Number of Good Paths

Problem Highlights

• 🔗 Leetcode Link:
• 💡 Problem Difficulty:
• ⏰ Time to complete: 20 mins
• 🛠️ Topics: Graph
• 🗒️ Similar Questions:

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

For Graph Problems, common solution patterns include:

• DFS/BFS: We could use either BFS or DFS. DFS is fewer lines of code, but BFS makes use of the adjacency dictionary data structure.
• Adjacency List: We already have an adjacency list, let's make it a adjacency dictionary.
• Adjacency Matrix: We can use an adjacency matrix to store the graph, but this will make the problem more complicated.
• Topological Sort: In order to have a topological sorting, the graph must not contain any cycles. We cannot apply this sort to this problem because we can have cycles in our graph.
• Union Find: Are there find and union operations here? Can you perform a find operation where you can determine which subset a particular element is in? This can be used for determining if two elements are in the same subset. Can you perform a union operation where you join two subsets into a single subset? Can you check if the two subsets belong to same set? If no, then we cannot perform union.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

⚠️ Common Mistakes

4: I-mplement

Implement the code to solve the algorithm.

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

• Trace through your code with an input to check for the expected output
• Catch possible edge cases and off-by-one errors

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

Assume V represents the number of vertices/nodes. Assume E represents the number of edges

• Time Complexity: O(V+E) We may need to visit each vertex/nodes and their edges.
• Space Complexity: O(V+E) accounting for the use of a adjacency dictionary.