Solution: Paths in Maze That Lead to Same Room

Discover how to solve the problem of identifying cycles of length three in a maze represented as a graph. This lesson guides you through using adjacency lists to efficiently detect triangular cycles by examining shared neighbors of connected rooms. Understand both naive and optimized approaches along with their time and space complexity implications. By the end, you'll be able to implement effective graph traversal solutions to evaluate maze confinements and complexity.

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 $1 → 2 → 3 → 4$ ...