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Copy pathpaths.go
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Copy pathpaths.go
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333 lines (273 loc) · 8.69 KB
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package graph
import (
"errors"
"fmt"
"math"
)
var ErrTargetNotReachable = errors.New("target vertex not reachable from source")
// CreatesCycle determines whether adding an edge between the two given vertices
// would introduce a cycle in the graph. CreatesCycle will not create an edge.
//
// A potential edge would create a cycle if the target vertex is also a parent
// of the source vertex. In order to determine this, CreatesCycle runs a DFS.
func CreatesCycle[K comparable, T any](g Graph[K, T], source, target K) (bool, error) {
if _, err := g.Vertex(source); err != nil {
return false, fmt.Errorf("could not get vertex with hash %v: %w", source, err)
}
if _, err := g.Vertex(target); err != nil {
return false, fmt.Errorf("could not get vertex with hash %v: %w", target, err)
}
if source == target {
return true, nil
}
predecessorMap, err := g.PredecessorMap()
if err != nil {
return false, fmt.Errorf("failed to get predecessor map: %w", err)
}
stack := newStack[K]()
visited := make(map[K]bool)
stack.push(source)
for !stack.isEmpty() {
currentHash, _ := stack.pop()
if _, ok := visited[currentHash]; !ok {
// If the adjacent vertex also is the target vertex, the target is a
// parent of the source vertex. An edge would introduce a cycle.
if currentHash == target {
return true, nil
}
visited[currentHash] = true
for adjacency := range predecessorMap[currentHash] {
stack.push(adjacency)
}
}
}
return false, nil
}
// ShortestPath computes the shortest path between a source and a target vertex
// under consideration of the edge weights. It returns a slice of hash values of
// the vertices forming that path.
//
// The returned path includes the source and target vertices. If the target is
// not reachable from the source, ErrTargetNotReachable will be returned. Should
// there be multiple shortest paths, and arbitrary one will be returned.
//
// ShortestPath has a time complexity of O(|V|+|E|log(|V|)).
func ShortestPath[K comparable, T any](g Graph[K, T], source, target K) ([]K, error) {
weights := make(map[K]float64)
visited := make(map[K]bool)
weights[source] = 0
visited[target] = true
queue := newPriorityQueue[K]()
adjacencyMap, err := g.AdjacencyMap()
if err != nil {
return nil, fmt.Errorf("could not get adjacency map: %w", err)
}
for hash := range adjacencyMap {
if hash != source {
weights[hash] = math.Inf(1)
visited[hash] = false
}
queue.Push(hash, weights[hash])
}
// bestPredecessors stores the cheapest or least-weighted predecessor for
// each vertex. Given an edge AC with weight=4 and an edge BC with weight=2,
// the cheapest predecessor for C is B.
bestPredecessors := make(map[K]K)
for queue.Len() > 0 {
vertex, _ := queue.Pop()
hasInfiniteWeight := math.IsInf(weights[vertex], 1)
for adjacency, edge := range adjacencyMap[vertex] {
edgeWeight := edge.Properties.Weight
// Setting the weight to 1 is required for unweighted graphs whose
// edge weights are 0. Otherwise, all paths would have a sum of 0
// and a random path would be returned.
if !g.Traits().IsWeighted {
edgeWeight = 1
}
weight := weights[vertex] + float64(edgeWeight)
if weight < weights[adjacency] && !hasInfiniteWeight {
weights[adjacency] = weight
bestPredecessors[adjacency] = vertex
queue.UpdatePriority(adjacency, weight)
}
}
}
path := []K{target}
current := target
for current != source {
// If the current vertex is not present in bestPredecessors, current is
// set to the zero value of K. Without this check, this would lead to an
// endless prepending of zero values to the path. Also, the target would
// not be reachable from one of the preceding vertices.
if _, ok := bestPredecessors[current]; !ok {
return nil, ErrTargetNotReachable
}
current = bestPredecessors[current]
path = append([]K{current}, path...)
}
return path, nil
}
type sccState[K comparable] struct {
adjacencyMap map[K]map[K]Edge[K]
components [][]K
stack *stack[K]
visited map[K]struct{}
lowlink map[K]int
index map[K]int
time int
}
// StronglyConnectedComponents detects all strongly connected components within
// the graph and returns the hashes of the vertices shaping these components, so
// each component is represented by a []K.
//
// StronglyConnectedComponents can only run on directed graphs.
func StronglyConnectedComponents[K comparable, T any](g Graph[K, T]) ([][]K, error) {
if !g.Traits().IsDirected {
return nil, errors.New("SCCs can only be detected in directed graphs")
}
adjacencyMap, err := g.AdjacencyMap()
if err != nil {
return nil, fmt.Errorf("could not get adjacency map: %w", err)
}
state := &sccState[K]{
adjacencyMap: adjacencyMap,
components: make([][]K, 0),
stack: newStack[K](),
visited: make(map[K]struct{}),
lowlink: make(map[K]int),
index: make(map[K]int),
}
for hash := range state.adjacencyMap {
if _, ok := state.visited[hash]; !ok {
findSCC(hash, state)
}
}
return state.components, nil
}
func findSCC[K comparable](vertexHash K, state *sccState[K]) {
state.stack.push(vertexHash)
state.visited[vertexHash] = struct{}{}
state.index[vertexHash] = state.time
state.lowlink[vertexHash] = state.time
state.time++
for adjacency := range state.adjacencyMap[vertexHash] {
if _, ok := state.visited[adjacency]; !ok {
findSCC(adjacency, state)
smallestLowlink := math.Min(
float64(state.lowlink[vertexHash]),
float64(state.lowlink[adjacency]),
)
state.lowlink[vertexHash] = int(smallestLowlink)
} else {
// If the adjacent vertex already is on the stack, the edge joining
// the current and the adjacent vertex is a back ege. Therefore, the
// lowlink value of the vertex has to be updated to the index of the
// adjacent vertex if it is smaller than the current lowlink value.
if state.stack.contains(adjacency) {
smallestLowlink := math.Min(
float64(state.lowlink[vertexHash]),
float64(state.index[adjacency]),
)
state.lowlink[vertexHash] = int(smallestLowlink)
}
}
}
// If the lowlink value of the vertex is equal to its DFS value, this is the
// head vertex of a strongly connected component that's shaped by the vertex
// and all vertices on the stack.
if state.lowlink[vertexHash] == state.index[vertexHash] {
var hash K
var component []K
for hash != vertexHash {
hash, _ = state.stack.pop()
component = append(component, hash)
}
state.components = append(state.components, component)
}
}
// AllPathsBetween computes and returns all paths between two given vertices. A
// path is represented as a slice of vertex hashes. The returned slice contains
// these paths.
//
// AllPathsBetween utilizes a non-recursive, stack-based implementation. It has
// an estimated runtime complexity of O(n^2) where n is the number of vertices.
func AllPathsBetween[K comparable, T any](g Graph[K, T], start, end K) ([][]K, error) {
adjacencyMap, err := g.AdjacencyMap()
if err != nil {
return nil, err
}
// The algorithm used relies on stacks instead of recursion. It is described
// here: https://boycgit.github.io/all-paths-between-two-vertex/
mainStack := newStack[K]()
viceStack := newStackOfStacks[K]()
checkEmpty := func() error {
if mainStack.isEmpty() || viceStack.isEmpty() {
return errors.New("empty stack")
}
return nil
}
buildLayer := func(element K) {
mainStack.push(element)
newElements := newStack[K]()
for e := range adjacencyMap[element] {
var contains bool
mainStack.forEach(func(k K) {
if e == k {
contains = true
}
})
if contains {
continue
}
newElements.push(e)
}
viceStack.push(newElements)
}
buildStack := func() error {
if err = checkEmpty(); err != nil {
return fmt.Errorf("unable to build stack: %w", err)
}
elements, _ := viceStack.top()
for !elements.isEmpty() {
element, _ := elements.pop()
buildLayer(element)
elements, _ = viceStack.top()
}
return nil
}
removeLayer := func() error {
if err = checkEmpty(); err != nil {
return fmt.Errorf("unable to remove layer: %w", err)
}
if e, _ := viceStack.top(); !e.isEmpty() {
return errors.New("the top element of vice-stack is not empty")
}
_, _ = mainStack.pop()
_, _ = viceStack.pop()
return nil
}
buildLayer(start)
allPaths := make([][]K, 0)
for !mainStack.isEmpty() {
v, _ := mainStack.top()
adjs, _ := viceStack.top()
if adjs.isEmpty() {
if v == end {
path := make([]K, 0)
mainStack.forEach(func(k K) {
path = append(path, k)
})
allPaths = append(allPaths, path)
}
err = removeLayer()
if err != nil {
return nil, err
}
} else {
if err = buildStack(); err != nil {
return nil, err
}
}
}
return allPaths, nil
}