// Copyright 2014 Sonia Keys
// License MIT: http://opensource.org/licenses/MIT

package graph

// dir_RO.go is code generated from dir_cg.go by directives in graph.go.
// Editing dir_cg.go is okay.  It is the code generation source.
// DO NOT EDIT dir_RO.go.
// The RO means read only and it is upper case RO to slow you down a bit
// in case you start to edit the file.

// Balanced returns true if for every node in g, in-degree equals out-degree.
//
// There are equivalent labeled and unlabeled versions of this method.
func (g Directed) Balanced() bool {
	for n, in := range g.InDegree() {
		if in != len(g.AdjacencyList[n]) {
			return false
		}
	}
	return true
}

// Copy makes a deep copy of g.
// Copy also computes the arc size ma, the number of arcs.
//
// There are equivalent labeled and unlabeled versions of this method.
func (g Directed) Copy() (c Directed, ma int) {
	l, s := g.AdjacencyList.Copy()
	return Directed{l}, s
}

// Cyclic determines if g contains a cycle, a non-empty path from a node
// back to itself.
//
// Cyclic returns true if g contains at least one cycle.  It also returns
// an example of an arc involved in a cycle.
// Cyclic returns false if g is acyclic.
//
// Also see Topological, which detects cycles.
//
// There are equivalent labeled and unlabeled versions of this method.
func (g Directed) Cyclic() (cyclic bool, fr NI, to NI) {
	a := g.AdjacencyList
	fr, to = -1, -1
	var temp, perm Bits
	var df func(NI)
	df = func(n NI) {
		switch {
		case temp.Bit(n) == 1:
			cyclic = true
			return
		case perm.Bit(n) == 1:
			return
		}
		temp.SetBit(n, 1)
		for _, nb := range a[n] {
			df(nb)
			if cyclic {
				if fr < 0 {
					fr, to = n, nb
				}
				return
			}
		}
		temp.SetBit(n, 0)
		perm.SetBit(n, 1)
	}
	for n := range a {
		if perm.Bit(NI(n)) == 1 {
			continue
		}
		if df(NI(n)); cyclic { // short circuit as soon as a cycle is found
			break
		}
	}
	return
}

// FromList transposes a labeled graph into a FromList.
//
// Receiver g should be connected as a tree or forest.  Specifically no node
// can have multiple incoming arcs.  If any node n in g has multiple incoming
// arcs, the method returns (nil, n) where n is a node with multiple
// incoming arcs.
//
// Otherwise (normally) the method populates the From members in a
// FromList.Path and returns the FromList and -1.
//
// Other members of the FromList are left as zero values.
// Use FromList.RecalcLen and FromList.RecalcLeaves as needed.
//
// Unusual cases are parallel arcs and loops.  A parallel arc represents
// a case of multiple arcs going to some node and so will lead to a (nil, n)
// return, even though a graph might be considered a multigraph tree.
// A single loop on a node that would otherwise be a root node, though,
// is not a case of multiple incoming arcs and so does not force a (nil, n)
// result.
//
// There are equivalent labeled and unlabeled versions of this method.
func (g Directed) FromList() (*FromList, NI) {
	paths := make([]PathEnd, len(g.AdjacencyList))
	for i := range paths {
		paths[i].From = -1
	}
	for fr, to := range g.AdjacencyList {
		for _, to := range to {
			if paths[to].From >= 0 {
				return nil, to
			}
			paths[to].From = NI(fr)
		}
	}
	return &FromList{Paths: paths}, -1
}

// InDegree computes the in-degree of each node in g
//
// There are equivalent labeled and unlabeled versions of this method.
func (g Directed) InDegree() []int {
	ind := make([]int, len(g.AdjacencyList))
	for _, nbs := range g.AdjacencyList {
		for _, nb := range nbs {
			ind[nb]++
		}
	}
	return ind
}

// IsTree identifies trees in directed graphs.
//
// Return value isTree is true if the subgraph reachable from root is a tree.
// Further, return value allTree is true if the entire graph g is reachable
// from root.
//
// There are equivalent labeled and unlabeled versions of this method.
func (g Directed) IsTree(root NI) (isTree, allTree bool) {
	a := g.AdjacencyList
	var v Bits
	v.SetAll(len(a))
	var df func(NI) bool
	df = func(n NI) bool {
		if v.Bit(n) == 0 {
			return false
		}
		v.SetBit(n, 0)
		for _, to := range a[n] {
			if !df(to) {
				return false
			}
		}
		return true
	}
	isTree = df(root)
	return isTree, isTree && v.Zero()
}

// Tarjan identifies strongly connected components in a directed graph using
// Tarjan's algorithm.
//
// The method calls the emit argument for each component identified.  Each
// component is a list of nodes.  A property of the algorithm is that
// components are emitted in reverse topological order of the condensation.
// (See https://en.wikipedia.org/wiki/Strongly_connected_component#Definitions
// for description of condensation.)
//
// There are equivalent labeled and unlabeled versions of this method.
//
// See also TarjanForward and TarjanCondensation.
func (g Directed) Tarjan(emit func([]NI) bool) {
	// See "Depth-first search and linear graph algorithms", Robert Tarjan,
	// SIAM J. Comput. Vol. 1, No. 2, June 1972.
	//
	// Implementation here from Wikipedia pseudocode,
	// http://en.wikipedia.org/w/index.php?title=Tarjan%27s_strongly_connected_components_algorithm&direction=prev&oldid=647184742
	var indexed, stacked Bits
	a := g.AdjacencyList
	index := make([]int, len(a))
	lowlink := make([]int, len(a))
	x := 0
	var S []NI
	var sc func(NI) bool
	sc = func(n NI) bool {
		index[n] = x
		indexed.SetBit(n, 1)
		lowlink[n] = x
		x++
		S = append(S, n)
		stacked.SetBit(n, 1)
		for _, nb := range a[n] {
			if indexed.Bit(nb) == 0 {
				if !sc(nb) {
					return false
				}
				if lowlink[nb] < lowlink[n] {
					lowlink[n] = lowlink[nb]
				}
			} else if stacked.Bit(nb) == 1 {
				if index[nb] < lowlink[n] {
					lowlink[n] = index[nb]
				}
			}
		}
		if lowlink[n] == index[n] {
			var c []NI
			for {
				last := len(S) - 1
				w := S[last]
				S = S[:last]
				stacked.SetBit(w, 0)
				c = append(c, w)
				if w == n {
					if !emit(c) {
						return false
					}
					break
				}
			}
		}
		return true
	}
	for n := range a {
		if indexed.Bit(NI(n)) == 0 && !sc(NI(n)) {
			return
		}
	}
}

// TarjanForward returns strongly connected components.
//
// It returns components in the reverse order of Tarjan, for situations
// where a forward topological ordering is easier.
func (g Directed) TarjanForward() [][]NI {
	var r [][]NI
	g.Tarjan(func(c []NI) bool {
		r = append(r, c)
		return true
	})
	scc := make([][]NI, len(r))
	last := len(r) - 1
	for i, ci := range r {
		scc[last-i] = ci
	}
	return scc
}

// TarjanCondensation returns strongly connected components and their
// condensation graph.
//
// Components are ordered in a forward topological ordering.
func (g Directed) TarjanCondensation() (scc [][]NI, cd AdjacencyList) {
	scc = g.TarjanForward()
	cd = make(AdjacencyList, len(scc))       // return value
	cond := make([]NI, len(g.AdjacencyList)) // mapping from g node to cd node
	for cn := NI(len(scc) - 1); cn >= 0; cn-- {
		c := scc[cn]
		for _, n := range c {
			cond[n] = NI(cn) // map g node to cd node
		}
		var tos []NI // list of 'to' nodes
		var m Bits   // tos map
		m.SetBit(cn, 1)
		for _, n := range c {
			for _, to := range g.AdjacencyList[n] {
				if ct := cond[to]; m.Bit(ct) == 0 {
					m.SetBit(ct, 1)
					tos = append(tos, ct)
				}
			}
		}
		cd[cn] = tos
	}
	return
}

// Topological computes a topological ordering of a directed acyclic graph.
//
// For an acyclic graph, return value ordering is a permutation of node numbers
// in topologically sorted order and cycle will be nil.  If the graph is found
// to be cyclic, ordering will be nil and cycle will be the path of a found
// cycle.
//
// There are equivalent labeled and unlabeled versions of this method.
func (g Directed) Topological() (ordering, cycle []NI) {
	a := g.AdjacencyList
	ordering = make([]NI, len(a))
	i := len(ordering)
	var temp, perm Bits
	var cycleFound bool
	var cycleStart NI
	var df func(NI)
	df = func(n NI) {
		switch {
		case temp.Bit(n) == 1:
			cycleFound = true
			cycleStart = n
			return
		case perm.Bit(n) == 1:
			return
		}
		temp.SetBit(n, 1)
		for _, nb := range a[n] {
			df(nb)
			if cycleFound {
				if cycleStart >= 0 {
					// a little hack: orderng won't be needed so repurpose the
					// slice as cycle.  this is read out in reverse order
					// as the recursion unwinds.
					x := len(ordering) - 1 - len(cycle)
					ordering[x] = n
					cycle = ordering[x:]
					if n == cycleStart {
						cycleStart = -1
					}
				}
				return
			}
		}
		temp.SetBit(n, 0)
		perm.SetBit(n, 1)
		i--
		ordering[i] = n
	}
	for n := range a {
		if perm.Bit(NI(n)) == 1 {
			continue
		}
		df(NI(n))
		if cycleFound {
			return nil, cycle
		}
	}
	return ordering, nil
}

// TopologicalKahn computes a topological ordering of a directed acyclic graph.
//
// For an acyclic graph, return value ordering is a permutation of node numbers
// in topologically sorted order and cycle will be nil.  If the graph is found
// to be cyclic, ordering will be nil and cycle will be the path of a found
// cycle.
//
// This function is based on the algorithm by Arthur Kahn and requires the
// transpose of g be passed as the argument.
//
// There are equivalent labeled and unlabeled versions of this method.
func (g Directed) TopologicalKahn(tr Directed) (ordering, cycle []NI) {
	// code follows Wikipedia pseudocode.
	var L, S []NI
	// rem for "remaining edges," this function makes a local copy of the
	// in-degrees and consumes that instead of consuming an input.
	rem := make([]int, len(g.AdjacencyList))
	for n, fr := range tr.AdjacencyList {
		if len(fr) == 0 {
			// accumulate "set of all nodes with no incoming edges"
			S = append(S, NI(n))
		} else {
			// initialize rem from in-degree
			rem[n] = len(fr)
		}
	}
	for len(S) > 0 {
		last := len(S) - 1 // "remove a node n from S"
		n := S[last]
		S = S[:last]
		L = append(L, n) // "add n to tail of L"
		for _, m := range g.AdjacencyList[n] {
			// WP pseudo code reads "for each node m..." but it means for each
			// node m *remaining in the graph.*  We consume rem rather than
			// the graph, so "remaining in the graph" for us means rem[m] > 0.
			if rem[m] > 0 {
				rem[m]--         // "remove edge from the graph"
				if rem[m] == 0 { // if "m has no other incoming edges"
					S = append(S, m) // "insert m into S"
				}
			}
		}
	}
	// "If graph has edges," for us means a value in rem is > 0.
	for c, in := range rem {
		if in > 0 {
			// recover cyclic nodes
			for _, nb := range g.AdjacencyList[c] {
				if rem[nb] > 0 {
					cycle = append(cycle, NI(c))
					break
				}
			}
		}
	}
	if len(cycle) > 0 {
		return nil, cycle
	}
	return L, nil
}