Problem
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 <= 104
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 * 104]
.
Solution
/**
* @param {number[][]} graph
* @return {number[]}
*/
var eventualSafeNodes = function(graph) {
var map = Array(graph.length);
var path = Array(graph.length);
var res = [];
for (var i = 0; i < graph.length; i++) {
if (isSafeNode(i, graph, map, path)) {
res.push(i);
}
}
return res;
};
var isSafeNode = function(i, graph, map, path) {
if (graph[i].length === 0 || map[i] === 1) return true;
if (map[i] === 2 || path[i] === 1) return false;
path[i] = 1;
for (var j = 0; j < graph[i].length; j++) {
var index = graph[i][j];
if (!isSafeNode(index, graph, map, path)) {
path[i] = 0;
map[i] = 2;
return false;
}
}
path[i] = 0;
map[i] = 1;
return true;
};
Explain:
DFS (Depth First Search).
Complexity:
n
nodes, m
edges.
- Time complexity : O(n + m).
- Space complexity : O(n + m).