The base topological sort was fine, but the lexicographic requirement tripped me up for a bit.
Model the constraints as a directed graph and use Kahn's algorithm for topological sorting, replacing the standard queue with a min-heap to ensure the lexicographically smallest ordering. If the heap empties before all items are processed, a cycle exists, so return 'IMPOSSIBLE'. Analyze complexity as O(V + E log V) time and O(V + E) space.
Pro tip: Explicitly state that you're using a min-heap instead of a queue to guarantee lexicographic order, and mention that this is a common interview twist that tests understanding of both topological sort and priority queues.
Confirm that items are identified by comparable IDs (e.g., integers or strings) and that constraints are directed edges. Ask about input size, whether duplicate edges are possible, and if the graph is guaranteed to be a DAG.
Create an adjacency list for the directed graph and an array to track in-degrees of each node. Iterate through all constraints to populate both structures.
Push all nodes with in-degree 0 into a min-heap (priority queue) to always extract the smallest available item, ensuring lexicographic order.
While the heap is not empty, pop the smallest node, append it to the result, and for each neighbor, decrement its in-degree; if it becomes 0, push it into the heap.
If the result length is less than n, a cycle exists, so return 'IMPOSSIBLE'. Otherwise, return the result. State time complexity O(V + E log V) and space complexity O(V + E).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the problem as a graph where each item and each group is a node, with directed edges for ordering constraints. Contract each group into a single node to enforce contiguity, then perform a topological sort on the condensed graph. If a cycle exists, return 'IMPOSSIBLE'; otherwise, expand the groups back into their items to produce a valid sequence.
Pro tip: Explicitly handle edge cases like empty groups, groups with a single item, and constraints that conflict with group contiguity (e.g., an item outside a group must come between two items of the same group). Discussing these shows thoroughness and can preempt interviewer concerns.
Confirm that groups must appear as contiguous blocks, and that both within-group and between-group ordering constraints must be respected. Ask about edge cases like empty groups or conflicting constraints.
Create nodes for each item and each group. Add directed edges for all ordering constraints. Then contract each group into a single node, merging all internal edges and redirecting external edges to the group node.
Run a cycle detection algorithm (e.g., DFS or Kahn's algorithm) on the condensed graph. If a cycle is found, return 'IMPOSSIBLE'. Otherwise, obtain a topological ordering of the condensed nodes.
Replace each group node in the topological order with its internal topological order of items. Verify that the final sequence respects all original constraints and that groups remain contiguous.
State the time and space complexity (O(V+E) for graph construction and topological sort). Mention potential optimizations like incremental cycle detection or handling dynamic constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.