added iterators for dfs and bfs (#163)

* added iterators for dfs and bfs

* fixed exisintg identifier issue

* added iterators for dfs and bfs

* fixed exisintg identifier issue

* add abstract iterator state and fix first iter arg

* iterator refactor

* created iterators src folder, added kruskal

* created iterators src folder, added kruskal

* multi source version for bfs and dfs

* fix

* remove kruskal

* Update Graphs.jl

* remove kruskal from pages

* format

* format 2

* format branch

* improve perf of bfs

* optimize bfs

* use copy of source nodes

* Update bfs.jl

* improve dfs

* Update bfs.jl

* use size unknown

* Update bfs.jl

* Clean up

* Fix typo

* Fix tests and length

* Remove ref

* Fix eltype

* address review comments

* some more comments

* Update bfs.jl

* Update bfs.jl

* Update dfs.jl

* formatting

* Apply suggestions from code review

---------

Co-authored-by: Tortar <adrianomeligrana1999@gmail.com>
Co-authored-by: Tortar <68152031+Tortar@users.noreply.github.com>
Co-authored-by: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>

docs/src/algorithms/iterators.md

@@ -0,0 +1,33 @@
+# Iterators
+
+_Graphs.jl_ includes various routines for iterating through graphs.
+
+## Index
+
+```@index
+Pages = ["iterators.md"]
+```
+
+## Full docs
+
+```@autodocs
+Modules = [Graphs]
+Pages   = [
+    "iterators/iterators.jl",
+    "iterators/bfs.jl",
+    "iterators/dfs.jl",
+]
+Private = false
+```
+
+The following names are internals, not part of the public API:
+
+```@autodocs
+Modules = [Graphs]
+Pages   = [
+    "iterators/iterators.jl",
+    "iterators/bfs.jl",
+    "iterators/dfs.jl",
+]
+Public = false
+```

src/Graphs.jl

@@ -186,6 +186,10 @@ export
     dfs_tree,
     dfs_parents,
 
+    # iterators
+    DFSIterator,
+    BFSIterator,
+
     # random
     randomwalk,
     self_avoiding_walk,
@@ -499,6 +503,8 @@ include("traversals/dfs.jl")
 include("traversals/maxadjvisit.jl")
 include("traversals/randomwalks.jl")
 include("traversals/diffusion.jl")
+include("iterators/bfs.jl")
+include("iterators/dfs.jl")
 include("traversals/eulerian.jl")
 include("traversals/all_simple_paths.jl")
 include("connectivity.jl")

src/iterators/bfs.jl

@@ -0,0 +1,109 @@
+"""
+    BFSIterator
+
+`BFSIterator` is used to iterate through graph vertices using a breadth-first search. 
+A source node(s) is optionally supplied as an `Int` or an array-like type that can be 
+indexed if supplying multiple sources.
+    
+# Examples
+```julia-repl
+julia> g = smallgraph(:house)
+{5, 6} undirected simple Int64 graph
+
+julia> for node in BFSIterator(g,3)
+           display(node)
+       end
+3
+1
+4
+5
+2
+```
+"""
+struct BFSIterator{S,G<:AbstractGraph}
+    graph::G
+    source::S
+    function BFSIterator(graph::G, source::S) where {S,G}
+        if any(node -> !has_vertex(graph, node), source)
+            error("Some source nodes for the iterator are not in the graph")
+        end
+        return new{S,G}(graph, source)
+    end
+end
+
+"""
+    BFSVertexIteratorState
+
+`BFSVertexIteratorState` is a struct to hold the current state of iteration
+in BFS which is needed for the `Base.iterate()` function. A queue is used to
+keep track of the vertices which will be visited during BFS. Since the queue
+can contains repetitions of already visited nodes, we also keep track of that
+in a `BitVector` so that to skip those nodes.
+"""
+mutable struct BFSVertexIteratorState
+    visited::BitVector
+    queue::Vector{Int}
+    neighbor_idx::Int
+    n_visited::Int
+end
+
+Base.IteratorSize(::BFSIterator) = Base.SizeUnknown()
+Base.eltype(::Type{BFSIterator{S,G}}) where {S,G} = eltype(G)
+
+"""
+    Base.iterate(t::BFSIterator)
+
+First iteration to visit vertices in a graph using breadth-first search.
+"""
+function Base.iterate(t::BFSIterator{<:Integer})
+    visited = falses(nv(t.graph))
+    visited[t.source] = true
+    return (t.source, BFSVertexIteratorState(visited, [t.source], 1, 1))
+end
+
+function Base.iterate(t::BFSIterator{<:AbstractArray})
+    visited = falses(nv(t.graph))
+    visited[first(t.source)] = true
+    state = BFSVertexIteratorState(visited, copy(t.source), 1, 1)
+    return (first(t.source), state)
+end
+
+"""
+    Base.iterate(t::BFSIterator, state::VertexIteratorState)
+
+Iterator to visit vertices in a graph using breadth-first search.
+"""
+function Base.iterate(t::BFSIterator, state::BFSVertexIteratorState)
+    graph, visited, queue = t.graph, state.visited, state.queue
+    while !isempty(queue)
+        if state.n_visited == nv(graph)
+            return nothing
+        end
+        # we visit the first node in the queue
+        node_start = first(queue)
+        if !visited[node_start]
+            visited[node_start] = true
+            state.n_visited += 1
+            return (node_start, state)
+        end
+        # which means we arrive here when the first node was visited.
+        neigh = outneighbors(graph, node_start)
+        if state.neighbor_idx <= length(neigh)
+            node = neigh[state.neighbor_idx]
+            # we update the idx of the neighbor we will visit,
+            # if it is already visited, we repeat
+            state.neighbor_idx += 1
+            if !visited[node]
+                push!(queue, node)
+                state.visited[node] = true
+                state.n_visited += 1
+                return (node, state)
+            end
+        else
+            # when the first node and its neighbors are visited
+            # we remove the first node of the queue
+            popfirst!(queue)
+            state.neighbor_idx = 1
+        end
+    end
+end

src/iterators/dfs.jl

@@ -0,0 +1,98 @@
+"""
+    DFSIterator
+
+`DFSIterator` is used to iterate through graph vertices using a depth-first search. 
+A source node(s) is optionally supplied as an `Int` or an array-like type that can be 
+indexed if supplying multiple sources.
+    
+# Examples
+```julia-repl
+julia> g = smallgraph(:house)
+{5, 6} undirected simple Int64 graph
+
+julia> for node in DFSIterator(g, 3)
+           display(node)
+       end
+1
+2
+4
+3
+5
+```
+"""
+struct DFSIterator{S,G<:AbstractGraph}
+    graph::G
+    source::S
+    function DFSIterator(graph::G, source::S) where {S,G}
+        if any(node -> !has_vertex(graph, node), source)
+            error("Some source nodes for the iterator are not in the graph")
+        end
+        return new{S,G}(graph, source)
+    end
+end
+
+"""
+    DFSVertexIteratorState
+
+`DFSVertexIteratorState` is a struct to hold the current state of iteration
+in DFS which is needed for the `Base.iterate()` function. A queue is used to
+keep track of the vertices which will be visited during DFS. Since the queue
+can contains repetitions of already visited nodes, we also keep track of that
+in a `BitVector` so that to skip those nodes.
+"""
+mutable struct DFSVertexIteratorState
+    visited::BitVector
+    queue::Vector{Int}
+end
+
+Base.IteratorSize(::DFSIterator) = Base.SizeUnknown()
+Base.eltype(::Type{DFSIterator{S,G}}) where {S,G} = eltype(G)
+
+"""
+    Base.iterate(t::DFSIterator)
+
+First iteration to visit vertices in a graph using depth-first search.
+"""
+function Base.iterate(t::DFSIterator{<:Integer})
+    visited = falses(nv(t.graph))
+    visited[t.source] = true
+    return (t.source, DFSVertexIteratorState(visited, [t.source]))
+end
+
+function Base.iterate(t::DFSIterator{<:AbstractArray})
+    visited = falses(nv(t.graph))
+    source_rev = reverse(t.source)
+    visited[last(source_rev)] = true
+    state = DFSVertexIteratorState(visited, source_rev)
+    return (last(source_rev), state)
+end
+
+"""
+    Base.iterate(t::DFSIterator, state::VertexIteratorState)
+
+Iterator to visit vertices in a graph using depth-first search.
+"""
+function Base.iterate(t::DFSIterator, state::DFSVertexIteratorState)
+    graph, visited, queue = t.graph, state.visited, state.queue
+    while !isempty(queue)
+        # we take the last node in the queue
+        node_start = last(queue)
+        # we first return it
+        if !visited[node_start]
+            visited[node_start] = true
+            return (node_start, state)
+        end
+        # and then we visit a neighbor and push it at the
+        # end of the queue
+        for node in outneighbors(graph, node_start)
+            if !visited[node]
+                push!(queue, node)
+                visited[node] = true
+                return (node, state)
+            end
+        end
+        # we pop the last node in the queue
+        # when it and all its neighbors were visited
+        pop!(queue)
+    end
+end

test/iterators/bfs.jl

@@ -0,0 +1,41 @@
+@testset "BFSIterator" begin
+    g = Graph()
+    error_exc = ErrorException("Some source nodes for the iterator are not in the graph")
+    @test_throws error_exc BFSIterator(g, 3)
+    g = path_graph(7)
+    add_edge!(g, 6, 3)
+    add_edge!(g, 3, 1)
+    add_edge!(g, 4, 7)
+    g2 = deepcopy(g)
+    add_vertex!(g2)
+    add_vertex!(g2)
+    add_edge!(g2, 8, 9)
+
+    for g in testgraphs(g)
+        nodes_visited = fill(0, nv(g))
+        for (i, node) in enumerate(BFSIterator(g, 6))
+            nodes_visited[i] = node
+        end
+        @test nodes_visited[1] == 6
+        @test any(nodes_visited[2] .== [3, 5, 7])
+        if nodes_visited[2] == 3
+            @test nodes_visited[3:4] == [5, 7] || nodes_visited[3:4] == [7, 5]
+        elseif nodes_visited[2] == 5
+            @test nodes_visited[3:4] == [3, 7] || nodes_visited[3:4] == [7, 3]
+        else
+            @test nodes_visited[3:4] == [3, 5] || nodes_visited[3:4] == [5, 3]
+        end
+        @test any(nodes_visited[5] .== [1, 2, 4])
+        if nodes_visited[5] == 1
+            @test nodes_visited[6:7] == [2, 4] || nodes_visited[6:7] == [4, 2]
+        elseif nodes_visited[5] == 2
+            @test nodes_visited[6:7] == [1, 4] || nodes_visited[6:7] == [4, 1]
+        else
+            @test nodes_visited[6:7] == [1, 2] || nodes_visited[6:7] == [2, 1]
+        end
+    end
+    nodes_visited = collect(BFSIterator(g2, [1, 6]))
+    @test nodes_visited == [1, 2, 3, 6, 5, 7, 4]
+    nodes_visited = collect(BFSIterator(g2, [8, 1, 6]))
+    @test nodes_visited == [8, 9, 1, 2, 3, 6, 5, 7, 4]
+end

test/iterators/dfs.jl

@@ -0,0 +1,41 @@
+@testset "DFSIterator" begin
+    g = Graph()
+    error_exc = ErrorException("Some source nodes for the iterator are not in the graph")
+    @test_throws error_exc DFSIterator(g, 3)
+    g = path_graph(7)
+    add_edge!(g, 6, 3)
+    add_edge!(g, 3, 1)
+    add_edge!(g, 4, 7)
+    g2 = deepcopy(g)
+    add_vertex!(g2)
+    add_vertex!(g2)
+    add_edge!(g2, 8, 9)
+
+    for g in testgraphs(g)
+        nodes_visited = fill(0, nv(g))
+        for (i, node) in enumerate(DFSIterator(g, 6))
+            nodes_visited[i] = node
+        end
+        @test nodes_visited[1:2] == [6, 3]
+        @test any(nodes_visited[3] .== [1, 4])
+        if nodes_visited[3] == 1
+            @test nodes_visited[4] == 2
+            @test nodes_visited[5] == 4
+            @test any(nodes_visited[6] .== [5, 7])
+            if nodes_visited[6] == 5
+                @test nodes_visited[7] == 7
+            end
+        else
+            @test any(nodes_visited[4] .== [5, 7])
+            if nodes_visited[4] == 5
+                @test nodes_visited[5] == 7
+            end
+            @test nodes_visited[6] == 1
+            @test nodes_visited[7] == 2
+        end
+    end
+    nodes_visited = collect(DFSIterator(g2, [1, 6]))
+    @test nodes_visited == [1, 2, 3, 4, 5, 6, 7]
+    nodes_visited = collect(DFSIterator(g2, [8, 1, 6]))
+    @test nodes_visited == [8, 9, 1, 2, 3, 4, 5, 6, 7]
+end

test/runtests.jl

@@ -108,6 +108,8 @@ tests = [
     "traversals/maxadjvisit",
     "traversals/randomwalks",
     "traversals/diffusion",
+    "iterators/bfs",
+    "iterators/dfs",
     "traversals/eulerian",
     "traversals/all_simple_paths",
     "community/cliques",