<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 getMin(vector<int>& keys , vector<bool>& mst)
    {
        int ans = -1;
        int temp = INT_MAX;
        for(int i=0 ; i<keys.size() ; i++)
        {
            if(keys[i] < temp && mst[i] == false)
            {
                ans = i;
                temp = keys[i];
            }
        }

        return ans;
    }

    int getWeight(int i , int j , vector<vector<int>>& points)
    {
        vector<int>p1 = points[i];
        vector<int>p2 = points[j];

        return abs(p1[0]-p2[0]) + abs(p1[1]-p2[1]);
    }

    int minCostConnectPoints(vector<vector<int>>& points) {
        vector<int>keys(points.size() , INT_MAX);
        vector<bool>mst(points.size() , false);
        vector<int>parent(points.size() , -1);

        //initializing the arrays
        keys[0] = 0;

        while(true)
        {
            //1. get the node with minimum key
            int index = getMin(keys , mst);

            if(index == -1)
            {
                break;
            }

            //2. add the current node to the mst
            mst[index] = true;

            //3. update the neighbours

            for(int i=0 ; i<points.size() ; i++)
            {
                if(i != index && mst[i] == false && getWeight(index , i , points) < keys[i])
                {
                    //update the parent and the key array
                    parent[i] = index;
                    keys[i] = getWeight(index , i , points);
                }
            }
        }

        int ans = 0;
        for(auto ele : keys)
        {
            ans+=ele;
        }

        return ans;

    }
};
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