Solution: Paths in Maze That Lead to Same Room

Explore how to detect cycles of length three in a maze represented as a graph. This lesson helps you apply graph theory concepts and adjacency lists to identify interconnected rooms forming triangular cycles. Understand the time and space complexities of naive and optimized approaches for solving this problem efficiently.

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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 $1 → 2 → 3 → 4$ ...