Start by clarifying the problem constraints and edge cases, then propose a single-pass solution that tracks the minimum price seen so far and the maximum profit. Explain the algorithm step-by-step, analyze its time and space complexity, and test with examples including no-profit scenarios.
Pro tip: Mention that you can solve it in one pass with O(1) space, which is optimal, and discuss how this approach scales to streaming data—a common follow-up at Uber.
Ask if the array can be empty, contain negative prices, or if multiple transactions are allowed. Confirm that you must buy before selling and return 0 if no profit is possible.
Propose a single-pass algorithm that iterates through prices while keeping track of the minimum price seen so far and the maximum profit. Explain that this avoids nested loops.
Describe the initialization of min_price and max_profit, then for each price update min_price and compute potential profit, updating max_profit if larger. Use a small example to illustrate.
State that time complexity is O(n) and space is O(1). Test with cases like increasing prices, decreasing prices, and empty array to verify correctness.
Mention how the solution can be adapted for multiple transactions or streaming data, and compare with brute-force O(n^2) approach to highlight efficiency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use a BFS or DFS to traverse the tree while tracking each node's column index (root at 0, left child -1, right child +1). Store nodes in a hash map keyed by column, then sort columns and within each column sort by depth (top to bottom) and value (ascending) to handle ties. Finally, output the sorted lists of node values.
Pro tip: Clarify the tie-breaking rule upfront: if two nodes share the same column and depth, sort by value ascending. Also, mention that BFS naturally processes nodes top-to-bottom, but you still need to sort within columns if using DFS.
Confirm the definition of vertical order: columns from leftmost to rightmost, nodes sorted top-to-bottom, ties by value ascending. Discuss edge cases like empty tree, single node, and duplicate values.
Decide between BFS (queue) or DFS (recursion/stack) to traverse the tree. For each node, record its column index and depth (or rely on BFS order for depth).
Use a hash map where keys are column indices and values are lists of (depth, value) pairs. Alternatively, store nodes directly and sort later.
Sort the column keys in ascending order. For each column, sort its nodes by depth ascending, then by value ascending. Extract the values into the final list of lists.
State time complexity: O(N log N) due to sorting (or O(N) if using BFS with ordered map). Space complexity: O(N). Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.