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Find Eventual Safe States

There is a directed graph of n nodes with each node labeled from 0 to n - 1.

There is a directed graph of n nodes with each node labeled from 0 to n - 1. The graph is represented by a 0-indexed 2D integer array graph where graph[i] is an integer array of nodes adjacent to node i, meaning there is an edge from node i to each node in graph[i].

A node is a terminal node if there are no outgoing edges. A node is a safe node if every possible path starting from that node leads to a terminal node (or another safe node).

Return an array containing all the safe nodes of the graph. The answer should be sorted in ascending order.

Find Eventual Safe States diagram

Example 1

Input: graph = [[1,2],[2,3],[5],[0],[5],[],[]]

Output: [2,4,5,6]

Explanation: The given graph is shown above. Nodes 5 and 6 are terminal nodes as there are no outgoing edges from either of them. Every path starting at nodes 2, 4, 5, and 6 all lead to either node 5 or 6.

Example 2

Input: graph = [[1,2,3,4],[1,2],[3,4],[0,4],[]]

Output: [4]

Explanation: Only node 4 is a terminal node, and every path starting at node 4 leads to node 4.

Constraints

  • n == graph.length
  • 1 <= n <= 10^4
  • 0 <= graph[i].length <= n
  • 0 <= graph[i][j] <= n - 1
  • graph[i] is sorted in a strictly increasing order.
  • The graph may contain self-loops.
  • The number of edges in the graph will be in the range [1, 4 * 10^4].

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