What is the most efficient way to count paths in a grid?
This classic problem checks your grasp of combinatorics or dynamic programming on grids. It measures how you handle constraints like obstacles or movement rules.
Why Interviewers Ask This
Recruiters use this to evaluate logical reasoning and algorithmic thinking. It reveals whether you can model real-world pathfinding scenarios mathematically. Candidates must demonstrate they understand both brute force and optimized approaches.
How to Answer This Question
Clarify movement constraints immediately, such as moving only right or down. Propose a recursive solution first to show the brute force logic. Then, introduce dynamic programming to store intermediate results and avoid redundant calculations. Finally, mention any mathematical shortcuts using combinations if no obstacles exist.
Key Points to Cover
- Clarify movement rules
- Apply dynamic programming
- Handle obstacle conditions
- Optimize space usage
Sample Answer
For a grid with no obstacles, I calculate paths using binomial coefficients based on total steps. If obstacles are present, I use a 2D DP array where each cell stores the number of ways to reach it. I initialize the star…
Common Mistakes to Avoid
- Failing to handle boundary conditions
- Overlooking obstacle placement logic
- Not optimizing space complexity
Sound confident on this question in 5 minutes
Answer once and get a 30-second AI critique of your structure, content, and delivery. First attempt is free — no signup needed.