LeetCode #993 — EASY

Cousins in Binary Tree

Build confidence with an intuition-first walkthrough focused on tree fundamentals.

Solve on LeetCode
The Problem

Problem Statement

Given the root of a binary tree with unique values and the values of two different nodes of the tree x and y, return true if the nodes corresponding to the values x and y in the tree are cousins, or false otherwise.

Two nodes of a binary tree are cousins if they have the same depth with different parents.

Note that in a binary tree, the root node is at the depth 0, and children of each depth k node are at the depth k + 1.

Example 1:

Input: root = [1,2,3,4], x = 4, y = 3
Output: false

Example 2:

Input: root = [1,2,3,null,4,null,5], x = 5, y = 4
Output: true

Example 3:

Input: root = [1,2,3,null,4], x = 2, y = 3
Output: false

Constraints:

  • The number of nodes in the tree is in the range [2, 100].
  • 1 <= Node.val <= 100
  • Each node has a unique value.
  • x != y
  • x and y are exist in the tree.
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 with unique values and the values of two different nodes of the tree x and y, return true if the nodes corresponding to the values x and y in the tree are cousins, or false otherwise. Two nodes of a binary tree are cousins if they have the same depth with different parents. Note that in a binary tree, the root node is at the depth 0, and children of each depth k node are at the depth k + 1.

Baseline thinking

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

Pattern signal: Tree

Example 1

[1,2,3,4]
4
3

Example 2

[1,2,3,null,4,null,5]
5
4

Example 3

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

Related Problems

  • Binary Tree Level Order Traversal (binary-tree-level-order-traversal)
  • Cousins in Binary Tree II (cousins-in-binary-tree-ii)
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 #993: Cousins in 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 boolean isCousins(TreeNode root, int x, int y) {
        Deque<TreeNode[]> q = new ArrayDeque<>();
        q.offer(new TreeNode[] {root, null});
        int d1 = 0, d2 = 0;
        TreeNode p1 = null, p2 = null;
        for (int depth = 0; !q.isEmpty(); ++depth) {
            for (int n = q.size(); n > 0; --n) {
                TreeNode[] t = q.poll();
                TreeNode node = t[0], parent = t[1];
                if (node.val == x) {
                    d1 = depth;
                    p1 = parent;
                } else if (node.val == y) {
                    d2 = depth;
                    p2 = parent;
                }
                if (node.left != null) {
                    q.offer(new TreeNode[] {node.left, node});
                }
                if (node.right != null) {
                    q.offer(new TreeNode[] {node.right, node});
                }
            }
        }
        return p1 != p2 && d1 == d2;
    }
}
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.