94. Binary Tree Inorder Traversal

Given a binary tree, return the inorder traversal of its nodes' values.

Example:

Input: [1,null,2,3]
   1
    \
     2
    /
   3

Output: [1,3,2]

Follow up: Recursive solution is trivial, could you do it iteratively?

 

Approach #1: recurisive.

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    vector<int> inorderTraversal(TreeNode* root) {
        vector<int> ans;
        helper(root, ans);
        return ans;
    }
    
private:
    void helper(TreeNode* root, vector<int>& ans) {
        if (root != NULL) {
            if (root->left != NULL) {
                helper(root->left, ans);
            }
            ans.push_back(root->val);
            if (root->right != NULL) {
                helper(root->right, ans);
            }
        }
    }
};

Runtime: 0 ms, faster than 100.00% of C++ online submissions for Binary Tree Inorder Traversal.

 

Approach #2: Iteration with stack.[Java]

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public List<Integer> inorderTraversal(TreeNode root) {
        List<Integer> res =  new ArrayList< > ();
        Stack<TreeNode> stack = new Stack< > ();
        TreeNode curr = root;
        while (curr != null || !stack.isEmpty()) {
            while (curr != null) {
                stack.push(curr);
                curr = curr.left;
            }
            curr = stack.pop();
            res.add(curr.val);
            curr = curr.right;
        }
        return res;
    }
}

Runtime: 1 ms, faster than 60.30% of Java online submissions for Binary Tree Inorder Traversal.

 

Approach #3: Morris Traversal.[python] 

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def inorderTraversal(self, root):
        """
        :type root: TreeNode
        :rtype: List[int]
        """
        res = []
        curr = root
        while curr:
            if not curr.left:
                res.append(curr.val)
                curr = curr.right
            else:
                pre = curr.left
                while pre.right:
                    pre = pre.right
                pre.right = curr
                temp = curr
                curr = curr.left
                temp.left = None
        return res            
            

Runtime: 24 ms, faster than 40.09% of Python online submissions for Binary Tree Inorder Traversal.

 

 Analysis: [Morris Traversal]

In this method, we have to use a new data structure-Threaded Binary Tree, and the strategy is as follows:

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

    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

For example:

          1
        /   \
       2     3
      / \   /
     4   5 6

First, 1 is the root, so initialize 1 as current, 1 has left child which is 2, the current's left subtree is

         2
        / \
       4   5

So in this subtree, the rightmost node is 5, then make the current(1) as the right child of 5. Set current = cuurent.left (current = 2). The tree now looks like:

         2
        / \
       4   5
            \
             1
              \
               3
              /
             6

For current 2, which has left child 4, we can continue with thesame process as we did above

        4
         \
          2
           \
            5
             \
              1
               \
                3
               /
              6

then add 4 because it has no left child, then add 2, 5, 1, 3 one by one, for node 3 which has left child 6, do the same as above. Finally, the inorder taversal is [4,2,5,1,6,3].