Morris莫里斯遍历

程序员代码面试指南（第2版）第3章 二叉树问题：遍历二叉树的神级方法

https://leetcode.com/articles/binary-tree-inorder-traversal/

Step 1: Initialize current as root

Step 2: While current is not NULL,

If current does not have left child

a. Add current’s value

b. Go to the right, i.e., current = current.right

Else

If rightmost node of current's left subtree has no right child
 a. In current's left subtree, make current the right child of the rightmost node

 b. Go to this left child, i.e., current = current.left
Else 
	a. Restore the origianl state, assign null value to the right child of the rightmost node

在了解Morris序后，通过对能到达2次的节点选择性的打印，可以很直观的得到前序遍历和中序遍历。

对于Morris序，先把左子树的右边界节点和cur连上，再处理左子树。(这个查找左子树右边界节点的过程不属于Morris遍历过程。)

cur被指针保存后，就可以放心的移动了。

有左子树的节点都会到达2次，每次都需要重新查找右边界。

1. Morris遍历

   public static void morris(Node head) {
       if (head == null) {
           return;
       }
       Node cur = head;
       //这个mostRight指的是左子树的mostRight,而不是当前节点的mostRight
       Node mostRight = null;
       while (cur != null) {
           mostRight = cur.left;
           if (mostRight != null) { // 如果当前cur有左子树
               // 找到cur左子树上最右的节点
               while (mostRight.right != null && mostRight.right != cur) {
                   mostRight = mostRight.right;
               }
               // 从上面的while里出来后，mostRight就是cur左子树上最右的节点
               if (mostRight.right == null) { // 如果mostRight.right是指向null的
                   mostRight.right = cur; // 让其指向cur
                   cur = cur.left; // cur向左移动
                   continue; // 回到最外层的while，继续判断cur的情况
               } else { // 如果mostRight.right是指向cur的
                   mostRight.right = null; // 让其指向null
               }
           }
           // cur如果没有左子树，cur向右移动
           // 或者cur左子树上最右节点的右指针是指向cur的，cur向右移动
           cur = cur.right;
       }
   }
   

2. Morris前序遍历

   对于只到达1次的节点，马上打印。

   对于到达2次的节点，只打印第1次。

   public static void morrisPre(Node head) {
       if (head == null) {
           return;
       }
       Node cur = head;
       Node mostRight = null;
       while (cur != null) {
           mostRight = cur.left;
           if (mostRight != null) {
               //到达2次的节点
               while (mostRight.right != null && mostRight.right != cur) {
                   mostRight = mostRight.right;
               }
               if (mostRight.right == null) {
                   //2次中的第1次
                   mostRight.right = cur;
                   System.out.print(cur.value + " ");
                   cur = cur.left;
                   continue;
               } else {
                   //2次中的第2次
                   mostRight.right = null;
               }
           } else {
               //只能到达1次的节点
               System.out.print(cur.value + " ");
           }
           cur = cur.right;
       }
       System.out.println();
   }
   

3. Morris中序遍历

   对于只到达1次的节点，马上打印。

   对于到达2次的节点，只打印第2次。

   public static void morrisIn(Node head) {
       if (head == null) {
           return;
       }
       Node cur = head;
       Node mostRight = null;
       while (cur != null) {
           mostRight = cur.left;
           if (mostRight != null) {
               while (mostRight.right != null && mostRight.right != cur) {
                   mostRight = mostRight.right;
               }
               if (mostRight.right == null) {
                   mostRight.right = cur;
                   cur = cur.left;
                   continue;
               } else {
                   mostRight.right = null;
               }
           }
           //只能到达1次的节点和能到达2次中的节点的第2次，会经过这里
           System.out.print(cur.value + " ");
           cur = cur.right;
       }
       System.out.println();
   }
   

4. Morris后序遍历

   对于第二次遇到的节点，打印其左子树的右边界。

   最后打印整棵树的右边界。

   public static void morrisPos(Node head) {
       Node cur = head;
       Node mostRight = null;
       while (cur != null) {
           mostRight = cur.left;
           if (mostRight != null) {
               while(mostRight.right != null && mostRight.right != cur) {
                   mostRight = mostRight.right;
               }
               if (mostRight.right == null) {
                   mostRight.right = cur;
                   cur = cur.left;
                   continue;
               } else {
                   mostRight.right = null;
                   traverseRightEdge(head);
               }
           }
           cur = cur.right;
       }
       traverseRightEdge(head);
   }
   
   private static void traverseRightEdge(Node head) {
       Node tail = reverseRightEdge(head);
       for (Node cur = tail; cur != null; cur = cur.right) {
           doSomething(cur);
       }
       reverseRightEdge(tail);
   }
   
   private static Node reverseRightEdge(Node head) {
       Node newHead = null;
       Node next = null;
       while (head != null) {
           next = head.right;
           head.right = newHead;
           newHead = head;
           head = next;
       }
       return newHead;
   }
   
   private static void doSomething() {}