Pretty clean recursive problem once you accept it's just a tree traversal.
Clarify the node structure (file vs directory, size attribute) and then present a recursive DFS solution that sums file sizes and recurses into subdirectories. Discuss iterative alternatives and edge cases like empty directories or cycles.
Pro tip: Mention that this is essentially a tree traversal problem and that you'd use post-order traversal to accumulate sizes; also note that for very deep trees, an iterative stack avoids recursion limits.
Ask about the node structure: does each node have a size attribute? How are files and directories distinguished? Are there symlinks or cycles?
Decide between recursive DFS, iterative DFS, or BFS. Recursive DFS is simplest and mirrors the tree structure.
For a given node: if it's a file, return its size; if it's a directory, sum the results of recursively calling the function on each child.
Time complexity is O(n) where n is the number of nodes; space complexity is O(h) for recursion stack, where h is the tree height.
Consider empty directories (return 0), null root (return 0 or throw), and potential cycles (use a visited set if needed).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Said O(N) time without hesitation, which is right.
State the time and space complexity of your solution clearly, using Big-O notation, and explain how you derived them from your code. Relate the complexities to the input size and any auxiliary data structures used, and briefly discuss trade-offs if applicable.
Pro tip: Always mention the worst-case complexity and clarify if average-case differs; also, if you optimized space at the cost of time or vice versa, explain your reasoning—this shows you consider practical constraints.
Define what N represents (e.g., number of elements, length of string) and any other relevant variables like M for a second input.
Break down your algorithm into loops, recursion, or operations, and count how many times each executes relative to N. Express the total as a Big-O term, ignoring constants and lower-order terms.
Consider all memory used: input storage (if modified), auxiliary data structures (arrays, hash maps, recursion stack), and output. Sum them and express as Big-O, again ignoring constants.
Briefly justify why the complexities are what they are, and if you made any trade-offs (e.g., using extra space to reduce time), mention them.
Conclude with a concise statement: 'The time complexity is O(...) and space complexity is O(...).'
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Treat the file system as a directed acyclic graph (DAG) where nodes can have multiple parents, and use memoization to cache subtree sizes for each node. When computing a node's subtree size, recursively compute and cache sizes of its children, reusing cached values to avoid redundant work. Discuss how to handle cycles if they are possible, and analyze time and space complexity.
Pro tip: Mention that memoization turns exponential recomputation into linear time relative to the number of unique nodes, but be prepared to discuss trade-offs like increased memory usage and the need for cycle detection if the graph isn't guaranteed acyclic.
Recognize that shared references create a directed acyclic graph (DAG) where nodes can have multiple parents. Clarify that if cycles are possible, you must detect and handle them to avoid infinite recursion.
Choose a unique identifier for each node (e.g., inode number or file path) to use as the key in a hash map that stores computed subtree sizes.
Implement a recursive function that checks the cache first; if the size is not cached, compute it by summing the sizes of all children (recursively) plus one for the node itself, then store the result in the cache.
If cycles are possible, use a visited set during recursion to detect cycles and either break them or report an error. For shared references, ensure that each node is computed only once, leveraging the cache across different parents.
Explain that with memoization, each node is visited once, giving O(N) time and O(N) space for the cache. Discuss trade-offs: memory overhead for caching, potential for stack overflow with deep recursion, and the need for cycle detection if the graph isn't a DAG.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.