<p>You are given an integer array <code>arr</code>. You can choose a set of integers and remove all the occurrences of these integers in the array.</p>

<p>Return <em>the minimum size of the set so that <strong>at least</strong> half of the integers of the array are removed</em>.</p>

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

<pre>
<strong>Input:</strong> arr = [3,3,3,3,5,5,5,2,2,7]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array).
Possible sets of size 2 are {3,5},{3,2},{5,2}.
Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has a size greater than half of the size of the old array.
</pre>

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

<pre>
<strong>Input:</strong> arr = [7,7,7,7,7,7]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only possible set you can choose is {7}. This will make the new array empty.
</pre>

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

<ul>
	<li><code>2 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>arr.length</code> is even.</li>
	<li><code>1 &lt;= arr[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def minSetSize(self, arr: List[int]) -> int:
        
        # Bucket sorting
        # O(N) O(N)
        counts = collections.Counter(arr)
        max_value = max(counts.values())
                
        # Put the counts into buckets.
        buckets = [0] * (max_value + 1)
        
        for count in counts.values():
            buckets[count] += 1

    
        # Determine set_size.
        set_size = 0
        total = len(arr)
        half = (total+1)//2
        bucket = max_value
        while half > 0:
            max_needed_from_bucket = math.ceil(half / bucket)
            set_size_increase = min(buckets[bucket], max_needed_from_bucket)
            set_size += set_size_increase
            half -= set_size_increase * bucket
            bucket -= 1
            
        return set_size

        # O(nlogn) O(n)
        total = len(arr)
        half = (total+1)//2
        counts = collections.Counter(arr)

        # Extract the counts in reverse-sorted order.
        # most_common gives (number, count) pairs, reverse sorted on count.
        #count_keys = [count for number, count in counts.most_common()] ######################

        counts = list(counts.values())
        counts.sort(reverse= True)

        total_removed = 0
        for i, count in enumerate(counts):
            total_removed += count
            if total_removed >= half:
                return i+1
            
        return -1
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