<p>You are given an array <code>points</code> representing integer coordinates of some points on a 2D-plane, where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>

<p>The cost of connecting two points <code>[x<sub>i</sub>, y<sub>i</sub>]</code> and <code>[x<sub>j</sub>, y<sub>j</sub>]</code> is the <strong>manhattan distance</strong> between them: <code>|x<sub>i</sub> - x<sub>j</sub>| + |y<sub>i</sub> - y<sub>j</sub>|</code>, where <code>|val|</code> denotes the absolute value of <code>val</code>.</p>

<p>Return <em>the minimum cost to make all points connected.</em> All points are connected if there is <strong>exactly one</strong> simple path between any two points.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/26/d.png" style="width: 214px; height: 268px;" />
<pre>
<strong>Input:</strong> points = [[0,0],[2,2],[3,10],[5,2],[7,0]]
<strong>Output:</strong> 20
<strong>Explanation:</strong> 
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/26/c.png" style="width: 214px; height: 268px;" />
We can connect the points as shown above to get the minimum cost of 20.
Notice that there is a unique path between every pair of points.
</pre>

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

<pre>
<strong>Input:</strong> points = [[3,12],[-2,5],[-4,1]]
<strong>Output:</strong> 18
</pre>

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

<ul>
	<li><code>1 &lt;= points.length &lt;= 1000</code></li>
	<li><code>-10<sup>6</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>6</sup></code></li>
	<li>All pairs <code>(x<sub>i</sub>, y<sub>i</sub>)</code> are distinct.</li>
</ul>

class Solution {
public:
    int distance(vector<int>& point1, vector<int>& point2){
        return abs(point1[0] - point2[0]) + abs(point1[1] - point2[1]);
    }
    int minCostConnectPoints(vector<vector<int>>& points) {
        int n = points.size();
        vector<bool> inMST(n, false);
        vector<int> minDist(n, INT_MAX);
        minDist[0] = 0;
        int usedEdges = 0;
        int totalCost = 0;
        while(usedEdges < n){
            int currPoint = -1;
            int currDist = INT_MAX;
            for(int i = 0; i < n; i++){
                if(!inMST[i] && minDist[i] < currDist){
                    currPoint = i;
                    currDist = minDist[i];
                }
            }
            usedEdges++;
            inMST[currPoint] = true;
            totalCost += currDist;
            for(int i = 0; i < n; i++){
                vector<int>& dest = points[i];
                int dist = distance(dest, points[currPoint]);
                if(!inMST[i] && dist < minDist[i]){
                    minDist[i] = dist;
                    
                }
            }
        }
        return totalCost;
    }
};
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