Classic DP problem but I second-guessed myself on the adjacency definition for a bit.
Start by clarifying the problem constraints and edge cases, then propose a dynamic programming solution that computes the minimum path sum in O(n^2) time and O(n) space. Explain how you can optimize space by updating the triangle in place or using a 1D array, and walk through a small example to demonstrate correctness.
Pro tip: Mention that you can solve it in-place by modifying the input triangle to store cumulative sums, which shows awareness of space optimization. Also, discuss how the problem relates to real-world scenarios like finding the cheapest path in a cost matrix, which can impress interviewers at product companies like Agoda.
Ask about input constraints (e.g., triangle size, value ranges), whether the triangle is mutable, and if negative numbers are allowed. Confirm that adjacent means indices i and i+1 in the next row.
Let dp[i][j] be the minimum path sum from the top to position (i, j). The recurrence is dp[i][j] = triangle[i][j] + min(dp[i-1][j-1], dp[i-1][j]) with boundary conditions.
Instead of a 2D DP table, use a 1D array or modify the triangle in place. Update from bottom to top or top to bottom carefully to avoid overwriting needed values.
Write clean code, handle edge cases (e.g., empty triangle, single row), and test with a small example. Analyze time and space complexity: O(n^2) time, O(n) space (or O(1) extra if in-place).
Compare top-down vs bottom-up DP, and mention that bottom-up avoids boundary checks. Also, note that if the triangle is large, in-place modification might not be allowed, so discuss alternatives.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.