← Bytedance Interview Insights
Use an auxiliary stack to keep track of the minimum element at each state. When pushing, compare the new value with the current minimum and push the smaller onto the auxiliary stack. When popping, pop from both stacks to maintain synchronization.
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 minimum, though it may introduce integer overflow concerns. Also, clarify that getMin should return the minimum element in the current stack, not remove it.
Confirm that all operations must be O(1) time, and discuss whether extra space is acceptable. Ask about potential edge cases like popping from an empty stack or calling getMin on an empty stack.
Propose using two stacks: one for the actual elements and another to track the minimum. Explain how the auxiliary stack maintains the minimum at each level.
Describe push: push onto main stack; if aux stack is empty or new value <= current min, push onto aux stack. Pop: pop from main stack; if popped value equals aux top, pop from aux stack. Top: return main stack top. getMin: return aux stack top.
State that all operations are O(1) time and O(n) space. Discuss handling empty stack scenarios and duplicate minimum values.
Mention the O(1) space approach using a single stack with encoded values, and note its trade-offs (e.g., integer overflow). Also, consider if the stack needs to support other operations.
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 constraints, then propose a data structure that balances time complexity for all operations. A common efficient solution uses two stacks: one for the main stack and one for tracking maximums, with careful handling for popMax. Discuss trade-offs between time and space, and consider edge cases like duplicates and empty stack.
Pro tip: Mention that using a single stack with a auxiliary stack for max tracking can achieve O(1) for peekMax and O(n) for popMax, but if popMax needs to be faster, consider a balanced BST or a doubly linked list with a max-heap, though that increases complexity. Showing awareness of these trade-offs demonstrates depth.
Ask about expected frequency of operations, whether all operations need to be O(1), and if duplicates are allowed. This shows you think about practical usage.
Describe a simple approach using two stacks: one for elements and one for max values. Explain how push, pop, peek, peekMax work in O(1), and popMax in O(n) by popping elements until max is found.
If O(n) for popMax is unacceptable, suggest using a balanced BST or a max-heap combined with a stack to achieve O(log n) for popMax, while maintaining O(1) for other operations.
Compare time and space complexity of different approaches. Mention handling duplicates, empty stack, and maintaining order of remaining elements after popMax.
Summarize the chosen approach based on likely interview constraints, and offer to code it if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Two heaps, max-heap for the lower half and min-heap for the upper half, rebalance on each insert.
Start by clarifying the problem requirements (e.g., stream size, data types, memory constraints) and then propose the two-heap solution (max-heap for lower half, min-heap for upper half) to achieve O(log n) insertion and O(1) median retrieval. Discuss the MaxStack design idea, explaining that while both involve maintaining order statistics, MaxStack's focus on stack operations and maximum tracking makes it less directly adaptable, but the two-heap approach is more suitable for median.
Pro tip: Mention that the two-heap solution can be extended to support deletion of arbitrary elements (e.g., using lazy deletion with a hash map) if the interviewer asks about handling removals, showing depth beyond the basic problem.
Ask about the expected size of the stream, whether all numbers are integers or floats, and if memory is a concern. This shows you consider practical aspects before diving into a solution.
Explain that you would maintain a max-heap for the smaller half and a min-heap for the larger half, balancing them after each insertion so their sizes differ by at most one. The median is then either the top of the larger heap or the average of the two tops.
State that insertion takes O(log n) time due to heap operations, and median retrieval is O(1). Discuss edge cases like empty stream, single element, and duplicate values.
Compare the two-heap median structure with MaxStack: both maintain order statistics, but MaxStack is tailored for stack operations (push/pop) and tracking the maximum, while median requires balancing two halves. The two-heap approach is more direct and efficient for median; adapting MaxStack would be convoluted and less optimal.
Mention that if deletions are required, a balanced binary search tree (e.g., order-statistic tree) or a Fenwick tree with coordinate compression could be used, but they come with increased complexity. Also note that for small streams, a sorted list with binary search insertion (O(n) insertion) might be acceptable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This tripped me up at first because I kept thinking about the classic root-to-leaf or any-direction path problems.
Clarify the problem constraints and edge cases, then propose a recursive DFS that, for each node, checks all contiguous upward paths starting at that node by accumulating sums while moving to ancestors. Optimize with a hash map of prefix sums from root to current node to achieve O(n) time, and discuss trade-offs.
Pro tip: Explicitly state that the path direction is upward (child to ancestor) and that you will treat the tree as rooted; this shows attention to detail and avoids misinterpretation. Also, mention that the O(n) prefix-sum method works because the path is a vertical chain, not arbitrary.
Confirm that the path must be a contiguous chain moving only upward (from a node to its ancestors), can start at any node, and cannot branch or revisit nodes. Discuss edge cases: empty tree, single node, negative values, and target zero.
For each node, traverse upward to the root, accumulating the sum and checking if it equals the target. This takes O(n^2) time in the worst case (skewed tree) and O(1) extra space.
Use a hash map to store prefix sums from the root to the current node during a DFS. For each node, check if (current_prefix_sum - target) exists in the map, which indicates a valid upward path ending at the current node. This achieves O(n) time and O(n) space.
Compare the brute-force O(n^2) time, O(1) space approach with the optimized O(n) time, O(n) space approach. Discuss when each is preferable (e.g., memory constraints vs. time constraints).
Walk through a small example (e.g., tree with values [1,2,3], target=3) to verify both approaches. Mention potential pitfalls like integer overflow or duplicate prefix sums.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.