使用C#实现数据结构堆的代码

雨点打透心脏的1/2处 2022-10-28 10:08 148阅读 0赞

一、 堆的介绍：  
　　堆是用来排序的，通常是一个可以被看做一棵树的数组对象。堆满足已下特性：

1. 堆中某个节点的值总是不大于或不小于其父节点的值

任意节点的值小于（或大于）它的所有后裔，所以最小元（或最大元）在堆的根节点上（堆序性）。堆有大根堆和小根堆，将根节点最大的堆叫做最大堆或大根堆，根节点最小的堆叫做最小堆或小根堆。

2. 堆总是一棵完全二叉树

除了最底层，其他层的节点都被元素填满，且最底层尽可能地从左到右填入。

堆示意图：

将堆元素从上往下从左到右放进数组对象中，子父节点索引满足关系：

parentIndex = （index+1）/ 2 - 1;

childLeftIndex = parentIndex \* 2 + 1;

childRightIndex = (parentIndex + 1) \* 2;

其中：index为任一节点索引；parentIndex该节点父索引；childLeftIndex该父节点下的子左节点；childRightIndex该父节点下的子右节点。

创建堆的大概思路：

1. 向堆中添加元素：

加到数组尾处，循环比对其父节点值（大根堆和小根堆比对策略不一样），比对结果的目标索引不是父节点索引则交换子父节点元素，继续向上比对其父父节点…；直至比对过程中目标索引为父节点索引或达到根节点结束，新堆创建完成。

2. 向堆中取出元素：

取出根节点元素，并将堆末尾元素插入根节点（为了保证堆的完全二叉树特性），从根部再循环向下比对父节点、子左节点、子右节点值，比对结果目标索引不为父节点交换目标索引和父节点的值，向下继续比对；直至比对过程中目标索引为父节点索引或达到堆尾部结束，新堆创建完成。

二、 代码实现：  
　　因为大根堆和小根堆只是比较策略不同，所以整合了两者，用的时候可以直接设置堆的类别；默认小根堆，默认比较器。实现代码如下：

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public class Heap<T>  
\{  
private T\[\] \_array;//数组，存放堆数据  
private int \_count;//堆数据数量  
private HeapType \_typeName;//堆类型  
private const int \_DefaultCapacity = 4;//默认数组容量/最小容量  
private const int \_ShrinkThreshold = 50;//收缩阈值（百分比）  
private const int \_MinimumGrow = 4;//最小扩容量  
private const int \_GrowFactor = 200; // 数组扩容百分比,默认2倍  
private IComparer<T> \_comparer;//比较器  
private Func<T, T, bool> \_comparerFunc;//比较函数  
  
//堆数据数量  
public int Count => \_count;  
//堆类型  
public HeapType TypeName => \_typeName;  
  
  
public Heap() : this(\_DefaultCapacity, HeapType.MinHeap, null) \{ \}  
public Heap(int capacity) : this(capacity, HeapType.MinHeap, null) \{ \}  
public Heap(HeapType heapType) : this(\_DefaultCapacity, heapType, null) \{ \}  
public Heap(int capacity, HeapType heapType, IComparer<T> comparer)  
\{  
Init(capacity, heapType, comparer);  
\}  
public Heap(IEnumerable<T> collection, HeapType heapType, IComparer<T> comparer)  
\{  
if (collection == null)  
throw new IndexOutOfRangeException();  
Init(collection.Count(), heapType, comparer);  
using (IEnumerator<T> en = collection.GetEnumerator())//避免T在GC堆中有非托管资源，GC不能释放，需手动  
\{  
while (en.MoveNext())  
Enqueue(en.Current);  
\}  
\}  
private void Init(int capacity, HeapType heapType, IComparer<T> comparer)  
\{  
if (capacity < 0)  
throw new IndexOutOfRangeException();  
\_count = 0;  
\_array = new T\[capacity\];  
\_comparer = comparer ?? Comparer<T>.Default;  
\_typeName = heapType;  
switch (heapType)  
\{  
default:  
case HeapType.MinHeap:  
\_comparerFunc = (T t1, T t2) => \_comparer.Compare(t1, t2) > 0;//目标对象t2小  
break;  
case HeapType.MaxHeap:  
\_comparerFunc = (T t1, T t2) => \_comparer.Compare(t1, t2) < 0;//目标对象t2大  
break;  
\}  
\}  
  
public T Dequeue()  
\{  
if (\_count == 0)  
throw new InvalidOperationException();  
T result = \_array\[0\];  
\_array\[0\] = \_array\[--\_count\];  
\_array\[\_count\] = default(T);  
  
if (\_array.Length > \_DefaultCapacity && \_count \* 100 <= \_array.Length \* \_ShrinkThreshold)//缩容  
\{  
int newCapacity = Math.Max(\_DefaultCapacity, (int)((long)\_array.Length \* (long)\_ShrinkThreshold / 100));  
SetCapacity(newCapacity);  
\}  
AdjustHeap(\_array, 0, \_count);  
return result;  
\}  
public void Enqueue(T item)  
\{  
if (\_count >= \_array.Length)//扩容  
\{  
int newCapacity = Math.Max(\_array.Length+\_MinimumGrow, (int)((long)\_array.Length \* (long)\_GrowFactor / 100));  
SetCapacity(newCapacity);  
\}  
  
\_array\[\_count++\] = item;  
int parentIndex;  
int targetIndex;  
int targetCount = \_count;  
while (targetCount > 1)  
\{  
parentIndex = targetCount / 2 - 1;  
targetIndex = targetCount - 1;  
if (!\_comparerFunc.Invoke(\_array\[parentIndex\], \_array\[targetIndex\]))  
break;  
Swap(\_array, parentIndex, targetIndex);  
targetCount = parentIndex + 1;  
\}  
\}  
private void AdjustHeap(T\[\] array, int parentIndex, int count)  
\{  
if (\_count < 2)  
return;  
int childLeftIndex = parentIndex \* 2 + 1;  
int childRightIndex = (parentIndex + 1) \* 2;  
  
int targetIndex = parentIndex;  
if (childLeftIndex < count && \_comparerFunc.Invoke(array\[parentIndex\], array\[childLeftIndex\]))  
targetIndex = childLeftIndex;  
if (childRightIndex < count && \_comparerFunc.Invoke(array\[targetIndex\], array\[childRightIndex\]))  
targetIndex = childRightIndex;  
if (targetIndex != parentIndex)  
\{  
Swap(\_array, parentIndex, targetIndex);  
AdjustHeap(\_array, targetIndex, \_count);  
\}  
\}  
  
private void SetCapacity(int capacity)  
\{  
T\[\] newArray = new T\[capacity\];  
Array.Copy(\_array, newArray, \_count);  
\_array = newArray;  
\}  
  
private void Swap(T\[\] array, int index1, int index2)  
\{  
T temp = array\[index1\];  
array\[index1\] = array\[index2\];  
array\[index2\] = temp;  
\}  
  
public void Clear()  
\{  
Array.Clear(\_array, 0, \_count);  
Init(\_DefaultCapacity, HeapType.MinHeap, null);  
\}  
\}  
  
public enum HeapType \{ MinHeap, MaxHeap \}  
三、 使用测试：　  
　　建一个Person类用来测试，例子中Person比较规则是：先按年龄比较，年龄相同再按身高比较。具体比较大小是由选择堆的类别进行不同的排序规则：如Person类中小根堆先按年龄小者排序，年龄相同者按身高大者排序；而使用大根堆则相反。两种比较器写法，前者直接使用默认比较器；后者需要将比较器注入到堆中。

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public class Person : IComparable<Person>  
\{  
public string name \{ get; set; \}  
public int Age \{ get; set; \}  
  
public int Height \{ get; set; \}  
public override string ToString()  
\{  
return $"我叫\{name\}，年龄\{Age\}，身高\{Height\}";  
\}  
  
//小根堆：先排年龄小，年龄相同，按身高大的先排；大根堆相反  
public int CompareTo(Person other)  
\{  
if (this.Age.CompareTo(other.Age) != 0)  
return this.Age.CompareTo(other.Age);  
else if (this.Height.CompareTo(other.Height) != 0)  
return ~this.Height.CompareTo(other.Height);  
else  
return 0;  
\}  
\}  
  
public class personComparer : IComparer<Person>  
\{  
//大根堆：先排年龄大，年龄相同，按身高大的先排；小根堆相反  
public int Compare(Person x, Person y)  
\{  
if (x.Age.CompareTo(y.Age) != 0)  
return x.Age.CompareTo(y.Age);  
else if (x.Height.CompareTo(y.Height) != 0)  
return x.Height.CompareTo(y.Height);  
else  
return 0;  
\}  
\}  
　　主函数调用：

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static void Main(string\[\] args)  
\{  
int\[\] array = \{ 3, 5, 8, 3, 7, 1 \};  
Heap<int> heap0 = new Heap<int>(array, HeapType.MaxHeap, null);  
Console.WriteLine(heap0.TypeName);  
Console.WriteLine(heap0.Dequeue());  
Console.WriteLine(heap0.Dequeue());  
Console.WriteLine(heap0.Dequeue());  
Console.WriteLine(heap0.Dequeue());  
int length = heap0.Count;  
for (int count = 0; count < length; count++)  
\{  
Console.WriteLine(heap0.Dequeue());  
\}  
  
Person person1 = new Person() \{ Age = 12, Height = 158, name = "张三" \};  
Person person2 = new Person() \{ Age = 13, Height = 160, name = "李四" \};  
Person person3 = new Person() \{ Age = 10, Height = 150, name = "王二" \};  
Person person4 = new Person() \{ Age = 10, Height = 152, name = "麻子" \};  
Person person5 = new Person() \{ Age = 12, Height = 150, name = "刘五" \};  
List<Person> people = new List<Person>();  
people.Add(person1);  
people.Add(person2);  
people.Add(person3);  
people.Add(person4);  
people.Add(person5);  
Heap<Person> heap2 = new Heap<Person>(people, HeapType.MinHeap, null);  
Person person6 = new Person() \{ Age = 9, Height = 145, name = "赵六" \};  
heap2.Enqueue(person6);  
Console.WriteLine(heap2.TypeName);  
Console.WriteLine(heap2.Dequeue());  
Console.WriteLine(heap2.Dequeue());  
Console.WriteLine(heap2.Dequeue());  
Console.WriteLine(heap2.Dequeue());  
  
PersonComparer personComparer = new PersonComparer();  
Heap<Person> heap3 = new Heap<Person>(1,HeapType.MaxHeap,personComparer);  
heap3.Enqueue(person1);  
heap3.Enqueue(person2);  
heap3.Enqueue(person3);  
heap3.Enqueue(person4);  
heap3.Enqueue(person5);  
heap3.Enqueue(person6);  
Console.WriteLine(heap3.TypeName);  
Console.WriteLine(heap3.Dequeue());  
Console.WriteLine(heap3.Dequeue());  
Console.WriteLine(heap3.Dequeue());  
Console.WriteLine(heap3.Dequeue());  
  
Console.ReadKey();  
\}