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package graph
// EulerDirected returns an Euler walk in a directed graph.
// If no such walk exists, it returns an empty walk and sets ok to false.
func EulerDirected(g Iterator) (walk []int, ok bool) {
n := g.Order()
degree := make([]int, n) // outdegree - indegree for each vertex
edgeCount := 0
for v := range degree {
g.Visit(v, func(w int, _ int64) (skip bool) {
edgeCount++
degree[v]++
degree[w]--
return
})
}
if edgeCount == 0 {
return []int{}, true
}
start, end := -1, -1
for v := range degree {
switch {
case degree[v] == 0:
case degree[v] == 1 && start == -1:
start = v
case degree[v] == -1 && end == -1:
end = v
default:
return []int{}, false
}
}
// Make a copy of g
h := make([][]int, n)
for v := range h {
g.Visit(v, func(w int, _ int64) (skip bool) {
h[v] = append(h[v], w)
return
})
}
// Find a starting point with neighbors.
if start == -1 {
for v, neighbors := range h {
if len(neighbors) > 0 {
start = v
break
}
}
}
for stack := []int{start}; len(stack) > 0; {
n := len(stack)
v := stack[n-1]
stack = stack[:n-1]
for len(h[v]) > 0 {
stack = append(stack, v)
v, h[v] = h[v][0], h[v][1:]
edgeCount--
}
walk = append(walk, v)
}
if edgeCount > 0 {
return []int{}, false
}
for i, j := 0, len(walk)-1; i < j; i, j = i+1, j-1 {
walk[i], walk[j] = walk[j], walk[i]
}
return walk, true
}
// EulerUndirected returns an Euler walk following undirected edges
// in only one direction. If no such walk exists, it returns an empty walk
// and sets ok to false.
func EulerUndirected(g Iterator) (walk []int, ok bool) {
n := g.Order()
out := make([]int, n) // outdegree for each vertex
edgeCount := 0
for v := range out {
g.Visit(v, func(w int, _ int64) (skip bool) {
edgeCount++
if v != w {
out[v]++
}
return
})
}
if edgeCount == 0 {
return []int{}, true
}
start, oddDeg := -1, 0
for v := range out {
if out[v]&1 == 1 {
start = v
oddDeg++
}
}
if !(oddDeg == 0 || oddDeg == 2) {
return []int{}, false
}
// Find a starting point with neighbors.
if start == -1 {
for v := 0; v < n; v++ {
if g.Visit(v, func(w int, _ int64) (skip bool) {
start = w
return true
}) {
break
}
}
}
h := Copy(g)
for stack := []int{start}; len(stack) > 0; {
n := len(stack)
v := stack[n-1]
stack = stack[:n-1]
for h.Degree(v) > 0 {
stack = append(stack, v)
var w int
h.Visit(v, func(u int, _ int64) (skip bool) {
w = u
return true
})
h.DeleteBoth(v, w)
edgeCount--
if v != w {
edgeCount--
}
v = w
}
walk = append(walk, v)
}
if edgeCount > 0 {
return []int{}, false
}
return walk, true
}
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