Y

```
// Kahn's algorithm computes a topological ordering of a directed acyclic graph (DAG).
// Time Complexity: O(V + E)
// Space Complexity: O(V + E)
// Reference: https://en.wikipedia.org/wiki/Topological_sorting#Kahn's_algorithm
// see graph.go, topological.go, kahn_test.go
package graph
// Kahn's algorithm computes a topological ordering of a directed acyclic graph (DAG).
// `n` is the number of vertices,
// `dependencies` is a list of directed edges, where each pair [a, b] represents
// a directed edge from a to b (i.e. b depends on a).
// Vertices are assumed to be labelled 0, 1, ..., n-1.
// If the graph is not a DAG, the function returns nil.
func Kahn(n int, dependencies [][]int) []int {
g := Graph{vertices: n, Directed: true}
// track the in-degree (number of incoming edges) of each vertex
inDegree := make([]int, n)
// populate g with edges, increase the in-degree counts accordingly
for _, d := range dependencies {
// make sure we don't add the same edge twice
if _, ok := g.edges[d[0]][d[1]]; !ok {
g.AddEdge(d[0], d[1])
inDegree[d[1]]++
}
}
// queue holds all vertices with in-degree 0
// these vertices have no dependency and thus can be ordered first
queue := make([]int, 0, n)
for i := 0; i < n; i++ {
if inDegree[i] == 0 {
queue = append(queue, i)
}
}
// order holds a valid topological order
order := make([]int, 0, n)
// process the dependency-free vertices
// every time we process a vertex, we "remove" it from the graph
for len(queue) > 0 {
// pop the first vertex from the queue
vtx := queue[0]
queue = queue[1:]
// add the vertex to the topological order
order = append(order, vtx)
// "remove" all the edges coming out of this vertex
// every time we remove an edge, the corresponding in-degree reduces by 1
// if all dependencies on a vertex is removed, enqueue the vertex
for neighbour := range g.edges[vtx] {
inDegree[neighbour]--
if inDegree[neighbour] == 0 {
queue = append(queue, neighbour)
}
}
}
// if the graph is a DAG, order should contain all the certices
if len(order) != n {
return nil
}
return order
}
```