Enumerate All Simple Directed Cycles

Given a directed graph as an adjacency list, return every distinct simple directed cycle. For this practice version, a simple directed cycle follows directed edges back to its starting vertex without repeating any other vertex. Represent a cycle as an array of its vertices without repeating the starting vertex at the end. The last vertex must have an edge to the first. A self-loop is a one-vertex cycle. ### Input - `graph`: an array of adjacency lists. Vertices are labeled `0` through `graph.length - 1`; `graph[u]` lists the vertices reachable by one directed edge from `u`. ### Output Return the cycles in canonical form: - Rotate each cycle so its smallest vertex label appears first. - List each such cycle once. Rotations of a sequence represent the same cycle. - Preserve edge direction. Reversing a sequence does not generally represent the same directed cycle. - Sort the resulting arrays lexicographically by their vertex sequences, using the shorter sequence first when one is a prefix of another. ### Constraints and Edge Cases - For this practice version, `1 <= graph.length <= 8`. - Adjacency lists may be unsorted but contain no repeated neighbors. - The graph may be disconnected and may contain self-loops. - If the graph contains no directed cycles, return an empty array. ### Example 1 ```text graph = [[1], [2], [0,1], []] output = [[0,1,2], [1,2]] ``` The cycles `[1,2,0]` and `[2,0,1]` are rotations of `[0,1,2]`, so they are not additional results. ### Example 2 ```text graph = [[0,1,2], [0,2], [0,1]] output = [[0], [0,1], [0,1,2], [0,2], [0,2,1], [1,2]] ``` Both `[0,1,2]` and `[0,2,1]` are valid because their directed edges exist, and they are distinct. The self-loop contributes `[0]`.