Serialize and Deserialize an N-ary Tree

Given an N-ary tree where every node has at-most N children. How to serialize and deserialize it? Serialization is to store tree in a file so that it can be later restored. The structure of tree must be maintained. Deserialization is reading tree back from file.
This post is mainly an extension of below post. 
Serialize and Deserialize a Binary Tree

In an N-ary tree, there are no designated left and right children. An N-ary tree is represented by storing an array or list of child pointers with every node. 

The idea is to store an ‘end of children’ marker with every node. The following diagram shows serialization where ‘)’ is used as end of children marker. 

Following is the implementation of the above idea.  

C++

// A C++ Program serialize and deserialize an N-ary tree
#include<cstdio>
#define MARKER ')'
#define N 5
using namespace std;

// A node of N-ary tree
struct Node {
   char key;
   Node *child[N];  // An array of pointers for N children
};

// A utility function to create a new N-ary tree node
Node *newNode(char key)
{
    Node *temp = new Node;
    temp->key = key;
    for (int i = 0; i < N; i++)
        temp->child[i] = NULL;
    return temp;
}

// This function stores the given N-ary tree in a file pointed by fp
void serialize(Node *root, FILE *fp)
{
    // Base case
    if (root == NULL) return;

    // Else, store current node and recur for its children
    fprintf(fp, "%c ", root->key);
    for (int i = 0; i < N && root->child[i]; i++)
         serialize(root->child[i],  fp);

    // Store marker at the end of children
    fprintf(fp, "%c ", MARKER);
}

// This function constructs N-ary tree from a file pointed by 'fp'.
// This function returns 0 to indicate that the next item is a valid
// tree key. Else returns 0
int deSerialize(Node *&root, FILE *fp)
{
    // Read next item from file. If there are no more items or next
    // item is marker, then return 1 to indicate same
    char val;
    if ( !fscanf(fp, "%c ", &val) || val == MARKER )
       return 1;

    // Else create node with this item and recur for children
    root = newNode(val);
    for (int i = 0; i < N; i++)
      if (deSerialize(root->child[i], fp))
         break;

    // Finally return 0 for successful finish
    return 0;
}

// A utility function to create a dummy tree shown in above diagram
Node *createDummyTree()
{
    Node *root = newNode('A');
    root->child[0] = newNode('B');
    root->child[1] = newNode('C');
    root->child[2] = newNode('D');
    root->child[0]->child[0] = newNode('E');
    root->child[0]->child[1] = newNode('F');
    root->child[2]->child[0] = newNode('G');
    root->child[2]->child[1] = newNode('H');
    root->child[2]->child[2] = newNode('I');
    root->child[2]->child[3] = newNode('J');
    root->child[0]->child[1]->child[0] = newNode('K');
    return root;
}

// A utility function to traverse the constructed N-ary tree
void traverse(Node *root)
{
    if (root)
    {
        printf("%c ", root->key);
        for (int i = 0; i < N; i++)
            traverse(root->child[i]);
    }
}

// Driver program to test above functions
int main()
{
    // Let us create an N-ary tree shown in above diagram
    Node *root = createDummyTree();

    // Let us open a file and serialize the tree into the file
    FILE *fp = fopen("tree.txt", "w");
    if (fp == NULL)
    {
        puts("Could not open file");
        return 0;
    }
    serialize(root, fp);
    fclose(fp);

    // Let us deserialize the stored tree into root1
    Node *root1 = NULL;
    fp = fopen("tree.txt", "r");
    deSerialize(root1, fp);

    printf("Constructed N-Ary Tree from file is \n");
    traverse(root1);

    return 0;
}

Python3

# A Python program to serialize and deserialize an N-ary tree
import sys

# A node of N-ary tree
class Node:
    def __init__(self, key):
        self.key = key
        self.children = []

# A utility function to create a new N-ary tree node
def newNode(key):
    temp = Node(key)
    return temp

# This function stores the given N-ary tree in a file pointed by fp
def serialize(root, fp):
    # Base case
    if not root:
        return

    # Else, store current node and recur for its children
    fp.write(root.key + " ")
    for child in root.children:
        serialize(child, fp)

    # Store marker at the end of children
    fp.write(") ")

# This function constructs N-ary tree from a file pointed by 'fp'.
# This function returns 0 to indicate that the next item is a valid
# tree key. Else returns 0
def deSerialize(fp):
    # Read next item from file. If there are no more items or next
    # item is marker, then return None to indicate same
    val = fp.read(1)
    if not val or val == ")":
        return None

    # Else create node with this item and recur for children
    root = newNode(val)
    while True:
        child = deSerialize(fp)
        if not child:
            break
        root.children.append(child)

    # Finally return the node for successful finish
    return root

# A utility function to create a dummy tree shown in above diagram
def createDummyTree():
    root = newNode('A')
    root.children = [newNode('B'), newNode('C'), newNode('D')]
    root.children[0].children = [newNode('E'), newNode('F')]
    root.children[2].children = [newNode('G'), newNode('H'), newNode('I'), newNode('J')]
    root.children[0].children[1].children = [newNode('K')]
    return root

# A utility function to traverse the constructed N-ary tree
def traverse(root):
    if root:
        print(root.key, end=" ")
        for child in root.children:
            traverse(child)

# Driver program to test above functions
def main():
    # Let us create an N-ary tree shown in above diagram
    root = createDummyTree()

    # Let us open a file and serialize the tree into the file
    fp = open("tree.txt", "w")
    serialize(root, fp)
    fp.close()

    # Let us deserialize the stored tree into root1
    fp = open("tree.txt", "r")
    root1 = deSerialize(fp)
    fp.close()

    print("Constructed N-Ary Tree from file is ")
    traverse(root1)

if __name__ == '__main__':
    main()

Java

import java.io.*;

public class NAryTreeSerialization {
    final static int N = 5;
    final static char MARKER = ')';

    // A node of N-ary tree
    static class Node {
        char key;
        Node[] child; // An array of pointers for N children

        Node(char key) {
            this.key = key;
            child = new Node[N];
        }
    }

    // This function stores the given N-ary tree in a file pointed by fp
    static void serialize(Node root, PrintWriter writer) {
        // Base case
        if (root == null) {
            return;
        }

        // Else, store current node and recur for its children
        writer.print(root.key + " ");
        for (int i = 0; i < N && root.child[i] != null; i++) {
            serialize(root.child[i], writer);
        }

        // Store marker at the end of children
        writer.print(MARKER + " ");
    }

    // This function constructs N-ary tree from a file pointed by 'reader'.
    static Node deSerialize(BufferedReader reader) throws IOException {
        // Read next item from file. If there are no more items or next
        // item is marker, then return null to indicate same
        int val = reader.read();
        if (val == -1 || val == MARKER) {
            return null;
        }
        char c = (char) val;

        // Else create node with this item and recur for children
        Node root = new Node(c);
        for (int i = 0; i < N; i++) {
            root.child[i] = deSerialize(reader);
            if (root.child[i] == null) {
                break;
            }
        }

        return root;
    }

    // A utility function to create a dummy tree shown in above diagram
    static Node createDummyTree() {
        Node root = new Node('A');
        root.child[0] = new Node('B');
        root.child[1] = new Node('C');
        root.child[2] = new Node('D');
        root.child[0].child[0] = new Node('E');
        root.child[0].child[1] = new Node('F');
        root.child[2].child[0] = new Node('G');
        root.child[2].child[1] = new Node('H');
        root.child[2].child[2] = new Node('I');
        root.child[2].child[3] = new Node('J');
        root.child[0].child[1].child[0] = new Node('K');
        return root;
    }

    // A utility function to traverse the constructed N-ary tree
    static void traverse(Node root) {
        if (root != null) {
            System.out.print(root.key + " ");
            for (int i = 0; i < N; i++) {
                traverse(root.child[i]);
            }
        }
    }

    // Driver program to test above functions
    public static void main(String[] args) throws IOException {
        // Let us create an N-ary tree shown in above diagram
        Node root = createDummyTree();

        // Let us open a file and serialize the tree into the file
        PrintWriter writer = new PrintWriter(new FileWriter("tree.txt"));
        serialize(root, writer);
        writer.close();

        // Let us deserialize the stored tree into root1
        Node root1;
        BufferedReader reader = new BufferedReader(new FileReader("tree.txt"));
        root1 = deSerialize(reader);
        reader.close();

        System.out.println("Constructed N-Ary Tree from file is: ");
        traverse(root1);
        }
}

C#

using System;
using System.IO;

public class GFG {
    const int N = 5;
    const char MARKER = ')';

    // A node of N-ary tree
    class Node {
        public char key;
        public Node[] child; // An array of pointers for N
                             // children

        public Node(char key)
        {
            this.key = key;
            child = new Node[N];
        }
    }

    // This function stores the given N-ary tree in a file
    // pointed by fp
    static void serialize(Node root, StreamWriter writer)
    {
        // Base case
        if (root == null) {
            return;
        }

        // Else, store current node and recur for its
        // children
        writer.Write(root.key + " ");
        for (int i = 0; i < N && root.child[i] != null;
             i++) {
            serialize(root.child[i], writer);
        }

        // Store marker at the end of children
        writer.Write(MARKER + " ");
    }

    // This function constructs N-ary tree from a file
    // pointed by 'reader'.
    static Node deSerialize(StreamReader reader)
    {
        // Read next item from file. If there are no more
        // items or next item is marker, then return null to
        // indicate same
        int val = reader.Read();
        if (val == -1 || val == MARKER) {
            return null;
        }
        char c = (char)val;

        // Else create node with this item and recur for
        // children
        Node root = new Node(c);
        for (int i = 0; i < N; i++) {
            root.child[i] = deSerialize(reader);
            if (root.child[i] == null) {
                break;
            }
        }

        return root;
    }
    // A utility function to create a dummy tree shown in
    // above diagram
    static Node createDummyTree()
    {
        Node root = new Node('A');
        root.child[0] = new Node('B');
        root.child[1] = new Node('C');
        root.child[2] = new Node('D');
        root.child[0].child[0] = new Node('E');
        root.child[0].child[1] = new Node('F');
        root.child[2].child[0] = new Node('G');
        root.child[2].child[1] = new Node('H');
        root.child[2].child[2] = new Node('I');
        root.child[2].child[3] = new Node('J');
        root.child[0].child[1].child[0] = new Node('K');
        return root;
    }

    // A utility function to traverse the constructed N-ary
    // tree
    static void traverse(Node root)
    {
        if (root != null) {
            Console.Write(root.key + " ");
            for (int i = 0; i < N; i++) {
                traverse(root.child[i]);
            }
        }
    }
    // Driver program to test above functions
    static void Main(string[] args)
    {
        // Let us create an N-ary tree shown in above
        // diagram
        Node root = createDummyTree();

        // Let us open a file and serialize the tree into
        // the file
        StreamWriter writer = new StreamWriter("tree.txt");
        serialize(root, writer);
        writer.Close();

        // Let us deserialize the stored tree into root1
        Node root1;
        StreamReader reader = new StreamReader("tree.txt");
        root1 = deSerialize(reader);
        reader.Close();

        Console.WriteLine(
            "Constructed N-Ary Tree from file is: ");
        traverse(root1);
    }
}

Output

Constructed N-Ary Tree from file is 
A B E F K C D G H I J 

Time Complexity: O(N), where n is number of nodes.

Auxiliary Space: O(H+N) , where h is height of tree and n is number of nodes.

The above implementation can be optimized in many ways for example by using a vector in place of array of pointers. We have kept it this way to keep it simple to read and understand.
This article is contributed by varun. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.