1. 引言
在实际的项目中，树还是用的比较多的一种，尤其是对于具有层次结构的数据。相信很多人都学过树的遍历，比如先序遍历，后序遍历等，利用递归还是很容易理解的。
今天给大家介绍下二叉树的几种遍历算法，包括递归和非递归的实现。
首先建立一棵二叉树 如：
[DebuggerDisplay("Value={Value}")]
public class Tree
{
public string Value;
public Tree Left;
public Tree Right;
}
public static Tree CreatFakeTree()
{
Tree tree = new Tree() {Value = "A"};
tree.Left = new Tree()
{
Value = "B",
Left = new Tree() {Value = "D", Left = new Tree() {Value = "G"}},
Right = new Tree() {Value = "E", Right = new Tree() {Value = "H"}}
};
tree.Right = new Tree() {Value = "C", Right = new Tree() {Value = "F"}};
return tree;
}
一棵简单的二叉树
2. 先序遍历
先序遍历还是很好理解的，一次遍历根节点，左子树，右子数
递归实现
public static void PreOrder(Tree tree)
{
if (tree == null)
return; System.Console.WriteLine(tree.Value);
PreOrder(tree.Left);
PreOrder(tree.Right);
}
非递归实现
public static void PreOrderNoRecursion(Tree tree)
{
if(tree == null)
return; System.Collections.Generic.Stack<Tree> stack = new System.Collections.Generic.Stack<Tree>();
Tree node = tree; while (node != null || stack.Any())
{
if (node != null)
{
stack.Push(node);
System.Console.WriteLine(node.Value);
node = node.Left;
}
else
{
var item = stack.Pop();
node = item.Right;
}
}
}
输出结果： 
3. 中序遍历
递归实现
public static void InOrder(Tree tree)
{
if(tree == null)
return; InOrder(tree.Left);
System.Console.WriteLine(tree.Value);
InOrder(tree.Right);
}
非递归实现
public static void InOrderNoRecursion(Tree tree)
{
if (tree == null)
return; System.Collections.Generic.Stack<Tree> stack = new System.Collections.Generic.Stack<Tree>();
Tree node = tree; while (node != null || stack.Any())
{
if (node != null)
{
stack.Push(node);
node = node.Left;
}
else
{
var item = stack.Pop();
System.Console.WriteLine(item.Value); node = item.Right;
}
}
}
输出结果：
4. 后序遍历
递归实现
public static void PostOrder(Tree tree)
{
if (tree == null)
return; PostOrder(tree.Left);
PostOrder(tree.Right);
System.Console.WriteLine(tree.Value);
}
非递归实现 比前两种稍微复杂一点。要保证左右节点都被访问后，才能访问根节点。这里给出两种形式。
public static void PostOrderNoRecursion(Tree tree)
{
if (tree == null)
return; System.Collections.Generic.Stack<Tree> stack = new System.Collections.Generic.Stack<Tree>();
Tree node = tree;
Tree pre = null;
stack.Push(node); while (stack.Any())
{
node = stack.Peek();
if ((node.Left == null && node.Right == null) ||
(pre != null && (pre == node.Left || pre == node.Right)))
{
System.Console.WriteLine(node.Value);
pre = node; stack.Pop();
}
else
{
if(node.Right != null)
stack.Push(node.Right); if(node.Left != null)
stack.Push(node.Left);
}
}
} public static void PostOrderNoRecursion2(Tree tree)
{
HashSet<Tree> visited = new HashSet<Tree>();
System.Collections.Generic.Stack<Tree> stack = new System.Collections.Generic.Stack<Tree>();
Tree node = tree; while (node != null || stack.Any())
{
if (node != null)
{
stack.Push(node);
node = node.Left;
}
else
{
var item = stack.Peek();
if (item.Right != null && !visited.Contains(item.Right))
{
node = item.Right;
}
else
{
System.Console.WriteLine(item.Value);
visited.Add(item);
stack.Pop();
}
}
}
}
输出结果: 
5. 层序遍历
层序遍历就是按照层次由左向右输出
public static void LevelOrder(Tree tree)
{
if(tree == null)
return; Queue<Tree> queue = new Queue<Tree>();
queue.Enqueue(tree); while (queue.Any())
{
var item = queue.Dequeue();
System.Console.Write(item.Value); if (item.Left != null)
{
queue.Enqueue(item.Left);
} if (item.Right != null)
{
queue.Enqueue(item.Right);
}
}
}
输出结果：
6. Z-型层序遍历
Z-层序遍历就是奇数层按照由左向右输出，偶数层按照由右向左输出，这里定义了几个辅助函数，比如计算节点所在的层次。算法思想是按照层次保存树形节点，应该是有更加优化的算法，希望大家指出。
public static int GetDepth(Tree tree, Tree node)
{
if (tree == null)
return ; if (tree == node)
return ; if (tree.Left == node || tree.Right == node)
return ; int lDepth = GetDepth(tree.Left, node);
lDepth = lDepth == ? : lDepth + ; int rDepth = GetDepth(tree.Right, node);
rDepth = rDepth == ? : rDepth + ; return lDepth >= rDepth ? lDepth : rDepth;
} public static void Z_LevelOrder(Tree tree, Dictionary<int, List<Tree>> dictionary)
{
if (tree == null)
return; Queue<Tree> queue = new Queue<Tree>();
queue.Enqueue(tree); while (queue.Any())
{
var item = queue.Dequeue();
var depth = GetDepth(tree, item); List<Tree> list;
if (!dictionary.TryGetValue(depth, out list))
{
list = new List<Tree>();
dictionary.Add(depth, list);
}
list.Add(item); if (item.Left != null)
{
queue.Enqueue(item.Left);
} if (item.Right != null)
{
queue.Enqueue(item.Right);
}
}
} public static void Z_LevelOrder(Tree tree)
{
if (tree == null)
return; Dictionary<int, List<Tree>> dictionary = new Dictionary<int, List<Tree>>();
Z_LevelOrder(tree, dictionary); foreach (KeyValuePair<int, List<Tree>> pair in dictionary)
{
if (pair.Key% == )
{
pair.Value.Reverse();
} pair.Value.ForEach(t=> { System.Console.Write(t.Value); });
}
}
输出结果：