<p>Given an array of integers&nbsp;<code>arr</code>&nbsp;and an integer <code>k</code>.&nbsp;Find the <em>least number of unique integers</em>&nbsp;after removing <strong>exactly</strong> <code>k</code> elements<b>.</b></p>

<ol>
</ol>

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

<pre>
<strong>Input: </strong>arr = [5,5,4], k = 1
<strong>Output: </strong>1
<strong>Explanation</strong>: Remove the single 4, only 5 is left.
</pre>
<strong class="example">Example 2:</strong>

<pre>
<strong>Input: </strong>arr = [4,3,1,1,3,3,2], k = 3
<strong>Output: </strong>2
<strong>Explanation</strong>: Remove 4, 2 and either one of the two 1s or three 3s. 1 and 3 will be left.</pre>

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

<ul>
	<li><code>1 &lt;= arr.length&nbsp;&lt;= 10^5</code></li>
	<li><code>1 &lt;= arr[i] &lt;= 10^9</code></li>
	<li><code>0 &lt;= k&nbsp;&lt;= arr.length</code></li>
</ul>
class Solution {
public:
    int findLeastNumOfUniqueInts(vector<int>& arr, int k) {
        // lame sauce
        ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);

        // count unique int frequencies
        unordered_map<int, int> F;
        int maxF = 0;
        for (int &x: arr) {
            F[x]++;
            maxF = max(maxF, F[x]);
        }
        // intialize num of unique elements
        int n = F.size();
        // count frequencies
        vector<int> fF(++maxF, 0);
        for (auto &[k, f]: F) {
            fF[f]++;
        }
        // look at frequencies from smallest to largest
        for(int i = 1; i < maxF; i++) {
            if (!fF[i]) continue;
            // subtract from k
            if(fF[i] * i <= k) {
                k -= fF[i] * i;
                n -= fF[i];
            }
            // if k >= 0, decrease total unique elements
            else {
                while (k >= i && fF[i]) {
                    k -= i;
                    fF[i]--;
                    n -= 1;
                }
                break;
            } 
        }

        return n;
    }
};
63000