Recursive solution came to me pretty fast: both null means true, one null means false, values differ means false, child list lengths differ means false, then recurse on each pair of children.
Use a recursive depth-first traversal that simultaneously compares the root values, the number of children, and recursively checks each corresponding child subtree. If any mismatch is found, return false; otherwise, return true after all children are compared.
Pro tip: Mention that the recursion can be implemented iteratively using a stack to avoid potential stack overflow for very deep trees, and discuss the trade-offs between recursive elegance and iterative robustness.
Confirm that 'identical' means both structure (same number of children at each node) and node values must match exactly. Ask if the trees can be empty or have nodes with null values.
Base cases: if both nodes are null, return true; if one is null and the other isn't, return false. Then compare current node values and the number of children.
Iterate through the children lists of both nodes simultaneously, recursively calling the function on each pair. If any recursive call returns false, propagate false.
State that time complexity is O(N) where N is the number of nodes (since each node is visited once), and space complexity is O(H) for recursion stack, where H is the height of the tree.
Mention handling of empty trees, trees with different heights, and potential iterative solution using a stack to avoid recursion depth limits. Also note that early termination on mismatch improves average performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Used two stacks running in parallel, popping one node from each and comparing them, then pushing their children in order.
Use an explicit stack (or queue) to simulate the recursion, pushing pairs of nodes to compare. Process each pair by checking value equality and pushing their children onto the stack. This avoids call stack overhead and handles deep trees safely.
Pro tip: Mention that an explicit stack can be implemented with a simple array or a deque, and that using a queue yields a BFS-style comparison while a stack yields DFS—both are valid. Also note that this approach avoids stack overflow on deep trees, which is a practical concern in production systems.
Briefly restate the recursive tree comparison: two trees are equal if both are null, or both are non-null with equal values and equal left and right subtrees. This sets the foundation for the iterative version.
Select an explicit stack (for DFS) or queue (for BFS) to store pairs of nodes to compare. Explain that a stack mimics the call stack of recursion, while a queue processes level by level.
Push the root pair onto the stack. While the stack is not empty, pop a pair, compare them, and if both are non-null and equal, push their left children as a pair and right children as a pair.
Check for null nodes: if one is null and the other isn't, return false. If both are null, continue. Also consider empty trees and single-node trees.
State that time complexity is O(n) where n is the number of nodes, and space complexity is O(h) for DFS (h = height) or O(w) for BFS (w = max width), due to the explicit data structure.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Said O(N) time for both since you visit every node once.
Start by clearly stating the time and space complexity for both recursive and iterative solutions, using Big-O notation. Then, explain the reasoning behind each complexity, focusing on the number of operations and memory usage. Finally, compare the trade-offs between the two approaches, highlighting scenarios where one might be preferred over the other.
Pro tip: Always relate the complexity analysis to the specific problem context and constraints, showing that you understand the practical implications. Mentioning potential optimizations or alternative approaches demonstrates deeper insight.
Begin by explicitly stating the time and space complexity for both recursive and iterative solutions using Big-O notation. This sets a clear foundation for your analysis.
Break down the recursive solution: analyze the number of recursive calls (time) and the maximum depth of the call stack (space). Consider if there are overlapping subproblems or if memoization is used.
Analyze the iterative solution: count the number of iterations (time) and the extra space used for variables, data structures, etc. (space). Highlight any differences from the recursive approach.
Discuss the trade-offs between the two approaches. For example, recursion may be more elegant but use more stack space, while iteration may be more efficient but less readable. Mention any tail recursion optimizations if applicable.
Connect the complexity analysis to the specific problem and its constraints. Explain which solution is more suitable given factors like input size, memory limits, or performance requirements.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.