source: branches/HeuristicLab.EvolutionTracking/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/TreeMatching/QueryMatch.cs @ 14426

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
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 * GNU General Public License for more details.
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#endregion

using System;
using System.Collections.Generic;
using System.Linq;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;

namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
  // this class implements the decision version of the tree pattern query matching algorithm 
  // by M. Götz, C. Koch and W. Martens in http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.5440
  public class QueryMatch {
    public ISymbolicExpressionTreeNodeEqualityComparer EqualityComparer { get; private set; }
    private readonly NodeInfo Inf = new NodeInfo { Index = int.MaxValue };
    private readonly NodeInfo Nil = new NodeInfo { Index = -1 };
    private readonly HashSet<string> commutativeSymbols = new HashSet<string> { "Addition", "Multiplication", "Average", "And", "Or", "Xor" };
    private readonly ISymbolicExpressionTreeNodeComparer nodeComparer = new SymbolicExpressionTreeNodeComparer();

    private QueryMatch() { }

    // whether matching nodes should also have matching parents
    // in theory, this restricts the matching so that parent-child
    // pairs in the query tree are matched by parent-child pairs in 
    // the data tree (and not ancestor-descendant pairs)
    public bool MatchParents { get; set; }

    public QueryMatch(ISymbolicExpressionTreeNodeEqualityComparer equalityComparer) {
      EqualityComparer = equalityComparer;
    }

    internal bool Match(List<NodeInfo> data, List<NodeInfo> query) {
      var dRoot = data.Last();
      var qRoot = query.Last();

      var result = Tmatch(dRoot, query.First(), qRoot);
      return result == qRoot;
    }

    public bool Match(ISymbolicExpressionTree data, ISymbolicExpressionTree query) {
      return Match(data.Root.GetSubtree(0).GetSubtree(0), query.Root.GetSubtree(0).GetSubtree(0));
    }

    public bool Match(ISymbolicExpressionTreeNode data, ISymbolicExpressionTreeNode query) {
      if (!EqualityComparer.Equals(data, query))
        return false;

      var dNodes = InitializePostOrder(data);
      var qNodes = InitializePostOrder(query);

      var dRoot = dNodes.Last();
      var qRoot = qNodes.Last();
      var result = Tmatch(dRoot, qNodes.First(), qRoot);
      return result == qRoot;
    }

    public IEnumerable<ISymbolicExpressionTree> GetMatchingTrees(IEnumerable<ISymbolicExpressionTree> data, ISymbolicExpressionTree query) {
      var qRoot = query.Root.GetSubtree(0).GetSubtree(0);
      var filtered = data.Where(x => x.Length >= query.Length && EqualityComparer.Equals(x.Root.GetSubtree(0).GetSubtree(0), qRoot));
      var qNodes = InitializePostOrder(query.Root.GetSubtree(0).GetSubtree(0));
      return from d in filtered let dNodes = InitializePostOrder(d.Root.GetSubtree(0).GetSubtree(0)) where Match(dNodes, qNodes) select d;
    }

    private bool AreMatching(NodeInfo d, NodeInfo q) {
      // force the nodes to be on the same level
      if (d.Level != q.Level)
        return false;

      // compare nodes
      bool equals = EqualityComparer.Equals(d.Node, q.Node);

      if (!equals)
        return false;

      // compare node parents
      if (MatchParents && !EqualityComparer.Equals(d.Node.Parent, q.Node.Parent))
        return false;

      // compare children to make sure they are the same
      if (d.Node.SubtreeCount > 0 && q.Node.SubtreeCount > 0) {
        var dSubtrees = d.Node.Subtrees.ToList();

        if (commutativeSymbols.Contains(d.Node.Symbol.Name)) {
          var qSubtrees = q.Node.Subtrees.Where(x => !(x is AnyNode || x is AnySubtree)).ToList();

          dSubtrees.Sort(nodeComparer);
          qSubtrees.Sort(nodeComparer);

          var nw = q.Node.SubtreeCount - qSubtrees.Count; // number of wildcards 
          if (nw == 0)
            return dSubtrees.SequenceEqual(qSubtrees, EqualityComparer);

          for (int i = 0, j = 0; i < dSubtrees.Count && j < qSubtrees.Count;) {
            if (EqualityComparer.Equals(dSubtrees[i], qSubtrees[j])) {
              ++i;
              ++j;
            } else {
              if (nw == 0)
                return false;
              ++i;
              --nw;
            }
          }
        } else {
          var qSubtrees = q.Node.Subtrees;
          return dSubtrees.SequenceEqual(qSubtrees, EqualityComparer);
        }
      }
      return true;
    }

    private NodeInfo Tmatch(NodeInfo d, NodeInfo qFrom, NodeInfo qUntil) {
      var qBest = d.IsLeaf ? qFrom.Previous : Hmatch(d.LastChild, qFrom, qUntil);
      var next = qBest.Next;
      if (next <= qUntil && AreMatching(d, next)) {
        qBest = next;
        next = qBest.Next;
        var lastSibling = qBest.LastSibling;
        return next <= lastSibling ? Tmatch(d, next, lastSibling) : qBest;
      }
      return qBest;
    }

    private NodeInfo Hmatch(NodeInfo d, NodeInfo qFrom, NodeInfo qUntil) {
      if (d.IsFirstSibling)
        return Tmatch(d, qFrom, qUntil);

      var qHedge = Hmatch(d.PreviousSibling, qFrom, qUntil);
      var qTree = Tmatch(d, qFrom, qUntil);

      for (;;) {
        if (qHedge == qTree)
          return qHedge;
        if (qTree < qHedge) {
          var rtop = Rtop(qTree.Next, qHedge);
          while (rtop < Inf && qHedge < rtop.LastSibling) {
            qTree = Tmatch(d, rtop.Next, rtop.LastSibling);
            rtop = Rtop(qTree.Next, qHedge);
          }
          if (qTree <= qHedge)
            return qHedge;
        } else {
          var rtop = Rtop(qHedge.Next, qTree);
          while (rtop < Inf && qTree < rtop.LastSibling) {
            qHedge = Hmatch(d.PreviousSibling, rtop.Next, rtop.LastSibling);
            rtop = Rtop(qHedge.Next, qTree);
          }
          if (qHedge <= qTree)
            return qTree;
        }
      }
    }

    /// <summary>
    /// Description from Götz et al. - Efficient Algorithms for Descendant-only Tree Pattern Queries, 2009:
    /// Given two nodes hFrom and hUntil, returns the rightmost node among the topmost nodes in the interval [hFrom, hUntil]
    /// More formally, Rtop(hFrom,hUntil) is the node u such that depth(u) is minimal and u is larger than every other node v 
    /// in [hFrom, hUntil] with depth(u)==depth(v).
    /// </summary>
    /// <param name="hFrom">The interval start</param>
    /// <param name="hUntil">The interval end</param>
    /// <returns>The rightmost node from the topmost nodes in the interval [hFrom, hUntil]</returns>
    private NodeInfo Rtop(NodeInfo hFrom, NodeInfo hUntil) {
      if (hFrom == hUntil)
        return hUntil;
      if (hFrom.Index > hUntil.Index)
        return Inf;
      // let u be the highest ancestor of hUntil that has a previous sibling s such that s >= hFrom
      // if no such u exists, then Rtop(hFrom, hUntil) = hUntil. Otherwise, rtop(hFrom, hUntil) = s
      var rtop = hUntil.Ancestors.OrderBy(x => x.Level).Select(x => x.PreviousSibling).FirstOrDefault(x => x != null && x >= hFrom);
      return rtop ?? hUntil;
    }

    internal static List<NodeInfo> InitializePostOrder(ISymbolicExpressionTreeNode node) {
      // levels will be computed below
      var nodes = node.IterateNodesPostfix().Select((x, i) => new NodeInfo { Node = x, Index = i, Level = 0 }).ToList();
      var map = nodes.ToDictionary(x => x.Node, x => x);
      nodes.First().Previous = new NodeInfo { Node = null, Index = -1, Next = nodes.First() };
      nodes.Last().Next = new NodeInfo { Node = null, Index = int.MaxValue, Previous = nodes.Last() };
      for (int i = nodes.Count - 1; i >= 0; --i) {
        var n = nodes[i];
        if (n != nodes.Last()) n.Next = nodes[n.Index + 1];
        if (n != nodes.First()) n.Previous = nodes[n.Index - 1];
        NodeInfo parentInfo = null;
        if (n.Node.Parent != null)
          map.TryGetValue(n.Node.Parent, out parentInfo);
        n.Parent = parentInfo;
        if (n.Parent == null) {
          n.PreviousSibling = n.NextSibling = n.LastSibling = null;
        } else {
          var parent = n.Parent.Node;
          int si = parent.IndexOfSubtree(n.Node);
          n.PreviousSibling = n.IsFirstSibling ? null : map[parent.GetSubtree(si - 1)];
          n.NextSibling = n.IsLastSibling ? null : map[parent.GetSubtree(si + 1)];
          n.LastSibling = map[parent.Subtrees.Last()];
          n.Level = n.Parent.Level + 1;
        }
        n.LastChild = n.IsLeaf ? null : n.Previous;
      }
      return nodes;
    }
  }

  /// <summary>
  /// NodeInfo objects are useful for keeping sibling, parent, index and depth information for tree nodes
  /// </summary>
  internal class NodeInfo : IComparable<NodeInfo> {
    public ISymbolicExpressionTreeNode Node { get; set; }
    public int Index { get; set; }
    public int Level { get; set; }
    public NodeInfo Parent { get; set; }
    public NodeInfo Previous { get; set; }
    public NodeInfo PreviousSibling { get; set; }
    public NodeInfo Next { get; set; }
    public NodeInfo NextSibling { get; set; }
    public NodeInfo LastSibling { get; set; }
    public NodeInfo LastChild { get; set; }

    public bool IsLeaf {
      get { return Node.SubtreeCount == 0; }
    }

    public bool IsFirstSibling {
      get { return Parent != null && Node == Node.Parent.Subtrees.First(); }
    }

    public bool IsLastSibling {
      get { return Parent != null && Node == Node.Parent.Subtrees.Last(); }
    }

    public IEnumerable<NodeInfo> Ancestors {
      get {
        var p = Parent;
        while (p != null) {
          yield return p;
          p = p.Parent;
        }
      }
    }

    public int CompareTo(NodeInfo other) {
      return other == null ? 1 : Index.CompareTo(other.Index);
    }

    public static bool operator <(NodeInfo lsh, NodeInfo rhs) {
      return lsh.CompareTo(rhs) == -1;
    }

    public static bool operator >(NodeInfo lhs, NodeInfo rhs) {
      return lhs.CompareTo(rhs) == 1;
    }

    public static bool operator <=(NodeInfo lhs, NodeInfo rhs) {
      return lhs.CompareTo(rhs) <= 0;
    }

    public static bool operator >=(NodeInfo lhs, NodeInfo rhs) {
      return lhs.CompareTo(rhs) >= 0;
    }
  }
}