Min Cost to Connect All Points
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1500-1599/1584.Min%20Cost%20to%20Connect%20All%20Points/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1500-1599/1584.Min%20Cost%20to%20Connect%20All%20Points/images/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>
Union Find; Graph; Array; Minimum Spanning Tree
func minCostConnectPoints(points [][]int) (ans int) {
	n := len(points)
	g := make([][]int, n)
	vis := make([]bool, n)
	dist := make([]int, n)
	for i := range g {
		g[i] = make([]int, n)
		dist[i] = 1 << 30
	}
	for i := range g {
		x1, y1 := points[i][0], points[i][1]
		for j := i + 1; j < n; j++ {
			x2, y2 := points[j][0], points[j][1]
			t := abs(x1-x2) + abs(y1-y2)
			g[i][j] = t
			g[j][i] = t
		}
	}
	dist[0] = 0
	for i := 0; i < n; i++ {
		j := -1
		for k := 0; k < n; k++ {
			if !vis[k] && (j == -1 || dist[k] < dist[j]) {
				j = k
			}
		}
		vis[j] = true
		ans += dist[j]
		for k := 0; k < n; k++ {
			if !vis[k] {
				dist[k] = min(dist[k], g[j][k])
			}
		}
	}
	return
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}