Use DFS/BFS to find each island, then compute a canonical representation of its shape by normalizing the coordinates (e.g., subtracting the min row and min col). Store these canonical forms in a set to count distinct shapes. For the extension, generate all 8 transformations (rotations and reflections) of each shape, normalize each, and use the lexicographically smallest as the canonical key.
Pro tip: Clarify upfront that you assume translation only for the first part, and that the grid is binary and islands are 4-connected. For the extension, mention that you can precompute all 8 transformations and pick the minimum to avoid redundant comparisons.
Confirm connectivity (4-directional), grid size, and that translation is the only allowed transformation for the first part. Ask if the grid can be large to discuss complexity.
Use DFS or BFS to traverse each unvisited land cell, collecting all coordinates of the island. Mark visited cells to avoid reprocessing.
For each island, subtract the minimum row and column from all coordinates to normalize its position. This yields a translation-invariant representation.
Insert each canonical representation into a hash set. The size of the set is the number of distinct island shapes.
For each island, generate all 8 transformations (rotations by 0°, 90°, 180°, 270° and their reflections). Normalize each transformed shape, then choose the lexicographically smallest as the canonical key. Use that key in the set.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem and edge cases, then present the optimal O(n) solution using a monotonic deque, explaining its linear time complexity. Next, describe a heap-based approach and compare their time/space complexities and practical trade-offs, concluding with when to use each.
Pro tip: Emphasize that the deque approach achieves O(n) because each element is added and removed at most once, and mention that while a heap is simpler to implement, it may be slower in practice due to higher constant factors and O(n log k) time.
Restate the problem, confirm input/output format, and discuss edge cases like k=1, k=n, empty array, or k>n.
Explain the monotonic deque approach: maintain a deque of indices with decreasing values, remove out-of-window indices, and add the front element to the result for each window.
Argue that each element is pushed and popped at most once, so total operations are O(n); space is O(k) for the deque and O(n-k+1) for the output.
Describe using a max-heap of size k: insert first k elements, then for each slide, remove the outgoing element (lazy deletion) and insert the new one, recording the max. Complexity: O(n log k) time, O(k) space.
Compare: deque is O(n) time and O(k) space, but more complex; heap is O(n log k) time and O(k) space, simpler but slower for large n. Mention that for small k, heap may be competitive due to lower constant factors.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.