Optimize Water Distribution in a Village
Difficulty: Hard
Category: DSA
Topics: Union Find, Graph
Asked at: Google, Facebook, Yahoo
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] = [house1j, house2j, costj]` represents the cost to connect `house1j` and `house2j` together using a pipe. Connections are bidirectional.
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.
Constraints:
`1 <= n <= 104`
`wells.length == n`
`0 <= wells[i] <= 105`
`1 <= pipes.length <= 104`
`pipes[j].length == 3`
`1 <= house1j, house2j <= n`
`0 <= costj <= 105`
`house1j != house2j`