<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>
struct Element {
    int val;
    int count;
};

class Compare {
    public:
       bool operator()(Element a, Element b){
           if(a.count > b.count){
               return true;
           }
           return false;
      }
};


class Solution {
public:
    int findLeastNumOfUniqueInts(vector<int>& arr, int k) {
        int size = arr.size();

        int uniqueCount = 0;
        priority_queue<Element, vector<Element>, Compare> pq;
        map<int, int> mp;

        for(int i=0; i<size; i++) {
            if(mp.find(arr[i]) == mp.end()) {
                uniqueCount++;
                mp[arr[i]] = 1;
            }else {
                mp[arr[i]]++;
            }
        }

        if(k == 0 || size == 0) {
            return uniqueCount;
        }

        for(auto it=mp.begin(); it!=mp.end(); it++) {
            pq.push(Element(it->first, it->second));
        }

        int decreaseCount = k;

        while(decreaseCount > 0 && !pq.empty()) {
            Element e = pq.top();
            pq.pop();

            // element count is greater than what we can reduce
            if(decreaseCount < e.count) {
                return uniqueCount;
            }else {
                decreaseCount = decreaseCount - e.count;
                uniqueCount--;
            }
        }

        return uniqueCount;
    }
};
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