2360. Longest Cycle in a Graph
Description
You are given a directed graph of n
nodes numbered from 0
to n - 1
, where each node has at most one outgoing edge.
The graph is represented with a given 0-indexed array edges
of size n
, indicating that there is a directed edge from node i
to node edges[i]
. If there is no outgoing edge from node i
, then edges[i] == -1
.
Return the length of the longest cycle in the graph. If no cycle exists, return -1
.
A cycle is a path that starts and ends at the same node.
Example 1:
Input: edges = [3,3,4,2,3] Output: 3 Explanation: The longest cycle in the graph is the cycle: 2 -> 4 -> 3 -> 2. The length of this cycle is 3, so 3 is returned.
Example 2:
Input: edges = [2,-1,3,1] Output: -1 Explanation: There are no cycles in this graph.
Constraints:
n == edges.length
2 <= n <= 105
-1 <= edges[i] < n
edges[i] != i
Solutions
Solution 1: Traverse Starting Points
We can traverse each node in the range $[0,..,n-1]$. If a node has not been visited, we start from this node and search for adjacent nodes until we encounter a cycle or a node that has already been visited. If we encounter a cycle, we update the answer.
The time complexity is $O(n)$ and the space complexity is $O(n)$, where $n$ is the number of nodes.
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