802. Find Eventual Safe States

Find Eventual Safe States (LeetCode 802) is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Graph Traversal Patterns (DFS & BFS) pattern, in the Graph DFS - Cycle Detection (Directed Graph) subpattern.

How to solve Find Eventual Safe States

Find Eventual Safe States is a Cycle Detection in Directed Graph problem, part of Graph Traversal Patterns (DFS & BFS). Detect cycles in directed graphs using DFS with coloring (white, gray, black) approach.

Work towards the solution in these steps:

1. Consider representing the graph using adjacency lists and think about how graph traversal techniques like DFS or BFS could help explore paths from each node.
2. Recall that safe nodes are those from which all paths eventually lead to terminal nodes; detecting cycles in the graph is crucial since nodes involved in cycles can never be safe.
3. Use a DFS approach with a color or state array to track the visitation status of nodes (e.g., unvisited, visiting, visited) to help identify cycles efficiently.

The reference solution runs in O(|V| + |E|) time and O(|V|) space.

The Find Eventual Safe States solution and editorial walks through the full approach with reference code.

Problem statement

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.

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].

Topics and companies

Topics: Depth-First Search, Breadth-First Search, Graph, Topological Sort.

Reported in interviews at Amazon.

How to practise Find Eventual Safe States on Thita.ai

Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(|V| + |E|) time and O(|V|) space.

Open Find Eventual Safe States in the code editor, or read the Find Eventual Safe States editorial for a worked solution with its approach and complexity analysis.

Where Find Eventual Safe States sits in the DSA pattern sheet

• Graph Traversal Patterns (DFS & BFS) pattern guide
• Graph DFS - Cycle Detection (Directed Graph) subpattern
• The full DSA patterns sheet

Problems related to Find Eventual Safe States

Other problems that use the same Graph DFS - Cycle Detection (Directed Graph) and Graph Traversal Patterns (DFS & BFS) techniques:

• All Paths from Source Lead to Destination — Medium, same subpattern
• Course Schedule — Medium, same subpattern
• Course Schedule II — Medium, same subpattern
• Accounts Merge — Medium, same pattern
• Alien Dictionary — Hard, same pattern
• Build a Matrix With Conditions — Hard, same pattern

Find Eventual Safe States FAQ