<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 minCostConnectPoints(vector<vector<int>>& points) {
        //Prim's algorithm, T-O(nlogn), S-O(n)
        int n = points.size(), mstCost = 0, edgesUsed = 0;
        std::vector<int> minDistance(n, INT_MAX);
        std::vector<int> inMST(n, false);
        minDistance[0] = 0;

        std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>, std::greater<std::pair<int, int>>> minHeap;//{cost, node}
        minHeap.push({0, 0});

        while(edgesUsed < n) {
            int cost = minHeap.top().first, node = minHeap.top().second;
            minHeap.pop();
            if(inMST[node]) continue;

            inMST[node] = true;
            mstCost += cost;
            ++edgesUsed;

            for(int nextNode = 0; nextNode < n; ++nextNode) {
                if(!inMST[nextNode]) {
                    int newDist = std::abs(points[node][0] - points[nextNode][0]) + std::abs(points[node][1] - points[nextNode][1]);
                    if(newDist < minDistance[nextNode]) {
                        minDistance[nextNode] = newDist;
                        minHeap.push({newDist, nextNode});
                    }
                }
            }
        }

        return mstCost;

    }
};
19175