morris Traversal

O(n)时间，O(1)空间对二叉树进行前序、中序、后序遍历。详细讲解看参考。 

 

public class Solution {

    public static void morrisPreorder(TreeNode root) {
        TreeNode cur = root;
        TreeNode pre = null;

        while (cur != null) {
            if (cur.left == null) {
                System.out.print(cur.val + " ");
                cur = cur.right;
            } else {
                // find predecessor
                pre = cur.left;
                while (pre.right != null && pre.right != cur)
                    pre = pre.right;

                if (pre.right == null) {
                    System.out.print(cur.val + " ");
                    pre.right = cur;
                    cur = cur.left;
                } else {
                    pre.right = null;
                    cur = cur.right;
                }

            }

        }
        System.out.println();

    }

    public static void morrisInorder(TreeNode root) {
        TreeNode cur = root;
        TreeNode pre = null;

        while (cur != null) {
            if (cur.left == null) {
                System.out.print(cur.val + " ");
                cur = cur.right;
            } else {
                // find predecessor
                pre = cur.left;
                while (pre.right != null && pre.right != cur)
                    pre = pre.right;

                if (pre.right == null) {
                    pre.right = cur;
                    cur = cur.left;

                } else {
                    pre.right = null;
                    System.out.print(cur.val + " ");
                    cur = cur.right;
                }

            }

        }

        System.out.println();
    }

    public static void morrisPostorder(TreeNode root) {
        TreeNode dump = new TreeNode(0);
        dump.left = root;
        TreeNode cur = dump;
        TreeNode pre = null;

        while (cur != null) {
            if (cur.left == null) {
                cur = cur.right;
            } else {
                // find predecessor
                pre = cur.left;
                while (pre.right != null && pre.right != cur)
                    pre = pre.right;

                if (pre.right == null) {
                    pre.right = cur;
                    cur = cur.left;
                } else {
                    pre.right = null;
                    printRev(cur.left, pre);
                    cur = cur.right;
                }

            }
        }
        System.out.println();

    }

    private static void printRev(TreeNode from, TreeNode to) {
        reverse(from, to);

        TreeNode p = to;
        while (true) {
            System.out.print(p.val + " ");
            if (p == from)
                break;
            p = p.right;
        }
        reverse(to, from);
    }

    private static void reverse(TreeNode from, TreeNode to) {
        if (from == to)
            return;
        TreeNode pre = from, cur = from.right, post = null;
        while (pre != to) {
            post = cur.right;
            cur.right = pre;
            pre = cur;
            cur = post;
        }

    }

    public static void main(String[] args) {
        String s = "6 2 1 # # 4 3 # # 5 # # 7 # 9 # 8 # #";
        TreeNode root = TreeUtils.makeTree(s);
        TreeUtils.printTree(root);
        morrisPreorder(root);
        morrisInorder(root);
        morrisPostorder(root);

    }

}

 

复杂度分析：

空间复杂度：O(1)，因为只用了两个辅助指针。

时间复杂度：O(n)。证明时间复杂度为O(n)，最大的疑惑在于寻找中序遍历下二叉树中所有节点的前驱节点的时间复杂度是多少，即以下两行代码：

while (pre.right != null && pre.right != cur)
    pre = pre.right;

 

直觉上，认为它的复杂度是O(nlgn)，因为找单个节点的前驱节点与树的高度有关。但事实上，寻找所有节点的前驱节点只需要O(n)时间。n个节点的二叉树中一共有n-1条边，整个过程中每条边最多只走2次，一次是为了定位到某个节点，另一次是为了寻找上面某个节点的前驱节点，如下图所示，其中红色是为了定位到某个节点，黑色线是为了找到前驱节点。所以复杂度为O(n)。

         

 

参考（讲的太好了）：

http://www.cnblogs.com/AnnieKim/archive/2013/06/15/MorrisTraversal.html