Floyd's two-pointer thing, slow and fast pointer.
Start by clarifying the problem and constraints, then propose Floyd's cycle-finding algorithm (tortoise and hare) using two pointers moving at different speeds. Explain how the pointers will eventually meet if a cycle exists, and why the algorithm uses O(1) extra space.
Pro tip: Mention that Floyd's algorithm not only detects cycles but can also find the start of the cycle, which is often a follow-up question. Also, discuss edge cases like empty list or single node without cycle.
Ask if the linked list can be modified, if there are constraints on time complexity, and confirm that O(1) space means no additional data structures like hash sets.
Describe using two pointers: slow moves one step, fast moves two steps. If they meet, there is a cycle; if fast reaches null, no cycle.
Write clean code with a while loop that advances slow and fast pointers, checking for null and equality. Handle edge cases like empty list or single node.
Justify that if a cycle exists, the fast pointer will eventually catch up to the slow pointer inside the cycle due to relative speed difference of 1.
State that time complexity is O(n) and space complexity is O(1), and discuss why the algorithm is optimal for this problem.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by explaining the standard DFS-based cycle detection using a recursion stack or color marking, then generalize to directed graphs with multiple children. Address the follow-up scenarios (disconnected graphs, large graphs) by extending the algorithm with techniques like iterative DFS, external memory, or distributed processing, and discuss trade-offs.
Pro tip: Emphasize that cycle detection in directed graphs requires tracking the current recursion stack (or using three colors) to avoid false positives from cross edges. For large graphs, mention that iterative DFS with explicit stack avoids recursion depth limits and can be adapted for external memory.
Restate the problem: given a starting node in a directed graph, determine if any cycle is reachable. Clarify whether the graph is static, if nodes have multiple children (out-degree > 1), and if the graph is connected or not.
Describe DFS with a recursion stack (or three-color marking: white, gray, black) to detect cycles. Explain that a back edge to a gray node indicates a cycle. Mention that BFS with topological sorting (Kahn's algorithm) can also detect cycles but may be less efficient for reachability from a single node.
If the graph is disconnected, run the cycle detection from the given starting node only. If the question implies checking the entire graph, iterate over all unvisited nodes. But since the question specifies 'reachable from it', focus on the starting node's connected component.
Discuss strategies: use external memory algorithms (e.g., sort-based or streaming), distributed processing (e.g., MapReduce, Pregel), or iterative deepening DFS with disk-based storage. Mention that cycle detection can be done via repeated reachability queries or by computing strongly connected components (SCCs) using algorithms like Tarjan's or Kosaraju's, which can be adapted for external memory.
For in-memory DFS: O(V+E) time, O(V) space for recursion stack and visited set. For large graphs: external memory algorithms may increase I/O complexity; distributed algorithms add communication overhead. Discuss trade-offs between time, space, and scalability.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.