The 'define your own input format' part threw me a little, felt like a trick but it's probably just them being flexible.
Model this as a graph connectivity problem where stones 'block' the river if a connected chain of overlapping or touching circles spans from one bank to the other. Represent each circle as a node, add edges between circles that overlap or touch, then use Union-Find or BFS/DFS to check if any component connects the top bank to the bottom bank. This cleanly separates the geometric overlap detection from the connectivity logic.
Pro tip: Proactively define your input format and coordinate system before coding — for example, 'river flows along the x-axis, width spans y=0 to y=W, each stone is (cx, cy, r)' — this signals strong problem-framing skills and avoids ambiguity that interviewers often use to trip candidates up.
Explicitly state your chosen input format (e.g., list of tuples (cx, cy, r)) and clarify the river model — river width W, banks at y=0 and y=W, stones block if they touch or overlap each other and reach both banks. Ask about edge cases like a single stone spanning the full width.
Treat each stone as a node and add a virtual 'top bank' node and 'bottom bank' node. Two stones are connected if the distance between their centers is less than or equal to the sum of their radii; a stone connects to a bank if it touches or crosses that bank's boundary.
For each pair of circles, compute the Euclidean distance between centers and compare it to r1 + r2 to determine adjacency. Also check if cy - r <= 0 (touches top bank) or cy + r >= W (touches bottom bank) for bank connections.
Apply Union-Find (for O(α(n)) per union/find) or BFS/DFS starting from all stones touching the top bank, then check if any reachable stone also touches the bottom bank. Return true if such a path exists.
Discuss the O(n²) pairwise overlap check as the bottleneck and mention that spatial indexing (e.g., a grid or R-tree) could reduce this to O(n log n) for large inputs. Acknowledge that Union-Find is preferable over BFS here for incremental updates.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Started with a stack-based approach which felt pretty natural for matching open/close tags.
Start by clarifying the token types and expected output format, then design a stack-based parser that builds the DOM tree in a single pass. For the follow-up, extend the node structure to support parent pointers and implement insert/delete operations with proper tree updates.
Pro tip: Mention that you would use a sentinel root node to simplify edge cases like inserting before the first child or deleting the root, and discuss how to handle malformed input gracefully.
Ask about token format, whether tags can be self-closing, how to handle mismatched tags, and what the printed output should look like. Confirm if the follow-up operations need to maintain any specific order.
Define a Node class with tag name, children list, and parent pointer. Use a stack to keep track of the current open element during parsing.
Iterate through tokens: on open tag, create a node, append to current parent, and push onto stack; on text, append to current node; on close tag, pop from stack. Handle errors like unexpected close tags.
Use depth-first traversal with indentation to print the tree structure, showing tag names and text content clearly.
For insert, create a new node and splice it into the parent's children list at the given index, updating parent pointers. For delete, remove the node from its parent's children and optionally recursively free its subtree.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.