Search⌘ K
AI Features
Home
Courses
Grokking the Coding Interview Patterns in C++

Solution: Optimize Water Distribution in a Village

Explore how to solve the water distribution problem in a village by applying Union-Find data structures to optimize connections and costs. Understand constructing a virtual node, sorting edges by cost, and performing efficient union operations to guarantee water access while minimizing expenses, all within the constraints of a C++ coding interview context.

We'll cover the following...

Statement

There are nn houses in a village, and we want to supply water to every house. To do this, we have two options:

  1. Build a well directly at a house: The costs for building wells are given in the wells array, where wells[i - 1] represents the cost to build a well at house i (houses are numbered from 11 to nn, but the array is 0-indexed).

  2. Lay water pipes to connect two houses: Allowing one to receive water from the other. The costs for building these connections are given in the pipes array. Each pipe entry is written as [house1, house2, cost], meaning it costs to construct a pipe connecting house1 and house2. The connection is two-way (water can flow in both directions).

In the given data, multiple pipe entries may connect the same pair of houses, but with different costs. Each entry represents an available option; you may choose the most cost-effective one.

Your task is to determine the minimum total cost to ensure every house gets access to water, either by building a well directly at it or connecting it via pipes to another house with access to water.

Constraints:

  • 2<=n<=1042 <= n <= 10^4

  • wells.length ==n== n

  • 0<=0 <= ...