<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) {
        std::unordered_map<int,int> num_to_count_map;
        for (const int num: arr)    num_to_count_map[num] += 1;

        std::map<int, int> frequency_to_numbers_count_map;
        for (const auto &[num,count]: num_to_count_map) frequency_to_numbers_count_map[count] += 1;

        int num_unique_ints = 0;
        int last_count_key = 0;
        int rem_elements = 0;
        for (const auto& [count, total_nums] : frequency_to_numbers_count_map) {
            ++last_count_key;
            if (k - num_unique_ints <= total_nums*count) {
                rem_elements = std::ceil((total_nums*count - (k - num_unique_ints))/static_cast<double>(count));
                break;
            }
            num_unique_ints += total_nums*count;
        }

        int curr_count_key = 0;
        for (const auto& [count, total_nums] : frequency_to_numbers_count_map) {
            if (++curr_count_key <= last_count_key) continue;
            rem_elements += total_nums;
        }
        
        return rem_elements;
    }
};
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