 //
//
// Microsoft Windows Client Platform
// Copyright (C) Microsoft Corporation. All rights reserved.
//
// File: PriorityQueue.cs
//
// Contents: Implementation of PriorityQueue class.
//
// Created: 2142005 Niklas Borson (niklasb)
//
//
using System;
using System.Diagnostics;
using System.Collections.Generic;
namespace MS.Internal
{
/// <summary>
/// PriorityQueue provides a stacklike interface, except that objects
/// "pushed" in arbitrary order are "popped" in order of priority, i.e.,
/// from least to greatest as defined by the specified comparer.
/// </summary>
/// <remarks>
/// Push and Pop are each O(log N). Pushing N objects and them popping
/// them all is equivalent to performing a heap sort and is O(N log N).
/// </remarks>
internal class PriorityQueue<T>
{
//
// The _heap array represents a binary tree with the "shape" property.
// If we number the nodes of a binary tree from lefttoright and top
// tobottom as shown,
//
// 0
// / \
// / \
// 1 2
// / \ / \
// 3 4 5 6
// /\ /
// 7 8 9
//
// The shape property means that there are no gaps in the sequence of
// numbered nodes, i.e., for all N > 0, if node N exists then node N1
// also exists. For example, the next node added to the above tree would
// be node 10, the right child of node 4.
//
// Because of this constraint, we can easily represent the "tree" as an
// array, where node number == array index, and parent/child relationships
// can be calculated instead of maintained explicitly. For example, for
// any node N > 0, the parent of N is at array index (N  1) / 2.
//
// In addition to the above, the first _count members of the _heap array
// compose a "heap", meaning each child node is greater than or equal to
// its parent node; thus, the root node is always the minimum (i.e., the
// best match for the specified style, weight, and stretch) of the nodes
// in the heap.
//
// Initially _count < 0, which means we have not yet constructed the heap.
// On the first call to MoveNext, we construct the heap by "pushing" all
// the nodes into it. Each successive call "pops" a node off the heap
// until the heap is empty (_count == 0), at which time we've reached the
// end of the sequence.
//
#region constructors
internal PriorityQueue(int capacity, IComparer<T> comparer)
{
_heap = new T[capacity > 0 ? capacity : DefaultCapacity];
_count = 0;
_comparer = comparer;
}
#endregion
#region internal members
/// <summary>
/// Gets the number of items in the priority queue.
/// </summary>
internal int Count
{
get { return _count; }
}
/// <summary>
/// Gets the first or topmost object in the priority queue, which is the
/// object with the minimum value.
/// </summary>
internal T Top
{
get
{
Debug.Assert(_count > 0);
if (!_isHeap)
{
Heapify();
}
return _heap[0];
}
}
/// <summary>
/// Adds an object to the priority queue.
/// </summary>
internal void Push(T value)
{
// Increase the size of the array if necessary.
if (_count == _heap.Length)
{
Array.Resize<T>(ref _heap, _count * 2);
}
// A common usage is to Push N items, then Pop them. Optimize for that
// case by treating Push as a simple append until the first Top or Pop,
// which establishes the heap property. After that, Push needs
// to maintain the heap property.
if (_isHeap)
{
SiftUp(_count, ref value, 0);
}
else
{
_heap[_count] = value;
}
_count++;
}
/// <summary>
/// Removes the first node (i.e., the logical root) from the heap.
/// </summary>
internal void Pop()
{
Debug.Assert(_count != 0);
if (!_isHeap)
{
Heapify();
}
if (_count > 0)
{
_count;
// discarding the root creates a gap at position 0. We fill the
// gap with the item x from the last position, after first sifting
// the gap to a position where inserting x will maintain the
// heap property. This is done in two phases  SiftDown and SiftUp.
//
// The onephase method found in many textbooks does 2 comparisons
// per level, while this method does only 1. The onephase method
// examines fewer levels than the twophase method, but it does
// more comparisons unless x ends up in the top 2/3 of the tree.
// That accounts for only n^(2/3) items, and x is even more likely
// to end up near the bottom since it came from the bottom in the
// first place. Overall, the twophase method is noticeably better.
T x = _heap[_count]; // lift item x out from the last position
int index = SiftDown(0); // sift the gap at the root down to the bottom
SiftUp(index, ref x, 0); // sift the gap up, and insert x in its rightful position
_heap[_count] = default(T); // don't leak x
}
}
#endregion
#region private members
// sift a gap at the given index down to the bottom of the heap,
// return the resulting index
private int SiftDown(int index)
{
// Loop invariants:
//
// 1. parent is the index of a gap in the logical tree
// 2. leftChild is
// (a) the index of parent's left child if it has one, or
// (b) a value >= _count if parent is a leaf node
//
int parent = index;
int leftChild = HeapLeftChild(parent);
while (leftChild < _count)
{
int rightChild = HeapRightFromLeft(leftChild);
int bestChild =
(rightChild < _count && _comparer.Compare(_heap[rightChild], _heap[leftChild]) < 0) ?
rightChild : leftChild;
// Promote bestChild to fill the gap left by parent.
_heap[parent] = _heap[bestChild];
// Restore invariants, i.e., let parent point to the gap.
parent = bestChild;
leftChild = HeapLeftChild(parent);
}
return parent;
}
// sift a gap at index up until it reaches the correct position for x,
// or reaches the given boundary. Place x in the resulting position.
private void SiftUp(int index, ref T x, int boundary)
{
while (index > boundary)
{
int parent = HeapParent(index);
if (_comparer.Compare(_heap[parent], x) > 0)
{
_heap[index] = _heap[parent];
index = parent;
}
else
{
break;
}
}
_heap[index] = x;
}
// Establish the heap property: _heap[k] >= _heap[HeapParent(k)], for 0<k<_count
// Do this "bottom up", by iterating backwards. At each iteration, the
// property inductively holds for k >= HeapLeftChild(i)+2; the body of
// the loop extends the property to the children of position i (namely
// k=HLC(i) and k=HLC(i)+1) by lifting item x out from position i, sifting
// the resulting gap down to the bottom, then sifting it back up (within
// the subtree under i) until finding x's rightful position.
//
// Iteration i does work proportional to the height (distance to leaf)
// of the node at position i. Half the nodes are leaves with height 0;
// there's nothing to do for these nodes, so we skip them by initializing
// i to the last nonleaf position. A quarter of the nodes have height 1,
// an eigth have height 2, etc. so the total work is ~ 1*n/4 + 2*n/8 +
// 3*n/16 + ... = O(n). This is much cheaper than maintaining the
// heap incrementally during the "Push" phase, which would cost O(n*log n).
private void Heapify()
{
if (!_isHeap)
{
for (int i = _count/2  1; i >= 0; i)
{
// we use a twophase method for the same reason Pop does
T x = _heap[i];
int index = SiftDown(i);
SiftUp(index, ref x, i);
}
_isHeap = true;
}
}
/// <summary>
/// Calculate the parent node index given a child node's index, taking advantage
/// of the "shape" property.
/// </summary>
private static int HeapParent(int i)
{
return (i  1) / 2;
}
/// <summary>
/// Calculate the left child's index given the parent's index, taking advantage of
/// the "shape" property. If there is no left child, the return value is >= _count.
/// </summary>
private static int HeapLeftChild(int i)
{
return (i * 2) + 1;
}
/// <summary>
/// Calculate the right child's index from the left child's index, taking advantage
/// of the "shape" property (i.e., sibling nodes are always adjacent). If there is
/// no right child, the return value >= _count.
/// </summary>
private static int HeapRightFromLeft(int i)
{
return i + 1;
}
private T[] _heap;
private int _count;
private IComparer<T> _comparer;
private bool _isHeap;
private const int DefaultCapacity = 6;
#endregion
}
}
