<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<vector<int>>& points, int i, int j){
        return abs(points[i][0] - points[j][0]) + abs(points[i][1] - points[j][1]);
    }

    bool find(vector<bool>& mark, int& pos){
        int n = mark.size();
        for (int i = 0; i < n; i++){
            if (!mark[i]){
                pos = i;
                return true;
            }
        }
        return false;
    }

    int minCostConnectPoints(vector<vector<int>>& points) {
        std::ios::sync_with_stdio(0);
        std::cin.tie(0);
        int n = points.size();
        vector<bool> mark(n, 0);
        vector<int> cost(n, INT_MAX);
        cost[0] = 0;
        mark[0] = 1;
        for (int i = 1; i < n; i++){
            cost[i] = distance(points, i, 0);
        }
        int pos = 0;
        int sum = 0;
        vector<vector<int>> vec(n, vector<int>(0));
        for (int i = 1; i < n; i++){
            for (int j = 0; j < n; j++){
                vec[i].push_back(distance(points, i, j));
            }
        }
        while (find(mark, pos)){
            int min = pos;
            for (int i = pos + 1; i < n; i++){
                if (mark[i] == 0 && cost[i] < cost[min]){
                    min = i;
                }
            }
            sum += cost[min];
            mark[min] = 1;
            for (int i = 1; i < n; i++){
                if (mark[i] == 0 && vec[i][min] < cost[i]){
                    cost[i] = vec[i][min];
                }
            }
        }
        return sum;
    }
};
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