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// Copyright 2024 CUE Authors
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
package toposort
import (
"slices"
)
type sccNodeState struct {
component *StronglyConnectedComponent
lowLink uint
index uint
visited bool
onStack bool
}
type StronglyConnectedComponent struct {
Nodes Nodes
Outgoing []*StronglyConnectedComponent
Incoming []*StronglyConnectedComponent
visited bool
}
// Calculate the Strongly Connected Components of the graph.
// https://en.wikipedia.org/wiki/Strongly_connected_component
//
// The components returned are topologically sorted (forwards), and
// form a DAG (this is the "condensation graph").
func (graph *Graph) StronglyConnectedComponents() []*StronglyConnectedComponent {
nodeStates := make([]sccNodeState, len(graph.nodes))
for i, node := range graph.nodes {
node.sccNodeState = &nodeStates[i]
}
scc := &sccFinderState{}
for _, node := range graph.nodes {
if !node.sccNodeState.visited {
scc.findSCC(node)
}
}
for _, node := range graph.nodes {
node.sccNodeState = nil
}
components := scc.components
for _, component := range components {
for _, next := range component.Outgoing {
next.Incoming = append(next.Incoming, component)
}
}
slices.Reverse(components)
return components
}
type sccFinderState struct {
components []*StronglyConnectedComponent
stack Nodes
counter uint
}
// This is Tarjan's algorithm from 1972.
//
// Robert Tarjan: Depth-first search and linear graph algorithms.
// SIAM Journal on Computing. Volume 1, Nr. 2 (1972), pp. 146-160.
//
// https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm
func (scc *sccFinderState) findSCC(cur *Node) {
num := scc.counter
scc.counter++
curScc := cur.sccNodeState
curScc.lowLink = num
curScc.index = num
curScc.visited = true
curScc.onStack = true
scc.stack = append(scc.stack, cur)
for _, next := range cur.Outgoing {
nextScc := next.sccNodeState
if !nextScc.visited {
scc.findSCC(next)
curScc.lowLink = min(curScc.lowLink, nextScc.lowLink)
} else if nextScc.onStack {
// If the next node is already on the stack, the edge joining
// the current node and the next node completes a cycle.
curScc.lowLink = min(curScc.lowLink, nextScc.index)
}
}
// If the lowlink value of the node is equal to its DFS value, this
// is the head node of a strongly connected component that's shaped
// by the node and all nodes on the stack.
if curScc.lowLink == curScc.index {
component := &StronglyConnectedComponent{visited: true}
var componentNodes Nodes
for i := len(scc.stack) - 1; i >= 0; i-- {
nodeN := scc.stack[i]
nodeNScc := nodeN.sccNodeState
nodeNScc.onStack = false
nodeNScc.component = component
componentNodes = append(componentNodes, nodeN)
if nodeNScc == curScc {
scc.stack = scc.stack[:i]
break
}
}
var outgoingComponents []*StronglyConnectedComponent
for _, node := range componentNodes {
for _, nextNode := range node.Outgoing {
// This algorithm is depth-first, which means we can rely
// on the next component always existing before our own
// component.
nextComponent := nextNode.sccNodeState.component
if !nextComponent.visited {
nextComponent.visited = true
outgoingComponents = append(outgoingComponents, nextComponent)
}
}
}
component.Nodes = componentNodes
component.Outgoing = outgoingComponents
component.visited = false
for _, component := range outgoingComponents {
component.visited = false
}
scc.components = append(scc.components, component)
}
}
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