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• CheckPathsBetweenNodes.java

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/*
 * Copyright 2008 The Closure Compiler Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package com.google.javascript.jscomp;

import com.google.common.base.Predicate;
import com.google.javascript.jscomp.graph.Annotation;
import com.google.javascript.jscomp.graph.DiGraph;
import com.google.javascript.jscomp.graph.DiGraph.DiGraphEdge;
import com.google.javascript.jscomp.graph.DiGraph.DiGraphNode;

/**
 * See constructor, {@link #CheckPathsBetweenNodes(DiGraph,
 * DiGraphNode, DiGraphNode, Predicate, Predicate)}, for a
 * description of this algorithm.
 *
 *
 * @param  The node type.
 * @param  The edge type.
 */
public final class CheckPathsBetweenNodes {

  private final Predicate nodePredicate;
  private final Predicate> edgePredicate;
  private final boolean inclusive;

  // This algorithm works in two stages. First, the depth-first search (DFS)
  // tree is calculated with A as the root. During when constructing the DFS
  // tree, back edges are recorded. A back edge is a non-tree edge (X -> Y)
  // where X is an descendant of Y in the DFS tree. The second step does a
  // recursive traversal of the graph. Back edges are ignored during the
  // recursive traversal, thus no cycles are encountered. Any recursive branch
  // that encounters B without yet satisfying the predicate represents a path
  // from the entry node to the exit without any nodes that satisfy the
  // predicate.
  //
  // The implementation of discoverBackEdges follows the DFS-Visit algorithm in
  // "Introduction to Algorithms" by Cormen, Leiseron, Rivest, and Stein, 2nd
  // ed., on page 541. The calculation of back edges is described on page 546.

  // A non-tree edge in the DFS that connects a node to one of its ancestors.
  private static final Annotation BACK_EDGE = new Annotation() {};
  private static final Annotation VISITED_EDGE = new Annotation() {};

  // Not yet visited.
  private static final Annotation WHITE = null;
  // Being visited.
  private static final Annotation GRAY = new Annotation() {};
  // Finished visiting.
  private static final Annotation BLACK = new Annotation() {};

  private final DiGraph graph;
  private final DiGraphNode start;
  private final DiGraphNode end;

  /**
   * Given a graph G with nodes A and B, this algorithm determines if all paths
   * from A to B contain at least one node satisfying a given predicate.
   *
   * Note that nodePredicate is not necessarily called for all nodes in G nor is
   * edgePredicate called for all edges in G.
   *
   * @param graph Graph G to analyze.
   * @param a The node A.
   * @param b The node B.
   * @param nodePredicate Predicate which at least one node on each path from an
   *     A node to B (inclusive) must match.
   * @param edgePredicate Edges to consider as part of the graph. Edges in
   *     graph that don't match edgePredicate will be ignored.
   * @param inclusive Includes node A and B in the test for the node predicate.
   */
  CheckPathsBetweenNodes(DiGraph graph, DiGraphNode a,
      DiGraphNode b, Predicate nodePredicate,
      Predicate> edgePredicate, boolean inclusive) {
    this.graph = graph;
    this.start = a;
    this.end = b;
    this.nodePredicate = nodePredicate;
    this.edgePredicate = edgePredicate;
    this.inclusive = inclusive;
  }

  /**
   * Inclusive check.
   */
  public CheckPathsBetweenNodes(DiGraph graph, DiGraphNode a,
      DiGraphNode b, Predicate nodePredicate,
      Predicate> edgePredicate) {
    this(graph, a, b, nodePredicate, edgePredicate, true);
  }


  /**
   * @return true iff all paths contain at least one node that satisfy the
   *     predicate
   */
  public boolean allPathsSatisfyPredicate() {
    setUp();
    boolean result = checkAllPathsWithoutBackEdges(start, end);
    tearDown();
    return result;
  }

  /**
   * @return true iff some paths contain at least one node that satisfy the
   *     predicate
   */
  public boolean somePathsSatisfyPredicate() {
    setUp();
    boolean result = checkSomePathsWithoutBackEdges(start, end);
    tearDown();
    return result;
  }

  private void setUp() {
    graph.pushNodeAnnotations();
    graph.pushEdgeAnnotations();
    discoverBackEdges(this.start);
  }

  private void tearDown() {
    graph.popNodeAnnotations();
    graph.popEdgeAnnotations();
  }

  private void discoverBackEdges(DiGraphNode u) {
    u.setAnnotation(GRAY);
    for (DiGraphEdge e : u.getOutEdges()) {
      if (ignoreEdge(e)) {
        continue;
      }
      DiGraphNode v = e.getDestination();
      if (v.getAnnotation() == WHITE) {
        discoverBackEdges(v);
      } else if (v.getAnnotation() == GRAY) {
        e.setAnnotation(BACK_EDGE);
      }
    }
    u.setAnnotation(BLACK);
  }

  private boolean ignoreEdge(DiGraphEdge e) {
    return !edgePredicate.apply(e);
  }

  /**
   * Verify that all non-looping paths from {@code a} to {@code b} pass
   * through at least one node where {@code nodePredicate} is true.
   */
  private boolean checkAllPathsWithoutBackEdges(DiGraphNode a,
      DiGraphNode b) {
    if (nodePredicate.apply(a.getValue()) &&
        (inclusive || (a != start && a != end))) {
      return true;
    }
    if (a == b) {
      return false;
    }
    for (DiGraphEdge e : a.getOutEdges()) {
      // Once we visited that edge once, we no longer need to
      // re-visit it again.
      if (e.getAnnotation() == VISITED_EDGE) {
        continue;
      }
      e.setAnnotation(VISITED_EDGE);

      if (ignoreEdge(e)) {
        continue;
      }
      if (e.getAnnotation() == BACK_EDGE) {
        continue;
      }

      DiGraphNode next = e.getDestination();
      if (!checkAllPathsWithoutBackEdges(next, b)) {
        return false;
      }
    }
    return true;
  }

  /**
   * Verify that some non-looping paths from {@code a} to {@code b} pass
   * through at least one node where {@code nodePredicate} is true.
   */
  private boolean checkSomePathsWithoutBackEdges(DiGraphNode a,
      DiGraphNode b) {
    if (nodePredicate.apply(a.getValue()) &&
        (inclusive || (a != start && a != end))) {
      return true;
    }
    if (a == b) {
      return false;
    }
    for (DiGraphEdge e : a.getOutEdges()) {
      // Once we visited that edge once, we no longer need to
      // re-visit it again.
      if (e.getAnnotation() == VISITED_EDGE) {
        continue;
      }
      e.setAnnotation(VISITED_EDGE);

      if (ignoreEdge(e)) {
        continue;
      }
      if (e.getAnnotation() == BACK_EDGE) {
        continue;
      }

      DiGraphNode next = e.getDestination();
      if (checkSomePathsWithoutBackEdges(next, b)) {
        return true;
      }
    }
    return false;
  }
}