<p>There are <code>n</code> soldiers standing in a line. Each soldier is assigned a <strong>unique</strong> <code>rating</code> value.</p>

<p>You have to form a team of 3 soldiers amongst them under the following rules:</p>

<ul>
	<li>Choose 3 soldiers with index (<code>i</code>, <code>j</code>, <code>k</code>) with rating (<code>rating[i]</code>, <code>rating[j]</code>, <code>rating[k]</code>).</li>
	<li>A team is valid if: (<code>rating[i] &lt; rating[j] &lt; rating[k]</code>) or (<code>rating[i] &gt; rating[j] &gt; rating[k]</code>) where (<code>0 &lt;= i &lt; j &lt; k &lt; n</code>).</li>
</ul>

<p>Return the number of teams you can form given the conditions. (soldiers can be part of multiple teams).</p>

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

<pre>
<strong>Input:</strong> rating = [2,5,3,4,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can form three teams given the conditions. (2,3,4), (5,4,1), (5,3,1). 
</pre>

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

<pre>
<strong>Input:</strong> rating = [2,1,3]
<strong>Output:</strong> 0
<strong>Explanation:</strong> We can&#39;t form any team given the conditions.
</pre>

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

<pre>
<strong>Input:</strong> rating = [1,2,3,4]
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>n == rating.length</code></li>
	<li><code>3 &lt;= n &lt;= 1000</code></li>
	<li><code>1 &lt;= rating[i] &lt;= 10<sup>5</sup></code></li>
	<li>All the integers in <code>rating</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
    unordered_map<int,int> c;
public:
    void merge(vector<int>& rating, int s, int m, int e) {
        vector<int> sorted(e-s+1);
        int i = s, j = m+1, k = 0;
        while (i<=m and j<=e) {
            if (rating[i] < rating[j]) {
                c[rating[i]] += (e-j+1);
                sorted[k++] = rating[i++];
            }
            else {
                sorted[k++] = rating[j++];
            }
        }
        while (i<=m)
            sorted[k++] = rating[i++];
        while (j<=e)
            sorted[k++] = rating[j++];

        for (int i=0; i<e-s+1; i++) {
            rating[i+s] = sorted[i];
        }
    }

    void mergeSort(vector<int>& rating, int s, int e) {
        if (s >= e)
            return;
        int m = s + (e-s)/2;
        mergeSort(rating, s, m);
        mergeSort(rating, m+1, e);
        merge(rating, s, m, e);
    }   

    int numTeams(vector<int>& rating) {
        vector<int> ratingCopy(rating.begin(), rating.end());
        mergeSort(ratingCopy, 0, rating.size()-1);
        
        int result = 0;
        for (int i=0; i<rating.size()-2; i++) {
            for (int j=i+1; j<rating.size()-1; j++) {
                if (rating[j] > rating[i])
                    result += c[rating[j]];
                else
                    result += (rating.size()-j-c[rating[j]]-1);
            }
        }
        return result;
    }
};
19796