Solution: Paths in Maze That Lead to Same Room

Discover how to analyze a maze with rooms connected by corridors to find all unique cycles of length three. Learn to build and use adjacency lists, perform intersections to detect common neighbors, and optimize your solution considering time and space complexity. This lesson helps you understand graph traversal techniques and cycle detection crucial for coding interviews involving graph problems.

We'll cover the following...

Statement
Solution
- Naive approach
- Optimized approach using graph algo

Statement

A maze consists of $n$ rooms numbered from $1 - n$ , and some rooms are connected by corridors. You are given a 2D integer array, corridors, where $corridors[i] = [room1, room2]$ indicates that there is a corridor connecting $room1$ and $room2$ , allowing a person in the maze to go from $room1$ to $room2$ and vice versa.

The designer of the maze wants to know how confusing the maze is. The confusion score of the maze is the number of different cycles of length 3.

For example, $1 → 2 → 3 → 1$ is a cycle of length $3$ , but $1 → 2 → 3 → 4$ ...