There are n houses in a village. We want to supply water for all the houses by building wells and laying pipes.

For each house i, we can either build a well inside it directly with cost wells[i - 1] (note the -1 due to 0-indexing), or pipe in water from another well to it. The costs to lay pipes between houses are given by the array pipes where each pipes[j] = [house1_j, house2_j, cost_j] represents the cost to connect house1_j and house2_j together using a pipe. Connections are bidirectional, and there could be multiple valid connections between the same two houses with different costs.

Return the minimum total cost to supply water to all houses.

Example 1:

Input: n = 3, wells = [1,2,2], pipes = [[1,2,1],[2,3,1]]
Output: 3
Explanation: 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.

Example 2:

Input: n = 2, wells = [1,1], pipes = [[1,2,1],[1,2,2]]
Output: 2
Explanation: 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 the cheapest option.

Constraints:

2 <= n <= 10⁴
wells.length == n
0 <= wells[i] <= 10⁵
1 <= pipes.length <= 10⁴
pipes[j].length == 3
1 <= house1_j, house2_j <= n
0 <= cost_j <= 10⁵
house1_j != house2_j

Optimize Water Distribution in a Village

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