Binary Tree Preorder Traversal (Recursive)

Easy Trees & BST Recursion Original on LeetCode

Binary Tree Preorder Traversal (Recursive) is a easy trees & bst problem solved with the recursion pattern. The best approach, iterative (stack), runs in O(n) time and O(h) space. Below are 2 approaches in Java, from recursive dfs up.

Problem

Return the preorder traversal (node, left, right) of a binary tree.

Examples

Example 1

Input: root = [4, 2, 6, 1, 3]
Output: [4, 2, 1, 3, 6]

Example 2

Input: root = [1, null, 2]
Output: [1, 2]

Constraints

The tree has 0 to 100 nodes.

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Solutions

Try it yourself first. Then compare: each approach lists its idea, the steps, its time and space, and the Java code.

Approach	Time	Space
Recursive DFS	`O(n)`	`O(h)`
Iterative (stack)	`O(n)`	`O(h)`

1Recursive DFS

TimeO(n)

SpaceO(h)

Record the node before visiting its children.

if node == null return.
add(node.val); preorder(left); preorder(right).

Java

class Solution {
    public List<Integer> preorderTraversal(TreeNode root) {
        List<Integer> out = new ArrayList<>();
        preorder(root, out);
        return out;
    }

    private void preorder(TreeNode node, List<Integer> out) {
        if (node == null) return;
        out.add(node.val);
        preorder(node.left, out);
        preorder(node.right, out);
    }
}

2Iterative (stack)

TimeO(n)

SpaceO(h)

Pop a node, record it, then push its right child before its left so the left is processed first.

Push root; while the stack is not empty: pop, add, push right, push left.

Java

class Solution {
    public List<Integer> preorderTraversal(TreeNode root) {
        List<Integer> out = new ArrayList<>();
        if (root == null) return out;
        Deque<TreeNode> st = new ArrayDeque<>();
        st.push(root);
        while (!st.isEmpty()) {
            TreeNode n = st.pop();
            out.add(n.val);
            if (n.right != null) st.push(n.right);
            if (n.left != null) st.push(n.left);
        }
        return out;
    }
}

Edge cases to test

Empty tree

Hints

Hint 1

Preorder = root first, then left, then right. It is the order used to copy or serialize a tree.

FAQ

What is the best time complexity for Binary Tree Preorder Traversal (Recursive)?

Iterative (stack) runs in O(n) time and O(h) extra space.

Which pattern does Binary Tree Preorder Traversal (Recursive) use?

It is a trees & bst problem that uses the recursion pattern. Other problems with the same pattern: Binary Tree Inorder Traversal (Recursive), Binary Tree Postorder Traversal (Recursive), Binary Tree Inorder Traversal (Iterative).

Is there a brute force solution for Binary Tree Preorder Traversal (Recursive)?

Yes. Recursive DFS takes O(n) time and O(h) space. Record the node before visiting its children.

Which edge cases should I test for Binary Tree Preorder Traversal (Recursive)?

Empty tree.