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Start by defining a simple TreeNode class with value, left, and right attributes. Then implement recursive traversals first, as they are straightforward, and use them as a reference to implement iterative versions using an explicit stack. Finally, analyze time and space complexity for each approach, noting that all traversals visit each node once (O(n) time) and space depends on tree height (O(h) for recursion/stack, O(n) worst-case).
Pro tip: Mention that iterative traversals can be unified using a stack of (node, state) pairs or by using Morris traversal for O(1) space, but clarify that the explicit stack approach is expected here. Also, emphasize that preorder and postorder iterative are easy with a stack, but inorder requires careful pointer manipulation.
Create a class with a constructor that initializes value, left, and right attributes. Keep it simple and generic.
Write preorder, inorder, and postorder functions that recursively visit left and right subtrees. Use a helper function that appends to a result list.
For preorder, push root and process; for inorder, traverse left while pushing; for postorder, use two stacks or reverse preorder. Ensure each returns a list.
State that all traversals run in O(n) time. Space is O(h) for recursion and explicit stack, where h is tree height; worst-case O(n) for skewed tree, best-case O(log n) for balanced tree.
Walk through a small tree (e.g., 1-2-3) to verify outputs. Mention edge cases like empty tree, single node, and skewed tree.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the graph representation and requirements, then outline BFS using a queue and visited set to track order, distances, and parents. Explain how to handle disconnected graphs by iterating over all nodes and running BFS from each unvisited node, resetting or accumulating results as needed.
Pro tip: Mention that BFS naturally finds shortest paths in unweighted graphs, and discuss trade-offs like using a deque for O(1) pops and the memory cost of storing parents for path reconstruction.
Confirm the graph is unweighted, adjacency list format, and whether the source is guaranteed to be in the graph. Ask if the graph is directed or undirected and if multiple components should be handled.
Use a queue to process nodes level by level, a visited set to avoid revisiting, and maintain arrays/maps for visit order, distances, and parents. Initialize distance of source to 0 and parent to null.
While queue is not empty, dequeue a node, record its visit order, and for each neighbor not visited, mark visited, set distance = current distance + 1, set parent, and enqueue.
After BFS from the source, check for unvisited nodes. For each unvisited node, run BFS from it, treating it as a new component. Decide whether to return separate results per component or a combined structure with component IDs.
State time complexity O(V+E) and space O(V). Mention edge cases: empty graph, source not present, self-loops, and multiple components. Explain how parent map enables path reconstruction via backtracking.
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 backtracking solution with a clear recursion tree, followed by the iterative solution that builds subsets layer by layer. Explain how each new element doubles the number of subsets, and analyze time and space complexity for both approaches.
Pro tip: Emphasize that the iterative approach naturally generates subsets in increasing size order, which can be useful for certain applications, and mention that the total number of subsets is 2^n, so any solution must take at least O(2^n) time.
Confirm that the array contains distinct integers and that the order of subsets does not matter. Discuss edge cases like empty array.
Explain the recursive backtracking approach: at each index, decide to include or exclude the current element, building subsets incrementally. Trace through a small example to illustrate.
Describe the iterative method: start with a list containing the empty subset. For each element, create new subsets by adding the element to all existing subsets and append them to the list.
Analyze time complexity: both methods generate 2^n subsets, each taking O(n) to copy, resulting in O(n * 2^n) time. Space complexity: O(n * 2^n) to store all subsets, plus O(n) recursion stack for backtracking.
Summarize the trade-offs: backtracking is more memory-efficient during generation but recursive; iterative is straightforward and avoids recursion overhead. Mention that both are optimal in terms of output size.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.