Clarify the rules of Conway's Game of Life and the in-place constraint. Propose using bit manipulation to encode the next state in the second bit of each cell, then shift to get the final state. Walk through the algorithm, analyze complexity, and discuss trade-offs.
Pro tip: Mention that using bit manipulation avoids extra space and is efficient, but note that it modifies the board during computation; if the board cannot be mutated, a different approach is needed. This shows awareness of constraints and trade-offs.
Confirm the rules of Conway's Game of Life: a live cell with 2 or 3 live neighbors survives, a dead cell with exactly 3 live neighbors becomes alive, and all other cells die or stay dead. Emphasize the in-place and O(1) space constraints.
Explain that each cell can store two bits: the least significant bit (LSB) for the current state and the next bit for the next state. Initially, only the LSB is set. After computing the next state, set the second bit accordingly.
Iterate through each cell, count live neighbors using the LSB of neighboring cells (considering boundaries). Apply the rules to determine the next state and set the second bit (e.g., if next state is alive, set the second bit to 1).
After processing all cells, iterate through the board again and right-shift each cell by 1 to discard the old state, leaving only the next state. This yields the final board.
State that time complexity is O(m*n) and space complexity is O(1). Discuss that this approach mutates the input board, which may not be allowed in some contexts, and mention alternative approaches if mutation is prohibited.
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