<p>Given an array of integers&nbsp;<code>arr</code>, replace each element with its rank.</p>

<p>The rank represents how large the element is. The rank has the following rules:</p>

<ul>
	<li>Rank is an integer starting from 1.</li>
	<li>The larger the element, the larger the rank. If two elements are equal, their rank must be the same.</li>
	<li>Rank should be as small as possible.</li>
</ul>

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

<pre>
<strong>Input:</strong> arr = [40,10,20,30]
<strong>Output:</strong> [4,1,2,3]
<strong>Explanation</strong>: 40 is the largest element. 10 is the smallest. 20 is the second smallest. 30 is the third smallest.</pre>

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

<pre>
<strong>Input:</strong> arr = [100,100,100]
<strong>Output:</strong> [1,1,1]
<strong>Explanation</strong>: Same elements share the same rank.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [37,12,28,9,100,56,80,5,12]
<strong>Output:</strong> [5,3,4,2,8,6,7,1,3]
</pre>

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

<ul>
	<li><code>0 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>9</sup>&nbsp;&lt;= arr[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    vector<int> arrayRankTransform(vector<int>& arr) {
      vector<int> copy{arr.begin(), arr.end()};
      sort(arr.begin(), arr.end());
      
      unordered_map<int, int> rank_map;
      
      int rank = 1;
      for(int i = 0; i < arr.size(); i++) {
        if (i == 0) {
          rank_map[arr[i]] = rank;
          continue;
        }
        
        if (arr[i] == arr[i - 1]) {
          rank_map[arr[i]] = rank;
        } else {
          rank_map[arr[i]] = ++rank;
        }
      }
      
      vector<int> result;
      
      for (auto& n : copy) {
        result.push_back(rank_map[n]);
      }
      
      
      return result;
    }
};
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