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//-----------------------------------------------------------------------------
//
// Copyright (C) Microsoft Corporation. All Rights Reserved.
//
//-----------------------------------------------------------------------------
/**
* Graph algorithms
*/
package chalice;
import scala.collection.mutable;
import scala.collection.immutable;
// Directed simple graph on T. Payload of nodes (of type T) should remain immutable while in graph.
class DiGraph[T] {
private class Node[T](t: T) {
val data: T = t;
var children = mutable.Set.empty[Node[T]];
// temporary variables
var index = -1;
var lowlink = -1;
var onstack = false;
}
private var rep = mutable.Map.empty[T, Node[T]];
def addNode(t: T) = {
if (hasNode(t))
false;
else {
rep(t) = new Node(t);
true;
}
}
def addEdge(a: T, b: T) = {
assert (hasNode(a));
assert (hasNode(b));
if (rep(a).children.contains(rep(b)))
false
else {
rep(a).children += rep(b);
true;
}
}
def hasNode(a: T) = rep contains a;
def nodes: immutable.Set[T] =
immutable.Set() ++ rep.keys
def children(t: T): immutable.Set[T] = {
assert (rep contains t);
immutable.Set() ++ (rep(t).children map {x => x.data})
}
// Compute topological sort (edges point in forward direction in the list)
// Terminates but incorrect if not a DAG.
def computeTopologicalSort: List[T] = {
rep.values foreach {v => assert(!v.onstack)}
var l: List[T] = Nil;
def tarjan(v: Node[T]) {
if (! v.onstack) {
v.onstack = true;
for (w <- v.children) tarjan(w)
l = v.data :: l;
}
}
rep.values foreach {v => tarjan(v)}
rep.values foreach {v => assert(v.onstack); v.onstack = false;}
l
}
// Compute condensation of the digraph.
// The resulting digraph has no self loops
def computeSCC: (DiGraph[List[T]],mutable.Map[T,List[T]]) = {
// Tarjan's algorithm for finding strongly connected components
// http://algowiki.net/wiki/index.php/Tarjan%27s_algorithm
rep.values foreach {x => assert(x.index == -1 && x.lowlink == -1 && !x.onstack)};
// morphism
val result = new DiGraph[List[T]];
val map = mutable.Map.empty[T,List[T]];
// algorithm
var index = 0;
var S:List[Node[T]] = Nil;
def tarjan(v: Node[T]) {
v.index = index;
v.lowlink = index;
index = index + 1;
S = v :: S; v.onstack = true;
for (w <- v.children) {
if (w.index == -1) {
tarjan(w);
v.lowlink = scala.math.min(v.lowlink, w.lowlink);
} else if (w.onstack)
v.lowlink = scala.math.min(v.lowlink, w.index);
}
if (v.lowlink == v.index) {
var scc:List[T] = Nil;
var w: Node[T] = null;
while (v != w) {
w = S.head;
S = S.tail; w.onstack = false;
scc = w.data :: scc;
}
result.addNode(scc);
scc foreach {t => map(t) = scc}
}
}
// compute SCCs
rep.values foreach {n => if(n.index == -1) tarjan(n)};
// compute SCCs edges
rep.values foreach {n => n.children foreach {m =>
if (map(n.data) != map(m.data))
result.addEdge(map(n.data), map(m.data))
}
}
// clean-up
rep.values foreach {x => x.index = -1; x.lowlink = -1; x.onstack = false};
(result,map);
}
}
object Test {
def main(args: Array[String]) {
val g = new DiGraph[Int];
assert(g.addNode(0));
assert(!g.addNode(0));
assert(g.addNode(1));
assert(g.addNode(2));
assert(g.addNode(3));
assert(g.addNode(4));
assert(g.addNode(5));
g.addEdge(0,1);
g.addEdge(0,1);
g.addEdge(0,2);
assert(g.children(0) == Set(1,2));
g.addEdge(1,1);
g.addEdge(2,3);
g.addEdge(3,4);
g.addEdge(3,5);
g.addEdge(5,4);
g.addEdge(4,2);
g.computeSCC;
val (d, h) = g.computeSCC;
assert(h.get(0).get == List(0));
assert(h.get(1).get == List(1));
assert(h.get(2).get.size == 4);
assert(h.get(3).get.size == 4);
assert(h.get(4).get.size == 4);
assert(h.get(5).get.size == 4);
assert(d.children(h.get(0).get) == Set(h.get(1).get, h.get(2).get));
assert(d.children(h.get(1).get) == Set());
assert(d.children(h.get(2).get) == Set());
}
}
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