<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 {
public:
    int minSetSize(vector<int>& arr) {
        // count the number of occurrences of each element
        std::unordered_map<int, int> occurrences;

        for (int i : arr) {
            auto it = occurrences.find(i);

            if (it == occurrences.end()) {
                occurrences[i] = 1;
                continue;
            }

            ++it->second;
        }

        // sort the elements by occurrence
        vector<int> sorted(occurrences.size());
        
        for (auto &p : occurrences) {
            sorted.emplace_back(p.second);
        }

        std::sort(sorted.begin(), sorted.end());

        // count the minimum number of elements that must be removed
        // so that the size of the array is halved
        int minElements = 0;
        int half = arr.size() / 2;

        for (auto it = sorted.rbegin(); half > 0; it++) {
            half -= *it;
            ++minElements;
        }

        return minElements;
    }
};
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