lib/src/graph.dart - dart2js_info - Git at Google

 // Copyright (c) 2015, the Dart project authors.  Please see the AUTHORS file
 // for details. All rights reserved. Use of this source code is governed by a
 // BSD-style license that can be found in the LICENSE file.

 /// A library to work with graphs. It contains a couple algorithms, including
 /// Tarjan's algorithm to compute strongly connected components in a graph and
 /// Cooper et al's dominator algorithm.
 ///
 /// Portions of the code in this library was adapted from
 /// `package:analyzer/src/generated/collection_utilities.dart`.
 // TODO(sigmund): move this into a shared place, like quiver?
 library dart2js_info.src.graph;

 import 'dart:math' as math;

 abstract class Graph<N> {
   Iterable<N> get nodes;
   bool get isEmpty;
   int get nodeCount;
   Iterable<N> targetsOf(N source);
   Iterable<N> sourcesOf(N source);

   /// Run a topological sort of the graph. Since the graph may contain cycles,
   /// this results in a list of strongly connected components rather than a list
   /// of nodes. The nodes in each strongly connected components only have edges
   /// that point to nodes in the same component or earlier components.
   List<List<N>> computeTopologicalSort() {
     _SccFinder<N> finder = new _SccFinder<N>(this);
     return finder.computeTopologicalSort();
   }

   /// Whether [source] can transitively reach [target].
   bool containsPath(N source, N target) {
     Set<N> seen = new Set<N>();
     bool helper(N node) {
       if (identical(node, target)) return true;
       if (!seen.add(node)) return false;
       return targetsOf(node).any(helper);
     }

     return helper(source);
   }

   /// Returns all nodes reachable from [root] in post order.
   Iterable<N> postOrder(N root) sync* {
     var seen = new Set<N>();
     Iterable<N> helper(N n) sync* {
       if (!seen.add(n)) return;
       for (var x in targetsOf(n)) {
         yield* helper(x);
       }
       yield n;
     }

     yield* helper(root);
   }

   /// Returns an iterable of all nodes reachable from [root] in preorder.
   Iterable<N> preOrder(N root) sync* {
     var seen = new Set<N>();
     var stack = <N>[root];
     while (stack.isNotEmpty) {
       var next = stack.removeLast();
       if (!seen.contains(next)) {
         seen.add(next);
         yield next;
         stack.addAll(targetsOf(next));
       }
     }
   }

   /// Returns a list of nodes that form a cycle containing the given node. If
   /// the node is not part of a cycle in this graph, then a list containing only
   /// the node itself will be returned.
   List<N> findCycleContaining(N node) {
     assert(node != null);
     _SccFinder<N> finder = new _SccFinder<N>(this);
     return finder._componentContaining(node);
   }

   /// Returns a dominator tree starting from root. This is a new graph, with the
   /// same nodes as this graph, but where edges exist between a node and the
   /// nodes it immediately dominates. For example, this graph:
   ///
   ///       root
   ///       /   \
   ///      a     b
   ///      |    / \
   ///      c   d   e
   ///       \ / \ /
   ///        f   g
   ///
   /// Produces this tree:
   ///
   ///       root
   ///       /|  \
   ///      a |   b
   ///      | |  /|\
   ///      c | d | e
   ///        |   |
   ///        f   g
   ///
   /// Internally we compute dominators using (Cooper, Harvey, and Kennedy's
   /// algorithm)[http://www.cs.rice.edu/~keith/EMBED/dom.pdf].
   Graph<N> dominatorTree(N root) {
     var iDom = (new _DominatorFinder(this)..run(root)).immediateDominators;
     var graph = new EdgeListGraph<N>();
     for (N node in iDom.keys) {
       if (node != root) graph.addEdge(iDom[node], node);
     }
     return graph;
   }
 }

 class EdgeListGraph<N> extends Graph<N> {
   /// Edges in the graph.
   Map<N, Set<N>> _edges = new Map<N, Set<N>>();

   /// The reverse of _edges.
   Map<N, Set<N>> _revEdges = new Map<N, Set<N>>();

   Iterable<N> get nodes => _edges.keys;
   bool get isEmpty => _edges.isEmpty;
   int get nodeCount => _edges.length;

   final _empty = new Set<N>();

   Iterable<N> targetsOf(N source) => _edges[source] ?? _empty;
   Iterable<N> sourcesOf(N source) => _revEdges[source] ?? _empty;

   void addEdge(N source, N target) {
     assert(source != null);
     assert(target != null);
     addNode(source);
     addNode(target);
     _edges[source].add(target);
     _revEdges[target].add(source);
   }

   void addNode(N node) {
     assert(node != null);
     _edges.putIfAbsent(node, () => new Set<N>());
     _revEdges.putIfAbsent(node, () => new Set<N>());
   }

   /// Remove the edge from the given [source] node to the given [target] node.
   /// If there was no such edge then the graph will be unmodified: the number of
   /// edges will be the same and the set of nodes will be the same (neither node
   /// will either be added or removed).
   void removeEdge(N source, N target) {
     _edges[source]?.remove(target);
   }

   /// Remove the given node from this graph. As a consequence, any edges for
   /// which that node was either a head or a tail will also be removed.
   void removeNode(N node) {
     _edges.remove(node);
     var sources = _revEdges[node];
     if (sources == null) return;
     for (var source in sources) {
       _edges[source].remove(node);
     }
   }

   /// Remove all of the given nodes from this graph. As a consequence, any edges
   /// for which those nodes were either a head or a tail will also be removed.
   void removeAllNodes(List<N> nodes) => nodes.forEach(removeNode);
 }

 /// Used by the [SccFinder] to maintain information about the nodes that have
 /// been examined. There is an instance of this class per node in the graph.
 class _NodeInfo<N> {
   /// Depth of the node corresponding to this info.
   int index = 0;

   /// Depth of the first node in a cycle.
   int lowlink = 0;

   /// Whether the corresponding node is on the stack. Used to remove the need
   /// for searching a collection for the node each time the question needs to be
   /// asked.
   bool onStack = false;

   /// Component that contains the corresponding node.
   List<N> component;

   _NodeInfo(int depth)
       : index = depth,
         lowlink = depth,
         onStack = false;
 }

 /// Implements Tarjan's Algorithm for finding the strongly connected components
 /// in a graph.
 class _SccFinder<N> {
   /// The graph to process.
   final Graph<N> _graph;

   /// The index used to uniquely identify the depth of nodes.
   int _index = 0;

   /// Nodes that are being visited in order to identify components.
   List<N> _stack = new List<N>();

   /// Information associated with each node.
   Map<N, _NodeInfo<N>> _info = <N, _NodeInfo<N>>{};

   /// All strongly connected components found, in topological sort order (each
   /// node in a strongly connected component only has edges that point to nodes
   /// in the same component or earlier components).
   List<List<N>> _allComponents = new List<List<N>>();

   _SccFinder(this._graph);

   /// Return a list containing the nodes that are part of the strongly connected
   /// component that contains the given node.
   List<N> _componentContaining(N node) => _strongConnect(node).component;

   /// Run Tarjan's algorithm and return the resulting list of strongly connected
   /// components. The list is in topological sort order (each node in a strongly
   /// connected component only has edges that point to nodes in the same
   /// component or earlier components).
   List<List<N>> computeTopologicalSort() {
     for (N node in _graph.nodes) {
       var nodeInfo = _info[node];
       if (nodeInfo == null) _strongConnect(node);
     }
     return _allComponents;
   }

   /// Remove and return the top-most element from the stack.
   N _pop() {
     N node = _stack.removeAt(_stack.length - 1);
     _info[node].onStack = false;
     return node;
   }

   /// Add the given node to the stack.
   void _push(N node) {
     _info[node].onStack = true;
     _stack.add(node);
   }

   /// Compute the strongly connected component that contains the given node as
   /// well as any components containing nodes that are reachable from the given
   /// component.
   _NodeInfo<N> _strongConnect(N v) {
     // Set the depth index for v to the smallest unused index
     var vInfo = new _NodeInfo<N>(_index++);
     _info[v] = vInfo;
     _push(v);

     for (N w in _graph.targetsOf(v)) {
       var wInfo = _info[w];
       if (wInfo == null) {
         // Successor w has not yet been visited; recurse on it
         wInfo = _strongConnect(w);
         vInfo.lowlink = math.min(vInfo.lowlink, wInfo.lowlink);
       } else if (wInfo.onStack) {
         // Successor w is in stack S and hence in the current SCC
         vInfo.lowlink = math.min(vInfo.lowlink, wInfo.index);
       }
     }

     // If v is a root node, pop the stack and generate an SCC
     if (vInfo.lowlink == vInfo.index) {
       var component = new List<N>();
       N w;
       do {
         w = _pop();
         component.add(w);
         _info[w].component = component;
       } while (!identical(w, v));
       _allComponents.add(component);
     }
     return vInfo;
   }
 }

 /// Computes dominators using (Cooper, Harvey, and Kennedy's
 /// algorithm)[http://www.cs.rice.edu/~keith/EMBED/dom.pdf].
 class _DominatorFinder<N> {
   final Graph<N> _graph;
   Map<N, N> immediateDominators = {};
   Map<N, int> postOrderId = {};
   _DominatorFinder(this._graph);

   run(N root) {
     immediateDominators[root] = root;
     bool changed = true;
     int i = 0;
     var nodesInPostOrder = _graph.postOrder(root).toList();
     for (var n in nodesInPostOrder) {
       postOrderId[n] = i++;
     }
     var nodesInReversedPostOrder = nodesInPostOrder.reversed;
     while (changed) {
       changed = false;
       for (var n in nodesInReversedPostOrder) {
         if (n == root) continue;
         bool first = true;
         N idom;
         for (var p in _graph.sourcesOf(n)) {
           if (immediateDominators[p] != null) {
             if (first) {
               idom = p;
               first = false;
             } else {
               idom = _intersect(p, idom);
             }
           }
         }
         if (immediateDominators[n] != idom) {
           immediateDominators[n] = idom;
           changed = true;
         }
       }
     }
   }

   N _intersect(N b1, N b2) {
     var finger1 = b1;
     var finger2 = b2;
     while (finger1 != finger2) {
       while (postOrderId[finger1] < postOrderId[finger2]) {
         finger1 = immediateDominators[finger1];
       }
       while (postOrderId[finger2] < postOrderId[finger1]) {
         finger2 = immediateDominators[finger2];
       }
     }
     return finger1;
   }
 }
	// Copyright (c) 2015, the Dart project authors. Please see the AUTHORS file
	// for details. All rights reserved. Use of this source code is governed by a
	// BSD-style license that can be found in the LICENSE file.

	/// A library to work with graphs. It contains a couple algorithms, including
	/// Tarjan's algorithm to compute strongly connected components in a graph and
	/// Cooper et al's dominator algorithm.
	///
	/// Portions of the code in this library was adapted from
	/// `package:analyzer/src/generated/collection_utilities.dart`.
	// TODO(sigmund): move this into a shared place, like quiver?
	library dart2js_info.src.graph;

	import 'dart:math' as math;

	abstract class Graph<N> {
	Iterable<N> get nodes;
	bool get isEmpty;
	int get nodeCount;
	Iterable<N> targetsOf(N source);
	Iterable<N> sourcesOf(N source);

	/// Run a topological sort of the graph. Since the graph may contain cycles,
	/// this results in a list of strongly connected components rather than a list
	/// of nodes. The nodes in each strongly connected components only have edges
	/// that point to nodes in the same component or earlier components.
	List<List<N>> computeTopologicalSort() {
	_SccFinder<N> finder = new _SccFinder<N>(this);
	return finder.computeTopologicalSort();
	}

	/// Whether [source] can transitively reach [target].
	bool containsPath(N source, N target) {
	Set<N> seen = new Set<N>();
	bool helper(N node) {
	if (identical(node, target)) return true;
	if (!seen.add(node)) return false;
	return targetsOf(node).any(helper);
	}

	return helper(source);
	}

	/// Returns all nodes reachable from [root] in post order.
	Iterable<N> postOrder(N root) sync* {
	var seen = new Set<N>();
	Iterable<N> helper(N n) sync* {
	if (!seen.add(n)) return;
	for (var x in targetsOf(n)) {
	yield* helper(x);
	}
	yield n;
	}

	yield* helper(root);
	}

	/// Returns an iterable of all nodes reachable from [root] in preorder.
	Iterable<N> preOrder(N root) sync* {
	var seen = new Set<N>();
	var stack = <N>[root];
	while (stack.isNotEmpty) {
	var next = stack.removeLast();
	if (!seen.contains(next)) {
	seen.add(next);
	yield next;
	stack.addAll(targetsOf(next));
	}
	}
	}

	/// Returns a list of nodes that form a cycle containing the given node. If
	/// the node is not part of a cycle in this graph, then a list containing only
	/// the node itself will be returned.
	List<N> findCycleContaining(N node) {
	assert(node != null);
	_SccFinder<N> finder = new _SccFinder<N>(this);
	return finder._componentContaining(node);
	}

	/// Returns a dominator tree starting from root. This is a new graph, with the
	/// same nodes as this graph, but where edges exist between a node and the
	/// nodes it immediately dominates. For example, this graph:
	///
	/// root
	/// / \
	/// a b
	/// \| / \
	/// c d e
	/// \ / \ /
	/// f g
	///
	/// Produces this tree:
	///
	/// root
	/// /\| \
	/// a \| b
	/// \| \| /\|\
	/// c \| d \| e
	/// \| \|
	/// f g
	///
	/// Internally we compute dominators using (Cooper, Harvey, and Kennedy's
	/// algorithm)[http://www.cs.rice.edu/~keith/EMBED/dom.pdf].
	Graph<N> dominatorTree(N root) {
	var iDom = (new _DominatorFinder(this)..run(root)).immediateDominators;
	var graph = new EdgeListGraph<N>();
	for (N node in iDom.keys) {
	if (node != root) graph.addEdge(iDom[node], node);
	}
	return graph;
	}
	}

	class EdgeListGraph<N> extends Graph<N> {
	/// Edges in the graph.
	Map<N, Set<N>> _edges = new Map<N, Set<N>>();

	/// The reverse of _edges.
	Map<N, Set<N>> _revEdges = new Map<N, Set<N>>();

	Iterable<N> get nodes => _edges.keys;
	bool get isEmpty => _edges.isEmpty;
	int get nodeCount => _edges.length;

	final _empty = new Set<N>();

	Iterable<N> targetsOf(N source) => _edges[source] ?? _empty;
	Iterable<N> sourcesOf(N source) => _revEdges[source] ?? _empty;

	void addEdge(N source, N target) {
	assert(source != null);
	assert(target != null);
	addNode(source);
	addNode(target);
	_edges[source].add(target);
	_revEdges[target].add(source);
	}

	void addNode(N node) {
	assert(node != null);
	_edges.putIfAbsent(node, () => new Set<N>());
	_revEdges.putIfAbsent(node, () => new Set<N>());
	}

	/// Remove the edge from the given [source] node to the given [target] node.
	/// If there was no such edge then the graph will be unmodified: the number of
	/// edges will be the same and the set of nodes will be the same (neither node
	/// will either be added or removed).
	void removeEdge(N source, N target) {
	_edges[source]?.remove(target);
	}

	/// Remove the given node from this graph. As a consequence, any edges for
	/// which that node was either a head or a tail will also be removed.
	void removeNode(N node) {
	_edges.remove(node);
	var sources = _revEdges[node];
	if (sources == null) return;
	for (var source in sources) {
	_edges[source].remove(node);
	}
	}

	/// Remove all of the given nodes from this graph. As a consequence, any edges
	/// for which those nodes were either a head or a tail will also be removed.
	void removeAllNodes(List<N> nodes) => nodes.forEach(removeNode);
	}

	/// Used by the [SccFinder] to maintain information about the nodes that have
	/// been examined. There is an instance of this class per node in the graph.
	class _NodeInfo<N> {
	/// Depth of the node corresponding to this info.
	int index = 0;

	/// Depth of the first node in a cycle.
	int lowlink = 0;

	/// Whether the corresponding node is on the stack. Used to remove the need
	/// for searching a collection for the node each time the question needs to be
	/// asked.
	bool onStack = false;

	/// Component that contains the corresponding node.
	List<N> component;

	_NodeInfo(int depth)
	: index = depth,
	lowlink = depth,
	onStack = false;
	}

	/// Implements Tarjan's Algorithm for finding the strongly connected components
	/// in a graph.
	class _SccFinder<N> {
	/// The graph to process.
	final Graph<N> _graph;

	/// The index used to uniquely identify the depth of nodes.
	int _index = 0;

	/// Nodes that are being visited in order to identify components.
	List<N> _stack = new List<N>();

	/// Information associated with each node.
	Map<N, _NodeInfo<N>> _info = <N, _NodeInfo<N>>{};

	/// All strongly connected components found, in topological sort order (each
	/// node in a strongly connected component only has edges that point to nodes
	/// in the same component or earlier components).
	List<List<N>> _allComponents = new List<List<N>>();

	_SccFinder(this._graph);

	/// Return a list containing the nodes that are part of the strongly connected
	/// component that contains the given node.
	List<N> _componentContaining(N node) => _strongConnect(node).component;

	/// Run Tarjan's algorithm and return the resulting list of strongly connected
	/// components. The list is in topological sort order (each node in a strongly
	/// connected component only has edges that point to nodes in the same
	/// component or earlier components).
	List<List<N>> computeTopologicalSort() {
	for (N node in _graph.nodes) {
	var nodeInfo = _info[node];
	if (nodeInfo == null) _strongConnect(node);
	}
	return _allComponents;
	}

	/// Remove and return the top-most element from the stack.
	N _pop() {
	N node = _stack.removeAt(_stack.length - 1);
	_info[node].onStack = false;
	return node;
	}

	/// Add the given node to the stack.
	void _push(N node) {
	_info[node].onStack = true;
	_stack.add(node);
	}

	/// Compute the strongly connected component that contains the given node as
	/// well as any components containing nodes that are reachable from the given
	/// component.
	_NodeInfo<N> _strongConnect(N v) {
	// Set the depth index for v to the smallest unused index
	var vInfo = new _NodeInfo<N>(_index++);
	_info[v] = vInfo;
	_push(v);

	for (N w in _graph.targetsOf(v)) {
	var wInfo = _info[w];
	if (wInfo == null) {
	// Successor w has not yet been visited; recurse on it
	wInfo = _strongConnect(w);
	vInfo.lowlink = math.min(vInfo.lowlink, wInfo.lowlink);
	} else if (wInfo.onStack) {
	// Successor w is in stack S and hence in the current SCC
	vInfo.lowlink = math.min(vInfo.lowlink, wInfo.index);
	}
	}

	// If v is a root node, pop the stack and generate an SCC
	if (vInfo.lowlink == vInfo.index) {
	var component = new List<N>();
	N w;
	do {
	w = _pop();
	component.add(w);
	_info[w].component = component;
	} while (!identical(w, v));
	_allComponents.add(component);
	}
	return vInfo;
	}
	}

	/// Computes dominators using (Cooper, Harvey, and Kennedy's
	/// algorithm)[http://www.cs.rice.edu/~keith/EMBED/dom.pdf].
	class _DominatorFinder<N> {
	final Graph<N> _graph;
	Map<N, N> immediateDominators = {};
	Map<N, int> postOrderId = {};
	_DominatorFinder(this._graph);

	run(N root) {
	immediateDominators[root] = root;
	bool changed = true;
	int i = 0;
	var nodesInPostOrder = _graph.postOrder(root).toList();
	for (var n in nodesInPostOrder) {
	postOrderId[n] = i++;
	}
	var nodesInReversedPostOrder = nodesInPostOrder.reversed;
	while (changed) {
	changed = false;
	for (var n in nodesInReversedPostOrder) {
	if (n == root) continue;
	bool first = true;
	N idom;
	for (var p in _graph.sourcesOf(n)) {
	if (immediateDominators[p] != null) {
	if (first) {
	idom = p;
	first = false;
	} else {
	idom = _intersect(p, idom);
	}
	}
	}
	if (immediateDominators[n] != idom) {
	immediateDominators[n] = idom;
	changed = true;
	}
	}
	}
	}

	N _intersect(N b1, N b2) {
	var finger1 = b1;
	var finger2 = b2;
	while (finger1 != finger2) {
	while (postOrderId[finger1] < postOrderId[finger2]) {
	finger1 = immediateDominators[finger1];
	}
	while (postOrderId[finger2] < postOrderId[finger1]) {
	finger2 = immediateDominators[finger2];
	}
	}
	return finger1;
	}
	}