Use an auxiliary stack to track the minimum value at each state, ensuring O(1) time for all operations. Explain how each operation maintains the auxiliary stack to keep getMin constant time.
Pro tip: Mention that this design uses O(n) extra space, but you can optimize to O(1) extra space by storing the difference between the value and the current minimum, which is a common follow-up.
Confirm that all operations must be O(1) time and discuss space complexity expectations. Ask if the stack can contain negative numbers or duplicates.
Describe using a main stack for values and a min stack that stores the minimum at each level. Explain how push, pop, top, and getMin work in O(1).
Trace operations like push(5), push(3), push(7), getMin(), pop(), getMin() to demonstrate correctness and O(1) time.
Mention the O(n) space overhead and the O(1) space optimization using difference encoding. Compare pros and cons.
Address empty stack operations, duplicate minima, and potential follow-ups like thread safety or generic types.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the requirements and edge cases, then propose a solution using two stacks: one for the main stack and one for tracking maximums. Discuss the time complexity of each operation, highlighting that popMax is O(n) in the simple approach, and then explore optimizations like a doubly linked list with a tree map for O(log n) operations.
Pro tip: Mention that in real-world ML systems, such as feature stores or model versioning, similar stack-like structures with max retrieval are used, and the tradeoff between simplicity and performance often depends on the frequency of popMax operations.
Ask about the expected frequency of operations, whether the stack can be empty, and if there are constraints on memory. Confirm that popMax should remove the topmost maximum element.
Use a main stack for all elements and a max stack that keeps track of the maximum value at each level. Explain how push, pop, top, and peekMax work in O(1), but popMax requires O(n) to find and remove the topmost maximum.
Compare the simple solution with more advanced data structures like a doubly linked list combined with a balanced BST (e.g., TreeMap) to achieve O(log n) for all operations. Discuss the overhead and implementation complexity.
Mention that if popMax is rare, the simple solution is acceptable. If frequent, consider the linked list + TreeMap approach, or a heap with lazy deletion, noting that lazy deletion can lead to O(n) worst-case for popMax if many stale entries.
Summarize the tradeoffs and suggest a solution based on the assumed operation frequencies. Emphasize that the choice depends on the specific use case and performance requirements.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use two heaps (a max-heap for the lower half and a min-heap for the upper half) to maintain the median in O(log n) insertion and O(1) query. Explain the balancing logic and how to handle even/odd counts, then discuss trade-offs with alternative approaches like balanced BSTs or sorted arrays.
Pro tip: Mention that this is a classic streaming median problem and that the two-heap approach is optimal for online queries; also note that for ML pipelines at TikTok, you might need to handle large-scale streams with distributed or approximate methods.
Ask about the expected volume of insertions, query frequency, memory limits, and whether exact median is required. This shows you consider real-world system constraints.
Describe maintaining a max-heap for the lower half and a min-heap for the upper half, ensuring their sizes differ by at most one. Explain how to insert and rebalance.
Walk through the insertion algorithm: add to appropriate heap, rebalance if needed. For median, if heaps are equal size, average the roots; otherwise return the root of the larger heap.
State O(log n) insertion and O(1) query time, O(n) space. Compare with alternatives like balanced BST (O(log n) insert, O(log n) query) or sorted list (O(n) insert).
Mention handling duplicates, negative numbers, and potential need for approximate medians in distributed streams. Relate to ML feature engineering or monitoring tasks.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The upward-only constraint tripped me up at first.
Clarify that the path must be upward-only (from any node to an ancestor) and then use a recursive DFS that passes down the current prefix sum from the root. At each node, check whether the difference between the current prefix sum and the target exists in a hash set of ancestor prefix sums, which detects any valid upward path ending at that node. Return true if any such path is found.
Pro tip: Mention that this is essentially the 'path sum III' pattern but restricted to upward paths, and that using a hash set of prefix sums gives O(n) time instead of O(n^2) brute force. Also note that because node values are positive, you can optionally prune when the prefix sum exceeds the target, but the hash set approach handles all cases cleanly.
Confirm that the path starts at any node and moves only upward toward the root, and that node values are positive integers. Ask whether the path must include at least one node and whether the target can be zero or negative (though values are positive).
Use DFS from the root, passing down the current prefix sum from the root to the current node. Maintain a hash set of prefix sums of all ancestors of the current node (including the current node's prefix sum before processing children).
At each node, compute the current prefix sum. If (current prefix sum - target) exists in the ancestor prefix sum set, then there is an upward path ending at this node that sums to the target. Return true immediately.
Add the current prefix sum to the set, recurse into left and right children, then remove the current prefix sum from the set before returning to the parent (backtracking).
If any recursive call returns true, propagate true up the call stack. If the entire tree is traversed without finding a valid path, return false.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.