#431HardPremium on LC~50 min
Encode N-ary Tree to Binary Tree
Time O(n) · Space O(h) · Official statement on LeetCode
Solutions
// Time: O(n)
// Space: O(h)
/*
// Definition for a Node.
class Node {
public:
int val = NULL;
vector<Node*> children;
Node() {}
Node(int _val, vector<Node*> _children) {
val = _val;
children = _children;
}
};
*/
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
class Codec {
public:
// Encodes an n-ary tree to a binary tree.
TreeNode* encode(Node* root) {
if (root == nullptr) {
return nullptr;
}
auto node = new TreeNode(root->val);
if (!root->children.empty()) {
node->right = encodeHelper(root->children[0], root, 0);
}
return node;
}
// Decodes your binary tree to an n-ary tree.
Node* decode(TreeNode* root) {
if (root == nullptr) {
return nullptr;
}
vector<Node*> children;
auto node = new Node(root->val, children);
decodeHelper(root->right, node);
return node;
}
private:
TreeNode *encodeHelper(Node *root, Node *parent, int index) {
if (root == nullptr) {
return nullptr;
}
auto node = new TreeNode(root->val);
if (index + 1 < parent->children.size()) {
node->left = encodeHelper(parent->children[index + 1], parent, index + 1);
}
if (!root->children.empty()) {
node->right = encodeHelper(root->children[0], root, 0);
}
return node;
}
void decodeHelper(TreeNode* root, Node* parent) {
if (!root) {
return;
}
vector<Node*> children;
auto node = new Node(root->val, children);
decodeHelper(root->right, node);
parent->children.push_back(node);
decodeHelper(root->left, parent);
}
};
// Your Codec object will be instantiated and called as such:
// Codec codec;
// codec.decode(codec.encode(root));
Beginner Explanation
What is Encode N-ary Tree to Binary Tree?
Encode N-ary Tree to Binary Tree (LeetCode #431) is a Hard problem that primarily trains tree.
How to think about it
- Restate the goal in your own words before coding.
- Work a tiny example by hand so the invariant becomes obvious.
- Identify the pattern — this problem aligns with tree traversal.
- Only then translate the idea into code.
Why this problem matters
Hard problems force you to combine patterns and prove complexity carefully — interview gold.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Encode N-ary Tree to Binary Tree
Opening (30–60 seconds)
- Clarify inputs/outputs and edge cases (empty input, single element, duplicates, overflow).
- State a brute force so the interviewer knows you can solve it naively.
- Propose the optimal direction tied to tree traversal.
Core solution narrative
- Define the state you track (pointers, DP cell, set membership, stack top, etc.).
- Explain the transition when you process the next element.
- Call out time (O(n)) and space (O(h)) before coding.
- Code cleanly; narrate variable names.
What interviewers listen for
- Correctness on edge cases
- Complexity honesty
- Ability to discuss trade-offs (e.g., hash map space vs. sort + two pointers)
Follow-up questions they may ask
- Can you solve it with less memory?
- What if the input stream is infinite / doesn't fit in RAM?
- How would tests look for adversarial inputs?
Optimized Approach
Optimized solution notes
The reference solutions on AlgoForge target O(n) time and O(h) space.
Pattern focus: tree traversal
Use the pattern as a checklist:
- tree traversal — confirm the invariant holds after each step
Multiple methods appear in the source solutions — compare them and explain when each is preferable.
Implementation tips
- Prefer readable names over micro-optimizations in interviews.
- Extract helpers only when they clarify (e.g., expand-around-center, DFS visit).
- After AC-level logic, re-scan for off-by-one and null checks.
Complexity Analysis
Complexity
| Measure | Bound |
|---|---|
| Time | O(n) |
| Space | O(h) |
How to justify this in an interview
- Time: count loops, map/set operations, and recursive branching; state average vs worst case if relevant.
- Space: include hash maps, recursion stack, and output allocation when the problem asks for it.
If your implementation differs from the reference, re-derive big-O from your code — never memorize a complexity you cannot defend.
Common Mistakes
Common mistakes on Encode N-ary Tree to Binary Tree
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for tree traversal — updating state too early or too late.
- Mutating input unexpectedly when the problem forbids it.
- Off-by-one in windows, ranges, or binary search bounds.
- Ignoring overflow / precision for integer arithmetic problems.
- Overengineering — jumping to an advanced structure when a simpler approach works.
Alternative Approaches
Alternatives
The source file includes more than one method. Compare:
- Primary optimized path — best complexity for typical interviews.
- Secondary approach — often brute force, sorting-based, or space-optimized variant.
Practice articulating when you would pick each (constraints, readability, follow-ups).
Edge Cases
Edge cases checklist
- Minimum input size
- Maximum input size / time limits
- Duplicates and already-sorted input
- Negative numbers / zeros (if applicable)
- Disconnected structures (graphs/trees)
- Single path vs branching recursion depth
Pattern Recognition
Spotting this pattern
Signal phrases that point to tree traversal:
- Sorted input or ability to sort without changing the answer class
- Need for contiguous subarray / substring → consider sliding window
- Need for O(1) membership → hash set/map
- Optimal substructure + overlapping subproblems → DP
- Connectivity / components → graph DFS/BFS or Union-Find
Primary topics: tree.
Follow-up Interview Questions
Follow-ups
- How does the solution change if the input is a stream?
- Can you solve it in-place?
- What if duplicates must be handled differently?
- How would you parallelize the approach?
- Design tests that would break a buggy implementation.
Practice Recommendations
What to practice next
- Re-solve Encode N-ary Tree to Binary Tree in a second language (cpp, python).
- Drill 3–5 more problems tagged tree.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Conceptual diagram for Encode N-ary Tree to Binary Tree: show input structure (tree), highlight the moving parts of the tree traversal approach, and annotate each step with the maintained invariant and complexity.
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the tree traversal approach
- Verify edge cases from the checklist
- State time and space complexity aloud
- Compare with the AlgoForge reference solution
- Schedule a revision session
Revision notes
Encode N-ary Tree to Binary Tree (#431) — Hard. Pattern: tree traversal. Complexity: O(n) time / O(h) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Encode N-ary Tree to Binary Tree?+
The reference solutions aim for O(n) time and O(h) space. Always re-derive complexity from the code you write in the interview.
What pattern does Encode N-ary Tree to Binary Tree use?+
It primarily maps to tree traversal, within the broader topic of tree.
Is Encode N-ary Tree to Binary Tree good for interviews?+
Yes — as a Hard problem it is a solid practice target. Pair it with related problems in the same pattern family for spaced repetition.
Where can I read the official statement?+
Open the official LeetCode page for constraints and examples: https://leetcode.com/problems/encode-n-ary-tree-to-binary-tree/