What is the optimal dynamic programming approach for a grid path problem?
This question involves finding the maximum value path in a grid, often maximizing collected items like rocks. It tests DP state definition and transition logic.
Why Interviewers Ask This
Grid problems are common in finance and tech interviews to test optimization skills. Interviewers want to see if you can break down a complex pathfinding problem into overlapping subproblems. They evaluate your ability to define states, derive recurrence relations, and reconstruct the solution path if required.
How to Answer This Question
Define the DP state clearly, such as dp[i][j] representing the max value to reach cell (i, j). Explain the base cases for the starting row and column. Describe the recurrence relation where the current cell depends on the previous valid cells (e.g., top or left). Discuss how to backtrack to find the actual path if needed.
Key Points to Cover
- Define DP state for max value
- Handle boundary conditions carefully
- Use recurrence relation for transitions
- Backtrack to reconstruct the path
Sample Answer
I would use dynamic programming where dp[i][j] stores the maximum rocks collected to reach cell (i, j). The base case initializes the bottom-left corner. For other cells, the value is the current cell's rocks plus the ma…
Common Mistakes to Avoid
- Ignoring invalid movement directions
- Not initializing the DP table correctly
- Failing to handle the path reconstruction logic
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