线程二叉树

可以使用递归或使用辅助堆栈来完成二叉树的中序遍历。线程二叉树的想法是使中序遍历更快，并且无需堆栈和递归即可完成。通过使通常为 NULL 的所有正确子指针指向节点的中序后继节点（如果存在），可以使二叉树成为线程化的。
有两种类型的线程二叉树。
单线程：其中 NULL 右指针指向中序后继（如果后继存在）
双线程：左右 NULL 指针分别指向有序前驱和有序后继。前导线程对于反向中序遍历和后序遍历很有用。
线程对于快速访问节点的祖先也很有用。
下图显示了一个示例单线程二叉树。虚线代表线程。

线程节点的 C 表示
以下是单线程节点的 C 表示。

C

struct Node
{
    int data;
    struct Node *left, *right;
    bool rightThread; 
}

线程节点的Java表示

以下是单线程节点的Java表示。

Java

static class Node
{
    int data;
    Node left, right;
    boolean rightThread; 
}
 
// This code contributed by aashish1995

Python3

class Node:
    def __init__(self, data,rightThread):
        self.data = data;
        self.left = None;
        self.right = None;
        self.rightThread = rightThread;
 
# This code is contributed by umadevi9616

C＃

public class Node
{
   public int data;
   public Node left, right;
   public bool rightThread; 
}
 
// This code is contributed by aashish1995

Javascript

 class Node {
        constructor(val) {
            this.data = val;
            this.left = null;
            this.right = null;
            this.rightThread = false;
        }
    }
 
// This code contributed by aashish1995

由于右指针有两个用途，布尔变量 rightThread 用于指示右指针是指向右子节点还是中序后继节点。同样，我们可以为双线程二叉树添加 leftThread。
使用线程的中序遍历
以下是线程二叉树中的中序遍历代码。

C

// Utility function to find leftmost node in a tree rooted
// with n
struct Node* leftMost(struct Node* n)
{
    if (n == NULL)
        return NULL;
 
    while (n->left != NULL)
        n = n->left;
 
    return n;
}
 
// C code to do inorder traversal in a threaded binary tree
void inOrder(struct Node* root)
{
    struct Node* cur = leftMost(root);
    while (cur != NULL) {
        printf("%d ", cur->data);
 
        // If this node is a thread node, then go to
        // inorder successor
        if (cur->rightThread)
            cur = cur->right;
        else // Else go to the leftmost child in right
             // subtree
            cur = leftmost(cur->right);
    }
}

Java

// Utility function to find leftmost node in a tree rooted
// with n
Node leftMost(Node n)
{
    if (n == null)
        return null;
 
    while (n.left != null)
        n = n.left;
 
    return n;
}
 
// C code to do inorder traversal in a threaded binary tree
static void inOrder(Node root)
{
    Node cur = leftMost(root);
    while (cur != null) {
        System.out.printf("%d ", cur.data);
 
        // If this node is a thread node, then go to
        // inorder successor
        if (cur.rightThread)
            cur = cur.right;
        else // Else go to the leftmost child in right
             // subtree
            cur = leftmost(cur.right);
    }
}
 
// This code contributed by aashish1995

Python3

# Utility function to find leftmost Node in a tree rooted
# with n
def leftMost(n):
 
    if (n == None):
        return None;
 
    while (n.left != None):
        n = n.left;
 
    return n;
 
 
# C code to do inorder traversal in a threaded binary tree
def inOrder(root):
 
    cur = leftMost(root);
    while (cur != None):
        print(cur.data," ");
 
        # If this Node is a thread Node, then go to
        # inorder successor
        if (cur.rightThread):
            cur = cur.right;
        else: # Else go to the leftmost child in right
             # subtree
            cur = leftmost(cur.right);
 
# This code is contributed by Rajput-Ji

C＃

// Utility function to find leftmost node in a tree rooted
// with n
Node leftMost(Node n)
{
  if (n == null)
    return null;
 
  while (n.left != null)
    n = n.left;
 
  return n;
}
 
// C code to do inorder traversal in a threaded binary tree
static void inOrder(Node root)
{
  Node cur = leftMost(root);
  while (cur != null)
  {
    Console.Write("{0} ", cur.data);
 
    // If this node is a thread node, then go to
    // inorder successor
    if (cur.rightThread)
      cur = cur.right;
    else // Else go to the leftmost child in right
      // subtree
      cur = leftmost(cur.right);
  }
}
 
// This code is contributed by gauravrajput1

Javascript

 
// Utility function to find leftmost node in a tree rooted
// with n
function leftMost(n)
{
    if (n == null)
        return null;
  
    while (n.left != null)
        n = n.left;
  
    return n;
}
 
// JavaScript code to do inorder traversal in
// a threaded binary tree
function inOrder(root)
{
    let cur = leftMost(root);
    while (cur != null) {
        document.write(cur.data+" ");
  
        // If this node is a thread node, then go to
        // inorder successor
        if (cur.rightThread)
            cur = cur.right;
        else // Else go to the leftmost child in right
             // subtree
            cur = leftmost(cur.right);
        }
}
 
// This code is contributed by unknown2108
 

下图演示了使用线程的中序遍历。