The propagation logic tripped me up more than I expected.
Clarify that the tree is a full binary tree with leaves storing 0/1 values, and internal nodes are computed as the AND of their children. For set/clear, update the leaf and then walk up to the root, recomputing each ancestor as the AND of its two children. This yields O(log n) time per operation, where n is the number of leaves.
Pro tip: Mention that you can store the tree as an array (like a heap) for cache efficiency, and that the update can early-terminate if a parent's value doesn't change. This shows awareness of practical optimizations beyond the basic algorithm.
Confirm that the tree is full (each internal node has exactly two children), leaves are initially 0, and internal nodes are 1 only if both children are 1. Ask about the expected number of leaves and operations to determine if O(log n) per operation is acceptable.
Represent the tree as an array where the root is at index 1, and for a node at index i, its left child is at 2i and right child at 2i+1. This allows O(1) access to any node and easy parent traversal (i/2).
For set(index), set the leaf to 1 and then while the current node is not the root, move to its parent and set its value to the logical AND of its two children. For clear(index), set the leaf to 0 and propagate upward similarly.
Each operation touches at most the height of the tree, which is O(log n) for n leaves. Discuss edge cases: setting an already set leaf, clearing an already clear leaf, and the root becoming 1 only when all leaves are 1.
Mention that if a parent's value doesn't change, you can stop propagating early. Also note that the same approach works for other associative operations (e.g., OR) by changing the combine function.
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 hash map combined with a doubly linked list to achieve O(1) operations. Explain how the hash map provides direct access to nodes, while the linked list maintains the usage order for eviction.
Pro tip: Mention that you would use a doubly linked list with sentinel head and tail nodes to simplify edge cases, and discuss thread-safety considerations if the cache might be accessed concurrently.
Ask about expected capacity, key/value types, thread-safety needs, and whether eviction should be based on access or insertion order. Confirm that both get and put must be O(1).
Propose a hash map (dictionary) for O(1) key lookup and a doubly linked list to track usage order. Explain that the hash map stores key -> node references, and the linked list nodes store key-value pairs.
Detail how get moves the accessed node to the front (most recently used) and returns its value. For put, if key exists, update value and move to front; if new, add to front and if capacity exceeded, remove the tail node (least recently used) and delete its key from the hash map.
Discuss handling of capacity 0 or 1, updating existing keys, and ensuring the linked list and hash map stay in sync. Mention using sentinel nodes to avoid null checks.
Confirm O(1) time for both operations and O(capacity) space. Optionally, discuss thread-safety using locks or concurrent data structures, and mention alternative implementations like using LinkedHashMap in Java.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.