I knew Game of Life but the no-copy constraint is what makes it interesting.
First, clarify the problem constraints and the bit-packing technique. Then, explain how to encode the old and new states in each cell using two bits, update the board in place by computing the next state based on the original states, and finally shift right to keep only the new state.
Pro tip: Emphasize that bit manipulation avoids extra space and is efficient, but also mention that it's crucial to handle edge cases like boundaries and ensure the encoding doesn't interfere with neighbor checks.
Restate the problem: compute the next state of a Game of Life board in place. Confirm that the board is binary and that we cannot use extra space for a deep copy.
Describe using two bits per cell: the least significant bit (LSB) for the current state and the next bit for the next state. Initially, only the LSB is set.
Iterate through each cell, count live neighbors using the LSB of each neighbor, and determine the next state. Store the next state in the second bit (e.g., set it to 1 if the cell will be alive).
After processing all cells, shift each cell right by 1 to discard the old state, leaving only the new state in the LSB.
Discuss time complexity O(m*n) and space complexity O(1). Mention that bit manipulation is efficient but may reduce readability; consider if clarity is more important in some contexts.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Switched to a sparse representation, basically a set of live cell coordinates.
First, clarify the specific problem and constraints (e.g., what operations are needed, memory limits). Then, discuss how to represent the infinite grid lazily, using data structures like hash maps or coordinate compression, and adapt algorithms to handle unbounded regions. Finally, analyze trade-offs and potential optimizations.
Pro tip: Demonstrate awareness of practical constraints: infinite grids often require lazy evaluation and efficient sparse representations; mention how you'd handle edge cases like infinite loops or memory blowup.
Ask clarifying questions to understand what operations are needed (e.g., traversal, search, pathfinding) and any constraints (memory, time, expected input size).
Decide on a data structure that only stores visited or relevant cells, such as a hash map with coordinate keys or a quadtree, to avoid allocating the entire grid.
Modify the algorithm to generate neighbors on-the-fly and process cells only when needed, ensuring termination conditions are based on problem-specific bounds or goals.
Define how to detect when to stop (e.g., target found, no more reachable cells) and handle cases where the search might otherwise run forever.
Discuss time and space complexity, compare alternative approaches (e.g., coordinate compression, bounding boxes), and suggest optimizations like caching or pruning.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the grid representation and fire spread rules, then propose a synchronous BFS-like expansion using a queue or double-buffering to avoid order dependence. For encoding, suggest using a separate bitmask or state enum that overlays existing cell states without altering their semantics.
Pro tip: Emphasize that fire spread must be computed synchronously (e.g., using a copy or two-phase update) to prevent cascading within a tick, and discuss how to encode fire as an additional bit in the cell state to keep memory overhead low.
Ask about grid size, cell state representation, and whether fire can coexist with other states (e.g., burning a tree). Confirm that spread is to live neighbors only and that each tick is a discrete step.
Use a queue of burning cells (BFS) or a double-buffer approach: compute next fire set from current fire set and live neighbors, then apply simultaneously. Avoid in-place updates that cause order-dependent cascades.
Add a separate bit or use a state enum (e.g., EMPTY, TREE, BURNING) to represent fire without overwriting original cell types. If preserving original state matters, use a bitmask where fire is an overlay flag.
Compare memory overhead of bitmask vs. enum, and time complexity of BFS vs. scanning the grid. Mention sparse representations if fire is localized, and early termination when no new cells ignite.
Recap the synchronous expansion and encoding choice, then ask if the interviewer wants to explore edge cases (e.g., fire spreading to already burning cells) or performance considerations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.