LeetCode #655 — MEDIUM

Print Binary Tree

Move from brute-force thinking to an efficient approach using tree strategy.

Solve on LeetCode
The Problem

Problem Statement

Given the root of a binary tree, construct a 0-indexed m x n string matrix res that represents a formatted layout of the tree. The formatted layout matrix should be constructed using the following rules:

  • The height of the tree is height and the number of rows m should be equal to height + 1.
  • The number of columns n should be equal to 2height+1 - 1.
  • Place the root node in the middle of the top row (more formally, at location res[0][(n-1)/2]).
  • For each node that has been placed in the matrix at position res[r][c], place its left child at res[r+1][c-2height-r-1] and its right child at res[r+1][c+2height-r-1].
  • Continue this process until all the nodes in the tree have been placed.
  • Any empty cells should contain the empty string "".

Return the constructed matrix res.

Example 1:

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

Example 2:

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

Constraints:

  • The number of nodes in the tree is in the range [1, 210].
  • -99 <= Node.val <= 99
  • The depth of the tree will be in the range [1, 10].
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: Given the root of a binary tree, construct a 0-indexed m x n string matrix res that represents a formatted layout of the tree. The formatted layout matrix should be constructed using the following rules: The height of the tree is height and the number of rows m should be equal to height + 1. The number of columns n should be equal to 2height+1 - 1. Place the root node in the middle of the top row (more formally, at location res[0][(n-1)/2]). For each node that has been placed in the matrix at position res[r][c], place its left child at res[r+1][c-2height-r-1] and its right child at res[r+1][c+2height-r-1]. Continue this process until all the nodes in the tree have been placed. Any empty cells should contain the empty string "". Return the constructed matrix res.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Tree

Example 1

[1,2]

Example 2

[1,2,3,null,4]
Step 02

Core Insight

What unlocks the optimal approach

  • No official hints in dataset. Start from constraints and look for a monotonic or reusable state.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #655: Print Binary Tree
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public List<List<String>> printTree(TreeNode root) {
        int h = height(root);
        int m = h + 1, n = (1 << (h + 1)) - 1;
        String[][] res = new String[m][n];
        for (int i = 0; i < m; ++i) {
            Arrays.fill(res[i], "");
        }
        dfs(root, res, h, 0, (n - 1) / 2);
        List<List<String>> ans = new ArrayList<>();
        for (String[] t : res) {
            ans.add(Arrays.asList(t));
        }
        return ans;
    }

    private void dfs(TreeNode root, String[][] res, int h, int r, int c) {
        if (root == null) {
            return;
        }
        res[r][c] = String.valueOf(root.val);
        dfs(root.left, res, h, r + 1, c - (1 << (h - r - 1)));
        dfs(root.right, res, h, r + 1, c + (1 << (h - r - 1)));
    }

    private int height(TreeNode root) {
        if (root == null) {
            return -1;
        }
        return 1 + Math.max(height(root.left), height(root.right));
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(h)

Approach Breakdown

LEVEL ORDER
O(n) time
O(n) space

BFS with a queue visits every node exactly once — O(n) time. The queue may hold an entire level of the tree, which for a complete binary tree is up to n/2 nodes = O(n) space. This is optimal in time but costly in space for wide trees.

DFS TRAVERSAL
O(n) time
O(h) space

Every node is visited exactly once, giving O(n) time. Space depends on tree shape: O(h) for recursive DFS (stack depth = height h), or O(w) for BFS (queue width = widest level). For balanced trees h = log n; for skewed trees h = n.

Shortcut: Visit every node once → O(n) time. Recursion depth = tree height → O(h) space.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Forgetting null/base-case handling

Wrong move: Recursive traversal assumes children always exist.

Usually fails on: Leaf nodes throw errors or create wrong depth/path values.

Fix: Handle null/base cases before recursive transitions.