Use a two-pointer technique: one pointer (write) tracks the position for the next distinct element, and the other (read) scans the array. Since the array is sorted, compare the current element with the last written element; if different, write it at the write pointer and increment. Return the write pointer as the new length. For the follow-up, allow up to k duplicates by counting occurrences and writing only if count < k.
Pro tip: Clarify edge cases upfront (empty array, k=0) and mention that the algorithm is optimal because it makes a single pass and uses O(1) extra space. For the follow-up, emphasize that the same two-pointer approach generalizes naturally by tracking a count.
Confirm the problem: in-place modification, return new length, O(1) space, O(n) time. Ask about empty arrays, k=0, and whether elements beyond the new length matter.
Describe using a write pointer to place the next unique element and a read pointer to scan. Since the array is sorted, duplicates are adjacent, so compare with the last written element.
Trace the algorithm on a small array (e.g., [1,1,2,3,3]) to demonstrate how the write pointer advances and the array is modified in-place.
State that time is O(n) because each element is read once, and space is O(1) because only two pointers are used.
Explain that the same two-pointer technique works by allowing up to k copies: write an element if it's different from the last written or if its count so far is less than k. Maintain a count for the current element.
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DFS with memoization is the standard move here and I got there.
Start by framing the problem as finding the longest path in a directed acyclic graph (DAG) where edges go from smaller to larger values. Use DFS with memoization to compute the longest path from each cell, and store parent pointers to reconstruct the path. For large inputs, replace recursion with an iterative topological sort (Kahn's algorithm) to avoid stack overflow.
Pro tip: Mention that you can optimize memory by using a 2D array for memoization and a separate 2D array for parent pointers, but if memory is tight, you can recompute the path by following the decreasing values from the end. Also, highlight that the problem is equivalent to finding the longest path in a DAG, which can be solved in O(mn) time.
Confirm that the path must be strictly increasing, moves are 4-directional, and the grid can be large. Discuss edge cases like empty grid, single cell, or all equal values.
Explain that each cell is a node, and directed edges go from a cell to its neighbors with strictly larger values. This forms a DAG, so we can find the longest path efficiently.
Use DFS with memoization: for each cell, recursively compute the longest path starting there, caching results. Alternatively, use topological sort (Kahn's algorithm) iteratively to avoid recursion depth issues.
During computation, store the next cell (parent) for each cell that gives the maximum length. After finding the global maximum, follow the parent pointers to reconstruct the path.
For very large grids, recursion depth may exceed the stack limit. Switch to an iterative approach: compute in-degrees, perform topological sort, and update longest paths in order. This avoids recursion and handles up to millions of cells.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This one was the most interesting of the three.
Start by clarifying the problem constraints (graph size, read/write patterns, latency requirements) and then walk through the data structures and algorithms for each method. Implement getCandidates using a hash set to track friends and a queue/BFS to collect friends-of-friends, then recommendRandom by sampling from the candidate set, and recommendTopK by counting mutual friends and sorting with a tie-breaker on user ID. Finally, discuss production extensions like weighted scoring, scalability, and real-time updates.
Pro tip: Mention that you would precompute and cache friend-of-friend candidates or use approximate algorithms for large-scale graphs, and emphasize the trade-off between freshness and performance.
Ask about graph size, expected latency, read/write ratio, and whether recommendations need to be real-time or can be batch-computed. This shows you think about system design before coding.
Represent the social graph as an adjacency list (e.g., Map<UserId, Set<UserId>>). For getCandidates, iterate over the user's friends, then their friends, excluding the user and direct friends, using a set to deduplicate.
For recommendRandom, convert the candidate set to a list and pick a random index. For recommendTopK, compute mutual friend counts for each candidate (by intersecting friend sets), then sort by count descending and user ID ascending, returning the top K.
Discuss time and space complexity: getCandidates O(F * avg_degree), recommendTopK O(C * avg_degree + C log C). Suggest optimizations like caching candidates or using approximate counting for large graphs.
Propose extending scoring with weighted signals (e.g., interaction frequency, recency, shared groups), machine learning ranking, and scalable architectures (e.g., precomputation, sharding, streaming updates).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.