二叉堆结构解释: http://www.apkbus.com/android-58533-1-1.html
代码实现方式:
using System;
using System.Collections.Generic;
namespace BinaryHeap
{
/// <summary>
/// 排序的枚举
/// </summary>
public enum Order
{
ASC = 0,
DESC = 1
}
/// <summary>
/// 二叉堆
/// </summary>
/// <typeparam name="T">填入你需要存储的类型</typeparam>
public class BinaryHeap<T> where T : IComparable<T>
{
/// <summary>
/// The size of the heap
/// </summary>
public int Size { get; set; }
private int length;
/// <summary>
/// 堆的长度
/// </summary>
public int Length
{
get
{
return length;
}
private set { length = value; }
}
private T[] Items { get; set; }
private Order Order = Order.ASC;
/// <summary>
/// The Cons of the heap
/// </summary>
/// <param name="size">The default size of the heap</param>
/// <param name="order">The order of the heap</param>
public BinaryHeap(int size, Order order)
{
if (size < 1)
{
throw new Exception("二叉堆最少长度2");
}
this.Size = size;
this.Order = order;
this.Size++;
Items = new T[this.Size];
this.length = 0;
}
/*
我们可以举一个例子，假设我们已经有了一个最小二叉堆（其中有7个元素），现在我们要插入一个元素17到这个二叉堆中去，那么插入后二叉堆大小就会加一变成8
10 30 20 34 38 30 24 17
现在17位下划线的那个，我们已经将他放在数组的最后位置了，然后我们比较他与他的父节点（位置为8/2 = 4），在位置4（从1开始数）的为34，由于17小于34，所以我们交换彼此，得到下图：
10 30 20 17 38 30 24 34
现在17跑到位置4中去了，然后我们比较17和他的新的父节点（位置为4/2 = 2），
在位置2（从1开始数）的为30，由于17还是小于30，所以交换彼此，得到下图：
10 17 20 30 38 30 24 34
现在17跑到第二位了，继续比较，父节点位置为2/2 = 1，由于17不小于10，所以这里就没有必要比较了，走到这一步我们的新元素17添加完成。现在的堆已经添加了元素17，堆中有8位按照最小二叉堆规则排序的元素。
*/
/// <summary>
/// 添加节点
/// </summary>
/// <param name="item"></param>
public void Add(T item)
{
if (this.length == 0)
{
Items[1] = item;
}
else
{
int len = this.length;
if (len >= this.Size)
{
throw new Exception("二叉堆已经满了,不能再添加了");
}
int endPos = len + 1;
Items[endPos] = item;
//从二叉堆最中间的数字 和 最末尾的数字第一次进行比较
int parentPos = endPos / 2;
bool isContinue = true;
while (parentPos != 0 && isContinue)
{
// 升序
if (Order == BinaryHeap.Order.ASC)
{
//实例比参数小就返回 -1
if (Items[endPos].CompareTo(Items[parentPos]) < 0)
{
//交换
Swap(ref Items[endPos], ref Items[parentPos]);
endPos = parentPos;
parentPos = endPos / 2;
}
else
{
isContinue = false;
}
}
else
{
//降序
if (Items[endPos].CompareTo(Items[parentPos]) > 0)
{
Swap(ref Items[endPos], ref Items[parentPos]);
endPos = parentPos;
parentPos = endPos / 2;
}
else
{
isContinue = false;
}
}
}
}
this.length++;
}
/// <summary>
/// 删除节点
/// </summary>
/// <returns>if the order is ASC, return the smallest one, if DESC, return the largest one.</returns>
public T Remove()
{
if (this.length == 0)
{
throw new Exception("二叉树为空");
}
// 把二叉堆的第一个元素删除掉
T removedItem = Items[1];
int len = this.length;
Items[1] = Items[len]; //把末尾的元素添加到第一位
// 减少二叉堆的长度
this.length--;
//先计算出第一次比较的两个节点
int currentPos = 1;
int leftChildPos = currentPos * 2;
int rightChildPos = currentPos * 2 + 1;
bool isContinue = true;
while ((leftChildPos <= len || rightChildPos <= len) && isContinue)
{
// Compare the removing item to its childrens, swap each other if needed
if (Order == BinaryHeap.Order.ASC)
{
#region 升序
if (leftChildPos <= len && rightChildPos <= len)
{
//当左节点小于右节点的时候,当前节点就跟左节点对比(是否交换)
if (Items[leftChildPos].CompareTo(Items[rightChildPos]) < 0 && Items[currentPos].CompareTo(Items[leftChildPos]) >= 0)
{
Swap(ref Items[currentPos], ref Items[leftChildPos]);
currentPos = leftChildPos;
}
//当左节点大于等于右节点的时候,当前节点就跟右节点对比(是否交换)
else if (Items[leftChildPos].CompareTo(Items[rightChildPos]) >= 0 && Items[currentPos].CompareTo(Items[rightChildPos]) >= 0)
{
Swap(ref Items[currentPos], ref Items[rightChildPos]);
currentPos = rightChildPos;
}
else
{
isContinue = false;
}
}
else if (leftChildPos <= len) //左节点比较
{
if (Items[currentPos].CompareTo(Items[leftChildPos]) >= 0)
{
Swap(ref Items[currentPos], ref Items[leftChildPos]);
currentPos = leftChildPos;
}
else
{
isContinue = false;
}
}
else if (rightChildPos <= len) //右节点比较
{
if (Items[currentPos].CompareTo(Items[rightChildPos]) >= 0)
{
Swap(ref Items[currentPos], ref Items[rightChildPos]);
currentPos = rightChildPos;
}
else
{
isContinue = false;
}
}
else
{
isContinue = false;
}
#endregion
leftChildPos = currentPos * 2;
rightChildPos = currentPos * 2 + 1;
}
else
{
#region 降序
if (leftChildPos <= len && rightChildPos <= len)
{
if (Items[leftChildPos].CompareTo(Items[rightChildPos]) > 0 && Items[currentPos].CompareTo(Items[leftChildPos]) <= 0)
{
Swap(ref Items[currentPos], ref Items[leftChildPos]);
currentPos = leftChildPos;
}
else if (Items[leftChildPos].CompareTo(Items[rightChildPos]) <= 0 && Items[currentPos].CompareTo(Items[rightChildPos]) <= 0)
{
Swap(ref Items[currentPos], ref Items[rightChildPos]);
currentPos = rightChildPos;
}
else
{
isContinue = false;
}
}
else if (leftChildPos <= len)
{
if (Items[currentPos].CompareTo(Items[leftChildPos]) <= 0)
{
Swap(ref Items[currentPos], ref Items[leftChildPos]);
currentPos = leftChildPos;
}
else
{
isContinue = false;
}
}
else if (rightChildPos <= len)
{
if (Items[currentPos].CompareTo(Items[rightChildPos]) <= 0)
{
Swap(ref Items[currentPos], ref Items[rightChildPos]);
currentPos = rightChildPos;
}
else
{
isContinue = false;
}
}
else
{
isContinue = false;
}
#endregion
leftChildPos = currentPos * 2;
rightChildPos = currentPos * 2 + 1;
}
}
return removedItem;
}
/// <summary>
/// 排序二叉堆
/// </summary>
/// <returns>Return the sorted heap array</returns>
public IEnumerable<T> Sort()
{
if (this.length == 0)
{
throw new Exception("The heap is empty");
}
while (this.length > 0)
{
yield return Remove();
}
}
#region Private method
/// <summary>
/// Swap each other
/// </summary>
/// <param name="t1">The first one</param>
/// <param name="t2">The second one</param>
private void Swap(ref T t1, ref T t2)
{
T temp = t1;
t1 = t2;
t2 = temp;
}
#endregion
}
}
时间： 2024-10-11 16:15:25