I knew it was a DP problem pretty fast, but I fumbled around with top-down recursion first before realizing I was overcomplicating the space usage.
Start by clarifying the problem constraints and edge cases, then propose a dynamic programming solution that computes the minimum path sum in O(n) space by modifying the triangle in place from bottom to top. Explain the recurrence and analyze time and space complexity, and if time permits, discuss potential optimizations or alternative approaches.
Pro tip: At Upstart, interviewers value not just correct solutions but also clear communication and the ability to connect algorithmic choices to business impact—mention how efficient algorithms can scale to large datasets and reduce computational costs.
Ask clarifying questions about input format, constraints (e.g., triangle size, integer range), and expected output. Confirm that adjacent means indices i and i+1 in the next row.
Mention that brute force (recursion) is exponential, then propose dynamic programming. Explain that we can solve it bottom-up by updating each element to the minimum sum from that point to the bottom.
For each element from second-last row up, set triangle[row][col] += min(triangle[row+1][col], triangle[row+1][col+1]). The answer is triangle[0][0]. This uses O(1) extra space if modifying in place.
Time complexity is O(n^2) where n is the number of rows, space is O(1) extra (or O(n) if not in-place). Handle edge cases: empty triangle, single row, negative numbers.
Walk through a small example to verify. If time, discuss variations like top-down DP with memoization or if the triangle is very large, consider memory optimization.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.