Optimize Water Distribution in a Village
<p>There are <code>n</code> houses in a village. We want to supply water for all the houses by building wells and laying pipes.</p>

<p>For each house <code>i</code>, we can either build a well inside it directly with cost <code>wells[i - 1]</code> (note the <code>-1</code> due to <strong>0-indexing</strong>), or pipe in water from another well to it. The costs to lay pipes between houses are given by the array <code>pipes</code> where each <code>pipes[j] = [house1<sub>j</sub>, house2<sub>j</sub>, cost<sub>j</sub>]</code> represents the cost to connect <code>house1<sub>j</sub></code> and <code>house2<sub>j</sub></code> together using a pipe. Connections are bidirectional, and there could be multiple valid connections between the same two houses with different costs.</p>

<p>Return <em>the minimum total cost to supply water to all houses</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1100-1199/1168.Optimize%20Water%20Distribution%20in%20a%20Village/images/1359_ex1.png" style="width: 189px; height: 196px;" />
<pre>
<strong>Input:</strong> n = 3, wells = [1,2,2], pipes = [[1,2,1],[2,3,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The image shows the costs of connecting houses using pipes.
The best strategy is to build a well in the first house with cost 1 and connect the other houses to it with cost 2 so the total cost is 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2, wells = [1,1], pipes = [[1,2,1],[1,2,2]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> We can supply water with cost two using one of the three options:
Option 1:
  - Build a well inside house 1 with cost 1.
  - Build a well inside house 2 with cost 1.
The total cost will be 2.
Option 2:
  - Build a well inside house 1 with cost 1.
  - Connect house 2 with house 1 with cost 1.
The total cost will be 2.
Option 3:
  - Build a well inside house 2 with cost 1.
  - Connect house 1 with house 2 with cost 1.
The total cost will be 2.
Note that we can connect houses 1 and 2 with cost 1 or with cost 2 but we will always choose <strong>the cheapest option</strong>. 
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>wells.length == n</code></li>
	<li><code>0 &lt;= wells[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= pipes.length &lt;= 10<sup>4</sup></code></li>
	<li><code>pipes[j].length == 3</code></li>
	<li><code>1 &lt;= house1<sub>j</sub>, house2<sub>j</sub> &lt;= n</code></li>
	<li><code>0 &lt;= cost<sub>j</sub> &lt;= 10<sup>5</sup></code></li>
	<li><code>house1<sub>j</sub> != house2<sub>j</sub></code></li>
</ul>
Union Find; Graph; Minimum Spanning Tree; Heap (Priority Queue)
function minCostToSupplyWater(n: number, wells: number[], pipes: number[][]): number {
    for (let i = 0; i < n; ++i) {
        pipes.push([0, i + 1, wells[i]]);
    }
    pipes.sort((a, b) => a[2] - b[2]);
    const p = Array(n + 1)
        .fill(0)
        .map((_, i) => i);
    const find = (x: number): number => {
        if (p[x] !== x) {
            p[x] = find(p[x]);
        }
        return p[x];
    };
    let ans = 0;
    for (const [a, b, c] of pipes) {
        const pa = find(a);
        const pb = find(b);
        if (pa === pb) {
            continue;
        }
        p[pa] = pb;
        ans += c;
        if (--n === 0) {
            break;
        }
    }
    return ans;
}
