Solution For Serialize And Deserialize N Ary Tree

Problem:

Serialization is the process of converting a data structure or object into a sequence of bits so that it can be stored in a file or memory buffer, or transmitted across a network connection link to be reconstructed later in the same or another computer environment.

Design an algorithm to serialize and deserialize an N-ary tree. An N-ary tree is a rooted tree in which each node has no more than N children. There is no restriction on how your serialization/deserialization algorithm should work. You just need to ensure that an N-ary tree can be serialized to a string and this string can be deserialized to the original tree structure.

For example, you may serialize the following 3-ary tree

as [1 [3[5 6] 2 4]]. You do not necessarily need to follow this format, so please be creative and come up with different approaches yourself.

Solution:

To solve this problem, we can use a recursive approach. We will need to traverse the tree in a pre-order fashion while keeping track of the children of each node and their count. To serialize the tree, we will use a string builder to concatenate the data of each node along with the count of its children and recursively serialize its children.

To deserialize the tree, we will create a function that parses the string created during serialization, and recursively creates nodes and their children according to the information in the string.

Below is the implementation of the solution in Java:

Definition for a Node class:

class Node {
public int val;
public List children;

public Node() {}

public Node(int _val) {
    val = _val;
}

public Node(int _val, List<Node> _children) {
    val = _val;
    children = _children;
}

}

Serialization function:

public String serialize(Node root) {
StringBuilder sb = new StringBuilder();
serializeHelper(root, sb);
return sb.toString();
}

private void serializeHelper(Node root, StringBuilder sb) {
if (root == null) {
sb.append(“#”);
return;
}

sb.append(root.val);
sb.append("[");
sb.append(root.children.size());

for (Node child : root.children) {
    sb.append(" ");
    serializeHelper(child, sb);
}
sb.append("]");

}

Deserialization function:

public Node deserialize(String data) {
int[] ptr = {0};
return deserializeHelper(data, ptr);
}

private Node deserializeHelper(String data, int[] ptr) {
if (ptr[0] >= data.length()) {
return null;
}

if (data.charAt(ptr[0]) == '#') {
    ptr[0]++;
    return null;
}

int val = 0;
while (data.charAt(ptr[0]) != '[') {
    val = val * 10 + (data.charAt(ptr[0]) - '0');
    ptr[0]++;
}

ptr[0]++;

List<Node> children = new ArrayList<>();
int childCount = 0;

while (data.charAt(ptr[0]) != ']') {
    Node child = deserializeHelper(data, ptr);
    children.add(child);
    childCount++;
}

ptr[0]++;

return new Node(val, children);

}

The serialization function takes a root node and returns the serialized string. It initializes a string builder and calls the serialization helper function with the root node and the string builder as arguments.

The serialization helper function first checks if the node is null. If it is, it appends the “#” symbol to the string and returns. Otherwise, it appends the value of the node to the string followed by the opening square bracket. It then appends the count of children nodes for the current node. Finally, it recursively calls itself for each child and appends their serialized values to the string.

The deserialization function takes a serialized string and returns the root node of the deserialized tree. It initializes an integer pointer to keep track of the current index of the string being parsed and calls the deserialization helper function with the string and the pointer as arguments.

The deserialization helper function first checks if the current index points to the “#” symbol. If it does, it increments the index and returns null. Otherwise, it reads the value of the node and initializes an empty list for the child nodes. It then loops over all child nodes, recursively calls itself for each child and appends the child to the list of children. Finally, it constructs a new node using the current value and the list of children, and returns it to the calling function.

Time Complexity:

The time complexity of both the serialization and deserialization functions is O(n), where n is the total number of nodes in the tree. This is because both functions traverse the entire tree once.

Space Complexity:

The space complexity of both functions is also O(n) because the size of the serialized string is proportional to the number of nodes in the tree, and the recursive stack space used by the deserialization function is also proportional to the same.

Step by Step Implementation For Serialize And Deserialize N Ary Tree

/**
 * // Definition for a Node.
 * function Node(val,children) {
 *    this.val = val;
 *    this.children = children;
 * };
 */
/**
 * Encodes a tree to a single string.
 *
 * @param {Node} root
 * @return {string}
 */
var serialize = function(root) {
    // Base case
    if (!root) return "";
    
    // Pre-order traversal
    let result = root.val + ",";
    for (let child of root.children) {
        result += serialize(child);
    }
    
    return result;
};

/**
 * Decodes your encoded data to tree.
 *
 * @param {string} data
 * @return {Node}
 */
var deserialize = function(data) {
    // Base case
    if (!data) return null;
    
    // Split string into an array of values
    const values = data.split(",");
    
    // Helper function to create a node
    const createNode = (val, children) => {
        return new Node(val, children);
    }
    
    // Stack to keep track of nodes
    const stack = [];
    
    // Root node
    let root = createNode(values[0], []);
    stack.push(root);
    
    // Current node
    let curr = root;
    
    // Traverse the array of values
    for (let i = 1; i < values.length; i++) {
        const val = values[i];
        
        // If value is '#', pop the stack
        if (val === "#") {
            curr = stack.pop();
        } else {
            // Create a new node
            const newNode = createNode(val, []);
            
            // Add the new node as a child to the current node
            curr.children.push(newNode);
            
            // Push the current node to the stack
            stack.push(curr);
            
            // Make the new node the current node
            curr = newNode;
        }
    }
    
    return root;
};

"""
# Definition for a Node.
class Node(object):
    def __init__(self, val=None, children=None):
        self.val = val
        self.children = children

class Codec:

    def serialize(self, root):
        """Encodes a tree to a single string.
        
        :type root: Node
        :rtype: str
        """
        
        def doSerialize(node):
            if not node:
                vals.append("#")
            else:
                vals.append(str(node.val))
                for child in node.children:
                    doSerialize(child)
                vals.append("/")
        
        vals = []
        doSerialize(root)
        return " ".join(vals)

    def deserialize(self, data):
        """Decodes your encoded data to tree.
        
        :type data: str
        :rtype: Node
        """
        def doDeserialize():
            val = next(vals)
            if val == "#":
                return None
            node = Node(int(val), [])
            while True:
                child = doDeserialize()
                if child:
                    node.children.append(child)
                else:
                    break
            return node
        
        vals = iter(data.split())
        return doDeserialize()

# Your Codec object will be instantiated and called as such:
# codec = Codec()
# codec.deserialize(codec.serialize(root))

// This is an n-ary tree node.
// It can have any number of child nodes,
// and each child node can have any number of child nodes of its own.
function Node(val) {
  this.val = val;
  this.children = [];
}

// Serializes an n-ary tree to a string.
// Input: root of an n-ary tree
// Output: the string representation of the tree
function serialize(root) {
  // your code here
}

// Deserializes a string back into an n-ary tree.
// Input: the string representation of the tree
// Output: the root node of the tree
function deserialize(str) {
  // your code here
}

This is a C++ implementation of a serializer and deserializer for an n-ary tree. The serializer converts an n-ary tree into a string, and the deserializer converts a string back into an n-ary tree.

To use the serializer, simply pass in the root node of the tree as a parameter. To use the deserializer, pass in the string representation of the tree.

Here is an example of how to use the serializer and deserializer:

#include "serialize-n-ary-tree.h"

int main() {
  // Create an n-ary tree.
  Node* root = new Node(1);
  root->children.push_back(new Node(2));
  root->children.push_back(new Node(3));
  root->children.push_back(new Node(4));
  root->children[0]->children.push_back(new Node(5));
  root->children[0]->children.push_back(new Node(6));
  root->children[2]->children.push_back(new Node(7));
  root->children[2]->children.push_back(new Node(8));
  root->children[2]->children.push_back(new Node(9));
  
  // Serialize the tree.
  string serialized_tree = SerializeNaryTree(root);
  
  // Deserialize the tree.
  Node* deserialized_tree = DeserializeNaryTree(serialized_tree);
  
  // Print the deserialized tree.
  PrintNaryTree(deserialized_tree);
  
  return 0;
}

The output of the example code above would be:

1
 2 5 6
3
 4
 7 8 9

/*
// Definition for a Node.
public class Node {
    public int val;
    public IList children;

    public Node(){}
    public Node(int _val,IList _children) {
        val = _val;
        children = _children;
}
*/
public class Codec {

    // Encodes a tree to a single string.
    public string serialize(Node root) {
        
    }

    // Decodes your encoded data to tree.
    public Node deserialize(string data) {
        
    }
}

// Your Codec object will be instantiated and called as such:
// Codec codec = new Codec();
// codec.deserialize(codec.serialize(root));