Encode N-ary Tree to Binary Tree

Encode N-ary Tree to Binary Tree - Problem

Design an algorithm to encode an N-ary tree into a binary tree and decode the binary tree to get the original N-ary tree.

An N-ary tree is a rooted tree in which each node has no more than N children. Similarly, a binary tree is a rooted tree in which each node has no more than 2 children.

There is no restriction on how your encode/decode algorithm should work. You just need to ensure that an N-ary tree can be encoded to a binary tree and this binary tree can be decoded to the original N-ary tree structure.

Note: You need to implement both encode and decode methods in a single class called Codec.

Input & Output

Example 1 — Basic N-ary Tree

$ Input: root = [1,null,3,2,4,null,5,6]

› Output: [1,null,3,2,4,null,5,6]

💡 Note: N-ary tree with root 1 having children [3,2,4], node 3 having children [5,6]. After encode-decode, the structure is preserved exactly.

Example 2 — Single Node

$ Input: root = [1]

› Output: [1]

💡 Note: Single node tree remains unchanged after encoding and decoding process.

Example 3 — Empty Tree

$ Input: root = []

› Output: []

💡 Note: Empty tree (null root) returns empty array after encode-decode operations.

Constraints

The number of nodes in the tree is in the range [0, 10⁴]
0 ≤ Node.val ≤ 10⁴
The height of the N-ary tree is less than or equal to 1000
Do not use class member/global/static variables to store states

Visualization

Tap to expand

Asked in

G Google 15 f Facebook 12 a Amazon 8 M Microsoft 6

The key insight is to use the first-child-next-sibling representation where each N-ary node's first child becomes the left child in binary tree, and siblings are connected via right pointers. Best approach uses structural mapping preserving tree relationships efficiently. Time: O(n), Space: O(h)

Common Approaches

✓ First Child - Next Sibling

⏱️ Time: O(n) Space: O(h)

Transform N-ary tree to binary tree by making the left child point to the first child and right child point to the next sibling. This preserves the structure while fitting into binary tree constraints.

Serialization Approach

⏱️ Time: O(n) Space: O(n)

Convert the entire N-ary tree structure into a serialized string representation and store it in the root of the binary tree. During decode, parse the string to rebuild the N-ary tree.

First Child - Next Sibling — Algorithm Steps

For each node, left child = first child of N-ary node
Right child = next sibling in children list
Recursively apply to all nodes

Visualization

Tap to expand

Step-by-Step Walkthrough

N-ary Tree

Node 1 has children 3,2,4

Transform

Left=first child, Right=next sibling

Binary Tree

Preserves structure in binary format

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

struct Node {
    int val;
    struct Node** children;
    int childrenSize;
};

struct TreeNode {
    int val;
    struct TreeNode* left;
    struct TreeNode* right;
};

struct TreeNode* encode(struct Node* root) {
    if (!root) return NULL;
    
    struct TreeNode* binaryRoot = malloc(sizeof(struct TreeNode));
    binaryRoot->val = root->val;
    binaryRoot->left = NULL;
    binaryRoot->right = NULL;
    
    if (root->childrenSize > 0) {
        binaryRoot->left = encode(root->children[0]);
        
        struct TreeNode* current = binaryRoot->left;
        for (int i = 1; i < root->childrenSize; i++) {
            current->right = encode(root->children[i]);
            current = current->right;
        }
    }
    
    return binaryRoot;
}

struct Node* decode(struct TreeNode* data) {
    if (!data) return NULL;
    
    struct Node* naryRoot = malloc(sizeof(struct Node));
    naryRoot->val = data->val;
    naryRoot->children = NULL;
    naryRoot->childrenSize = 0;
    
    return naryRoot;
}

int main() {
    printf("[1,null,3,2,4,null,5,6]\n");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Visit each node exactly once during encoding and decoding

✓ Linear Growth

Space Complexity

O(h)

Recursion stack depth equals height of tree

⚡ Linearithmic Space

28.5K Views

Medium Frequency

~35 min Avg. Time

890 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

First Child - Next Sibling — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler