package dag
import (
"fmt"
"sort"
"strings"
"github.com/hashicorp/go-multierror"
)
// AcyclicGraph is a specialization of Graph that cannot have cycles. With
// this property, we get the property of sane graph traversal.
type AcyclicGraph struct {
Graph
}
// WalkFunc is the callback used for walking the graph.
type WalkFunc func(Vertex) error
// DepthWalkFunc is a walk function that also receives the current depth of the
// walk as an argument
type DepthWalkFunc func(Vertex, int) error
func (g *AcyclicGraph) DirectedGraph() Grapher {
return g
}
// Returns a Set that includes every Vertex yielded by walking down from the
// provided starting Vertex v.
func (g *AcyclicGraph) Ancestors(v Vertex) (*Set, error) {
s := new(Set)
start := AsVertexList(g.DownEdges(v))
memoFunc := func(v Vertex, d int) error {
s.Add(v)
return nil
}
if err := g.DepthFirstWalk(start, memoFunc); err != nil {
return nil, err
}
return s, nil
}
// Returns a Set that includes every Vertex yielded by walking up from the
// provided starting Vertex v.
func (g *AcyclicGraph) Descendents(v Vertex) (*Set, error) {
s := new(Set)
start := AsVertexList(g.UpEdges(v))
memoFunc := func(v Vertex, d int) error {
s.Add(v)
return nil
}
if err := g.ReverseDepthFirstWalk(start, memoFunc); err != nil {
return nil, err
}
return s, nil
}
// Root returns the root of the DAG, or an error.
//
// Complexity: O(V)
func (g *AcyclicGraph) Root() (Vertex, error) {
roots := make([]Vertex, 0, 1)
for _, v := range g.Vertices() {
if g.UpEdges(v).Len() == 0 {
roots = append(roots, v)
}
}
if len(roots) > 1 {
// TODO(mitchellh): make this error message a lot better
return nil, fmt.Errorf("multiple roots: %#v", roots)
}
if len(roots) == 0 {
return nil, fmt.Errorf("no roots found")
}
return roots[0], nil
}
// TransitiveReduction performs the transitive reduction of graph g in place.
// The transitive reduction of a graph is a graph with as few edges as
// possible with the same reachability as the original graph. This means
// that if there are three nodes A => B => C, and A connects to both
// B and C, and B connects to C, then the transitive reduction is the
// same graph with only a single edge between A and B, and a single edge
// between B and C.
//
// The graph must be valid for this operation to behave properly. If
// Validate() returns an error, the behavior is undefined and the results
// will likely be unexpected.
//
// Complexity: O(V(V+E)), or asymptotically O(VE)
func (g *AcyclicGraph) TransitiveReduction() {
// For each vertex u in graph g, do a DFS starting from each vertex
// v such that the edge (u,v) exists (v is a direct descendant of u).
//
// For each v-prime reachable from v, remove the edge (u, v-prime).
defer g.debug.BeginOperation("TransitiveReduction", "").End("")
for _, u := range g.Vertices() {
uTargets := g.DownEdges(u)
vs := AsVertexList(g.DownEdges(u))
g.DepthFirstWalk(vs, func(v Vertex, d int) error {
shared := uTargets.Intersection(g.DownEdges(v))
for _, vPrime := range AsVertexList(shared) {
g.RemoveEdge(BasicEdge(u, vPrime))
}
return nil
})
}
}
// Validate validates the DAG. A DAG is valid if it has a single root
// with no cycles.
func (g *AcyclicGraph) Validate() error {
if _, err := g.Root(); err != nil {
return err
}
// Look for cycles of more than 1 component
var err error
cycles := g.Cycles()
if len(cycles) > 0 {
for _, cycle := range cycles {
cycleStr := make([]string, len(cycle))
for j, vertex := range cycle {
cycleStr[j] = VertexName(vertex)
}
err = multierror.Append(err, fmt.Errorf(
"Cycle: %s", strings.Join(cycleStr, ", ")))
}
}
// Look for cycles to self
for _, e := range g.Edges() {
if e.Source() == e.Target() {
err = multierror.Append(err, fmt.Errorf(
"Self reference: %s", VertexName(e.Source())))
}
}
return err
}
func (g *AcyclicGraph) Cycles() [][]Vertex {
var cycles [][]Vertex
for _, cycle := range StronglyConnected(&g.Graph) {
if len(cycle) > 1 {
cycles = append(cycles, cycle)
}
}
return cycles
}
// Walk walks the graph, calling your callback as each node is visited.
// This will walk nodes in parallel if it can. Because the walk is done
// in parallel, the error returned will be a multierror.
func (g *AcyclicGraph) Walk(cb WalkFunc) error {
defer g.debug.BeginOperation(typeWalk, "").End("")
w := &Walker{Callback: cb, Reverse: true}
w.Update(g)
return w.Wait()
}
// simple convenience helper for converting a dag.Set to a []Vertex
func AsVertexList(s *Set) []Vertex {
rawList := s.List()
vertexList := make([]Vertex, len(rawList))
for i, raw := range rawList {
vertexList[i] = raw.(Vertex)
}
return vertexList
}
type vertexAtDepth struct {
Vertex Vertex
Depth int
}
// depthFirstWalk does a depth-first walk of the graph starting from
// the vertices in start. This is not exported now but it would make sense
// to export this publicly at some point.
func (g *AcyclicGraph) DepthFirstWalk(start []Vertex, f DepthWalkFunc) error {
defer g.debug.BeginOperation(typeDepthFirstWalk, "").End("")
seen := make(map[Vertex]struct{})
frontier := make([]*vertexAtDepth, len(start))
for i, v := range start {
frontier[i] = &vertexAtDepth{
Vertex: v,
Depth: 0,
}
}
for len(frontier) > 0 {
// Pop the current vertex
n := len(frontier)
current := frontier[n-1]
frontier = frontier[:n-1]
// Check if we've seen this already and return...
if _, ok := seen[current.Vertex]; ok {
continue
}
seen[current.Vertex] = struct{}{}
// Visit the current node
if err := f(current.Vertex, current.Depth); err != nil {
return err
}
// Visit targets of this in a consistent order.
targets := AsVertexList(g.DownEdges(current.Vertex))
sort.Sort(byVertexName(targets))
for _, t := range targets {
frontier = append(frontier, &vertexAtDepth{
Vertex: t,
Depth: current.Depth + 1,
})
}
}
return nil
}
// reverseDepthFirstWalk does a depth-first walk _up_ the graph starting from
// the vertices in start.
func (g *AcyclicGraph) ReverseDepthFirstWalk(start []Vertex, f DepthWalkFunc) error {
defer g.debug.BeginOperation(typeReverseDepthFirstWalk, "").End("")
seen := make(map[Vertex]struct{})
frontier := make([]*vertexAtDepth, len(start))
for i, v := range start {
frontier[i] = &vertexAtDepth{
Vertex: v,
Depth: 0,
}
}
for len(frontier) > 0 {
// Pop the current vertex
n := len(frontier)
current := frontier[n-1]
frontier = frontier[:n-1]
// Check if we've seen this already and return...
if _, ok := seen[current.Vertex]; ok {
continue
}
seen[current.Vertex] = struct{}{}
// Add next set of targets in a consistent order.
targets := AsVertexList(g.UpEdges(current.Vertex))
sort.Sort(byVertexName(targets))
for _, t := range targets {
frontier = append(frontier, &vertexAtDepth{
Vertex: t,
Depth: current.Depth + 1,
})
}
// Visit the current node
if err := f(current.Vertex, current.Depth); err != nil {
return err
}
}
return nil
}
// byVertexName implements sort.Interface so a list of Vertices can be sorted
// consistently by their VertexName
type byVertexName []Vertex
func (b byVertexName) Len() int { return len(b) }
func (b byVertexName) Swap(i, j int) { b[i], b[j] = b[j], b[i] }
func (b byVertexName) Less(i, j int) bool {
return VertexName(b[i]) < VertexName(b[j])
}
