What are the steps to count all paths in an mXn matrix grid?
Candidates must explain how to traverse a grid from top-left to bottom-right avoiding obstacles or following specific rules. It tests recursion and combinatorics knowledge.
Why Interviewers Ask This
This question evaluates logical reasoning and the ability to handle grid-based traversal problems. Interviewers look for candidates who can identify constraints and choose between recursion, dynamic programming, or mathematical approaches. It also checks if the candidate considers edge cases like blocked cells or boundary conditions effectively.
How to Answer This Question
Clarify the movement rules (e.g., right and down only). Start with a recursive solution to establish the base logic. Optimize it using memoization or a DP table to avoid redundant calculations. If the grid has no obstacles, mention the combinatorial formula. Always discuss time and space complexity trade-offs.
Key Points to Cover
- Movement constraints define the direction of transitions
- Recursive solution has overlapping subproblems
- DP table reduces complexity to O(m*n)
- Combinatorics offers O(1) solution for obstacle-free grids
Sample Answer
To count paths in an mXn matrix, I assume movement is restricted to right and down directions. A simple recursive approach explores all paths but suffers from exponential time complexity due to overlapping subproblems. I…
Common Mistakes to Avoid
- Ignoring boundary checks during recursion
- Failing to optimize with memoization
- Misapplying combinatorial formulas when obstacles exist
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