to the next largest
            freq[next_largest] += count_largest
        
        return operations


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