I started with BFS and encoded the board as a flattened tuple so it could go into a visited set.
Start by encoding the puzzle state as a string or integer (e.g., tuple of tile positions) and use BFS to guarantee the shortest path in an unweighted graph. For larger N, discuss A* with an admissible heuristic like Manhattan distance or linear conflict to prune the search space, and handle unsolvability by checking parity of inversions.
Pro tip: Optiver values both correctness and efficiency: mention that BFS is simple but may be infeasible for large N, while A* with a strong heuristic is practical. Also, explicitly state how you detect unsolvable configurations (e.g., inversion parity) to avoid infinite search.
Encode the board as a tuple of integers (0 for empty) or a string; this allows hashing for visited sets and easy neighbor generation.
Use BFS for guaranteed shortest path in unweighted graph; for larger N, switch to A* with an admissible heuristic (e.g., Manhattan distance) to reduce explored states.
Define an admissible heuristic like sum of Manhattan distances of each tile to its goal position; optionally add linear conflict for stronger pruning while maintaining admissibility.
Before search, check if the puzzle is solvable by computing inversion parity (and blank row parity for odd/even grid sizes); if unsolvable, return -1 immediately.
Analyze time/space complexity (O(b^d) for BFS, O(b^d) worst-case for A* but often much less); mention bidirectional BFS or IDA* as alternatives for memory constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the token types and the exact condition, then design a state machine that processes each token in constant time and space. Maintain only the previous arrow direction and output the required bit based on the current token. Emphasize that no additional data structures are needed.
Pro tip: Explicitly state that you only need to remember the last arrow direction (or a sentinel if none) and that integer parity is checked on the fly, demonstrating true O(1) space. This shows you understand the problem's constraints and can avoid overcomplicating.
Confirm that tokens are either arrows (e.g., ←, →, ↑, ↓) or non-negative integers, and that the output is 1 if the token is an arrow matching the previous arrow's direction, or if it's an odd integer; otherwise 0.
Determine that the only state needed is the direction of the last arrow seen (or a sentinel if none). No other history is required.
For each token: if it's an arrow, compare its direction to the stored previous arrow direction; output 1 if they match, else 0. Then update the stored direction. If it's an integer, output 1 if odd, else 0 (and leave the stored arrow direction unchanged).
Consider the first token: if it's an arrow, there is no previous arrow, so output 0 (unless the problem specifies otherwise). If it's an integer, just check parity.
Confirm that each token is processed with a constant number of operations and that only a single variable (the previous arrow direction) is stored, achieving O(1) time and space per token.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the constraints (memory, disk, time) and then propose a hash-based solution using a hash map with string keys, discussing memory optimizations like storing hashes instead of full strings. Compare with external sort by sorting chunks and merging, and address Unicode normalization for semantic equivalence. Conclude with a recommendation based on trade-offs.
Pro tip: Mention that you would first normalize Unicode strings (e.g., NFC) to handle encoding differences, and consider using a cryptographic hash with a low collision probability to reduce memory usage, but be prepared to handle collisions by storing full strings only for candidates.
Ask about memory limits, whether the data fits in memory, time constraints, and if strings are semantically equivalent when encoded differently. This shows you consider practical aspects before diving into solutions.
Describe using a hash map (e.g., Python dict) to count frequencies, iterating through strings. Discuss memory usage: storing full strings may be too large, so consider storing hashes (e.g., 64-bit) and only storing full strings for collisions or when count > 1.
Explain sorting strings externally: divide into chunks that fit in memory, sort each chunk, write to disk, then merge sorted chunks while counting duplicates. This uses less memory but more disk I/O and time.
Compare hash-based (fast, memory-heavy) vs external sort (slower, memory-light). Discuss when to use each: if memory is sufficient, hash map is simpler; if not, external sort. Mention hybrid approaches like partitioning by hash.
Explain that strings may be semantically equivalent but encoded differently (e.g., NFC vs NFD). Propose normalizing all strings to a canonical form (e.g., NFC) before processing to ensure correct duplicate detection.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.