下面是我对.NET堆的尝试
public abstract class Heap<T> : IEnumerable<T>
{
private const int InitialCapacity = 0;
private const int GrowFactor = 2;
private const int MinGrow = 1;
private int _capacity = InitialCapacity;
private T[] _heap = new T[InitialCapacity];
private int _tail = 0;
public int Count { get { return _tail; } }
public int Capacity { get { return _capacity; } }
protected Comparer<T> Comparer { get; private set; }
protected abstract bool Dominates(T x, T y);
protected Heap() : this(Comparer<T>.Default)
{
}
protected Heap(Comparer<T> comparer) : this(Enumerable.Empty<T>(), comparer)
{
}
protected Heap(IEnumerable<T> collection)
: this(collection, Comparer<T>.Default)
{
}
protected Heap(IEnumerable<T> collection, Comparer<T> comparer)
{
if (collection == null) throw new ArgumentNullException("collection");
if (comparer == null) throw new ArgumentNullException("comparer");
Comparer = comparer;
foreach (var item in collection)
{
if (Count == Capacity)
Grow();
_heap[_tail++] = item;
}
for (int i = Parent(_tail - 1); i >= 0; i--)
BubbleDown(i);
}
public void Add(T item)
{
if (Count == Capacity)
Grow();
_heap[_tail++] = item;
BubbleUp(_tail - 1);
}
private void BubbleUp(int i)
{
if (i == 0 || Dominates(_heap[Parent(i)], _heap[i]))
return; //correct domination (or root)
Swap(i, Parent(i));
BubbleUp(Parent(i));
}
public T GetMin()
{
if (Count == 0) throw new InvalidOperationException("Heap is empty");
return _heap[0];
}
public T ExtractDominating()
{
if (Count == 0) throw new InvalidOperationException("Heap is empty");
T ret = _heap[0];
_tail--;
Swap(_tail, 0);
BubbleDown(0);
return ret;
}
private void BubbleDown(int i)
{
int dominatingNode = Dominating(i);
if (dominatingNode == i) return;
Swap(i, dominatingNode);
BubbleDown(dominatingNode);
}
private int Dominating(int i)
{
int dominatingNode = i;
dominatingNode = GetDominating(YoungChild(i), dominatingNode);
dominatingNode = GetDominating(OldChild(i), dominatingNode);
return dominatingNode;
}
private int GetDominating(int newNode, int dominatingNode)
{
if (newNode < _tail && !Dominates(_heap[dominatingNode], _heap[newNode]))
return newNode;
else
return dominatingNode;
}
private void Swap(int i, int j)
{
T tmp = _heap[i];
_heap[i] = _heap[j];
_heap[j] = tmp;
}
private static int Parent(int i)
{
return (i + 1)/2 - 1;
}
private static int YoungChild(int i)
{
return (i + 1)*2 - 1;
}
private static int OldChild(int i)
{
return YoungChild(i) + 1;
}
private void Grow()
{
int newCapacity = _capacity*GrowFactor + MinGrow;
var newHeap = new T[newCapacity];
Array.Copy(_heap, newHeap, _capacity);
_heap = newHeap;
_capacity = newCapacity;
}
public IEnumerator<T> GetEnumerator()
{
return _heap.Take(Count).GetEnumerator();
}
IEnumerator IEnumerable.GetEnumerator()
{
return GetEnumerator();
}
}
public class MaxHeap<T> : Heap<T>
{
public MaxHeap()
: this(Comparer<T>.Default)
{
}
public MaxHeap(Comparer<T> comparer)
: base(comparer)
{
}
public MaxHeap(IEnumerable<T> collection, Comparer<T> comparer)
: base(collection, comparer)
{
}
public MaxHeap(IEnumerable<T> collection) : base(collection)
{
}
protected override bool Dominates(T x, T y)
{
return Comparer.Compare(x, y) >= 0;
}
}
public class MinHeap<T> : Heap<T>
{
public MinHeap()
: this(Comparer<T>.Default)
{
}
public MinHeap(Comparer<T> comparer)
: base(comparer)
{
}
public MinHeap(IEnumerable<T> collection) : base(collection)
{
}
public MinHeap(IEnumerable<T> collection, Comparer<T> comparer)
: base(collection, comparer)
{
}
protected override bool Dominates(T x, T y)
{
return Comparer.Compare(x, y) <= 0;
}
}
一些测试:
[TestClass]
public class HeapTests
{
[TestMethod]
public void TestHeapBySorting()
{
var minHeap = new MinHeap<int>(new[] {9, 8, 4, 1, 6, 2, 7, 4, 1, 2});
AssertHeapSort(minHeap, minHeap.OrderBy(i => i).ToArray());
minHeap = new MinHeap<int> { 7, 5, 1, 6, 3, 2, 4, 1, 2, 1, 3, 4, 7 };
AssertHeapSort(minHeap, minHeap.OrderBy(i => i).ToArray());
var maxHeap = new MaxHeap<int>(new[] {1, 5, 3, 2, 7, 56, 3, 1, 23, 5, 2, 1});
AssertHeapSort(maxHeap, maxHeap.OrderBy(d => -d).ToArray());
maxHeap = new MaxHeap<int> {2, 6, 1, 3, 56, 1, 4, 7, 8, 23, 4, 5, 7, 34, 1, 4};
AssertHeapSort(maxHeap, maxHeap.OrderBy(d => -d).ToArray());
}
private static void AssertHeapSort(Heap<int> heap, IEnumerable<int> expected)
{
var sorted = new List<int>();
while (heap.Count > 0)
sorted.Add(heap.ExtractDominating());
Assert.IsTrue(sorted.SequenceEqual(expected));
}
}
