<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) {    
    struct Point {
        int x{};
        int y{};
        int idx{};
        Point(){};
        Point(int x, int y, int idx) : x(x), y(y), idx(idx){};
    };
        auto calc_dist = [](Point& p1, Point& p2) {
            return abs(p1.x - p2.x) + abs(p1.y - p2.y);
        };
        unordered_map<int, vector<Point>> mp;
        for (int i = 0; i < points.size(); i++) {
            Point pi = Point(points[i][0], points[i][1], i);
            for (int j = i + 1; j < points.size(); j++) {
                Point pj = Point(points[j][0], points[j][1], j);
                mp[i].push_back(pj);
                mp[j].push_back(pi);
            }
        }
        auto cmp = [](pair<int, Point>& p1, pair<int, Point>& p2) {return p1.first > p2.first;};
        priority_queue<pair<int, Point>, vector<pair<int, Point>>, decltype(cmp)> pq(cmp);
        pq.push(make_pair(0, Point(points[0][0], points[0][1], 0)));
        unordered_set<int> vis;
        int ret{};
        while (!pq.empty()) {
            auto [w, p] = pq.top(); pq.pop();
            if (vis.count(p.idx)) continue;
            vis.insert(p.idx);
            ret += w;
            for (auto it : mp[p.idx]) {
                pq.push(make_pair(calc_dist(p, it), it));
            }
        }
        return ret;
    }
};
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