Construct the full k-ary tree from its preorder traversal

Given an array that contains the preorder traversal of the full k-ary tree, construct the full k-ary tree and print its postorder traversal. A full k-ary tree is a tree where each node has either 0 or k children.

Examples:

Input : preorder[] = {1, 2, 5, 6, 7, 
                     3, 8, 9, 10, 4}
        k = 3
Output : Postorder traversal of constructed 
         full k-ary tree is: 5 6 7 2 8 9 10 
         3 4 1 
         Tree formed is:         1
                             /   |   \
                           2     3    4
                          /|\   /|\
                         5 6 7 8 9 10

Input : preorder[] = {1, 2, 5, 6, 7, 3, 4}
        k = 3 
Output : Postorder traversal of constructed 
         full k-ary tree is: 5 6 7 2 4 3 1
         Tree formed is:        1
                             /  |  \
                           2    3   4
                          /|\   
                         5 6 7  

We have discussed this problem for Binary tree in below post. 
Construct a special tree from given preorder traversal

In this post, solution for a k-ary tree is discussed.
In Preorder traversal, first root node is processed then followed by the left subtree and right subtree. Because of this, to construct a full k-ary tree, we just need to keep on creating the nodes without bothering about the previous constructed nodes. We can use this to build the tree recursively. 

Following are the steps to solve the problem: 

1. Find the height of the tree. 
2. Traverse the preorder array and recursively add each node 

Implementation:

C++

// C++ program to build full k-ary tree from
// its preorder traversal and to print the
// postorder traversal of the tree.
#include <bits/stdc++.h>
using namespace std;

// Structure of a node of an n-ary tree
struct Node {
    int key;
    vector<Node*> child;
};

// Utility function to create a new tree
// node with k children
Node* newNode(int value)
{
    Node* nNode = new Node;
    nNode->key = value;
    return nNode;
}

// Function to build full k-ary tree
Node* BuildKaryTree(int A[], int n, int k, int h, int& ind)
{
    // For null tree
    if (n <= 0)
        return NULL;

    Node* nNode = newNode(A[ind]);
    if (nNode == NULL) {
        cout << "Memory error" << endl;
        return NULL;
    }

    // For adding k children to a node
    for (int i = 0; i < k; i++) {

        // Check if ind is in range of array
        // Check if height of the tree is greater than 1
        if (ind < n - 1 && h > 1) {
            ind++;

            // Recursively add each child
            nNode->child.push_back(BuildKaryTree(A, n, k, h - 1, ind));
        } else {
            nNode->child.push_back(NULL);
        }
    }
    return nNode;
}

// Function to find the height of the tree
Node* BuildKaryTree(int* A, int n, int k, int ind)
{
    int height = (int)ceil(log((double)n * (k - 1) + 1)
                 / log((double)k));
    return BuildKaryTree(A, n, k, height, ind);
}

// Function to print postorder traversal of the tree
void postord(Node* root, int k)
{
    if (root == NULL)
        return;
    for (int i = 0; i < k; i++)
        postord(root->child[i], k);
    cout << root->key << " ";
}

// Driver program to implement full k-ary tree
int main()
{
    int ind = 0;
    int k = 3, n = 10;
    int preorder[] = { 1, 2, 5, 6, 7, 3, 8, 9, 10, 4 };
    Node* root = BuildKaryTree(preorder, n, k, ind);
    cout << "Postorder traversal of constructed"
             " full k-ary tree is: ";
    postord(root, k);
    cout << endl;
    return 0;
}

Java

// Java program to build full k-ary tree from
// its preorder traversal and to print the
// postorder traversal of the tree.
import java.util.*;

public class GFG
{

// Structure of a node of an n-ary tree
static class Node
{
    int key;
    Vector<Node> child;
};

// Utility function to create a new tree
// node with k children
static Node newNode(int value)
{
    Node nNode = new Node();
    nNode.key = value;
    nNode.child= new Vector<Node>();
    return nNode;
}

static int ind;

// Function to build full k-ary tree
static Node BuildKaryTree(int A[], int n,
                          int k, int h)
{
    // For null tree
    if (n <= 0)
        return null;

    Node nNode = newNode(A[ind]);
    if (nNode == null)
    {
        System.out.println("Memory error" );
        return null;
    }

    // For adding k children to a node
    for (int i = 0; i < k; i++)
    {

        // Check if ind is in range of array
        // Check if height of the tree is greater than 1
        if (ind < n - 1 && h > 1)
        {
            ind++;

            // Recursively add each child
            nNode.child.add(BuildKaryTree(A, n, k, h - 1));
        }
        else
        {
            nNode.child.add(null);
        }
    }
    return nNode;
}

// Function to find the height of the tree
static Node BuildKaryTree_1(int[] A, int n, int k, int in)
{
    int height = (int)Math.ceil(Math.log((double)n * (k - 1) + 1) /
                                Math.log((double)k));
    ind = in;
    return BuildKaryTree(A, n, k, height);
}

// Function to print postorder traversal of the tree
static void postord(Node root, int k)
{
    if (root == null)
        return;
    for (int i = 0; i < k; i++)
        postord(root.child.get(i), k);
    System.out.print(root.key + " ");
}

// Driver Code
public static void main(String args[])
{
    int ind = 0;
    int k = 3, n = 10;
    int preorder[] = { 1, 2, 5, 6, 7, 3, 8, 9, 10, 4 };
    Node root = BuildKaryTree_1(preorder, n, k, ind);
    System.out.println("Postorder traversal of " +
                       "constructed full k-ary tree is: ");
    postord(root, k);
    System.out.println();
}
}

// This code is contributed by Arnab Kundu

Python3

# Python3 program to build full k-ary tree
# from its preorder traversal and to print the
# postorder traversal of the tree.
from math import ceil, log

# Utility function to create a new
# tree node with k children
class newNode:
    def __init__(self, value):
        self.key = value
        self.child = []

# Function to build full k-ary tree
def BuildkaryTree(A, n, k, h, ind):

    # For None tree
    if (n <= 0):
        return None

    nNode = newNode(A[ind[0]])
    if (nNode == None):
        print("Memory error")
        return None

    # For adding k children to a node
    for i in range(k):

        # Check if ind is in range of array
        # Check if height of the tree is
        # greater than 1
        if (ind[0] < n - 1 and h > 1):
            ind[0] += 1

            # Recursively add each child
            nNode.child.append(BuildkaryTree(A, n, k,
                                             h - 1, ind))
        else:
            nNode.child.append(None)
    return nNode

# Function to find the height of the tree
def BuildKaryTree(A, n, k, ind):
    height = int(ceil(log(float(n) * (k - 1) + 1) /
                                      log(float(k))))
    return BuildkaryTree(A, n, k, height, ind)

# Function to print postorder traversal
# of the tree
def postord(root, k):
    if (root == None):
        return
    for i in range(k):
        postord(root.child[i], k)
    print(root.key, end = " ")

# Driver Code
if __name__ == '__main__':
    ind = [0]
    k = 3
    n = 10
    preorder = [ 1, 2, 5, 6, 7, 3, 8, 9, 10, 4]
    root = BuildKaryTree(preorder, n, k, ind)
    print("Postorder traversal of constructed",
                        "full k-ary tree is: ")
    postord(root, k)

# This code is contributed by pranchalK

C#

// C# program to build full k-ary tree from
// its preorder traversal and to print the
// postorder traversal of the tree.
using System;
using System.Collections.Generic;

class GFG
{

// Structure of a node of an n-ary tree
class Node
{
    public int key;
    public List<Node> child;
};

// Utility function to create a new tree
// node with k children
static Node newNode(int value)
{
    Node nNode = new Node();
    nNode.key = value;
    nNode.child= new List<Node>();
    return nNode;
}

static int ind;

// Function to build full k-ary tree
static Node BuildKaryTree(int []A, int n,
                          int k, int h)
{
    // For null tree
    if (n <= 0)
        return null;

    Node nNode = newNode(A[ind]);
    if (nNode == null)
    {
        Console.WriteLine("Memory error" );
        return null;
    }

    // For adding k children to a node
    for (int i = 0; i < k; i++)
    {

        // Check if ind is in range of array
        // Check if height of the tree is greater than 1
        if (ind < n - 1 && h > 1)
        {
            ind++;

            // Recursively add each child
            nNode.child.Add(BuildKaryTree(A, n, k, h - 1));
        }
        else
        {
            nNode.child.Add(null);
        }
    }
    return nNode;
}

// Function to find the height of the tree
static Node BuildKaryTree_1(int[] A, int n, int k, int iN)
{
    int height = (int)Math.Ceiling(Math.Log((double)n * (k - 1) + 1) /
                                   Math.Log((double)k));
    ind = iN;
    return BuildKaryTree(A, n, k, height);
}

// Function to print postorder traversal of the tree
static void postord(Node root, int k)
{
    if (root == null)
        return;
    for (int i = 0; i < k; i++)
        postord(root.child[i], k);
    Console.Write(root.key + " ");
}

// Driver Code
public static void Main(String []args)
{
    int ind = 0;
    int k = 3, n = 10;
    int []preorder = { 1, 2, 5, 6, 7, 3, 8, 9, 10, 4 };
    Node root = BuildKaryTree_1(preorder, n, k, ind);
    Console.WriteLine("Postorder traversal of " +
                      "constructed full k-ary tree is: ");
    postord(root, k);
    Console.WriteLine();
}
}

// This code is contributed by PrinciRaj1992

Javascript

<script>
    // Javascript program to build full k-ary tree from
    // its preorder traversal and to print the
    // postorder traversal of the tree.

    class Node
    {
        constructor(key) {
           this.child = [];
           this.key = key;
        }
    }

    // Utility function to create a new tree
    // node with k children
    function newNode(value)
    {
        let nNode = new Node(value);
        return nNode;
    }

    let ind;

    // Function to build full k-ary tree
    function BuildKaryTree(A, n, k, h)
    {
        // For null tree
        if (n <= 0)
            return null;

        let nNode = newNode(A[ind]);
        if (nNode == null)
        {
            document.write("Memory error" );
            return null;
        }

        // For adding k children to a node
        for (let i = 0; i < k; i++)
        {

            // Check if ind is in range of array
            // Check if height of the tree is greater than 1
            if (ind < n - 1 && h > 1)
            {
                ind++;

                // Recursively add each child
                nNode.child.push(BuildKaryTree(A, n, k, h - 1));
            }
            else
            {
                nNode.child.push(null);
            }
        }
        return nNode;
    }

    // Function to find the height of the tree
    function BuildKaryTree_1(A, n, k, In)
    {
        let height = Math.ceil(Math.log(n * (k - 1) + 1) / Math.log(k));
        ind = In;
        return BuildKaryTree(A, n, k, height);
    }

    // Function to print postorder traversal of the tree
    function postord(root, k)
    {
        if (root == null)
            return;
        for (let i = 0; i < k; i++)
            postord(root.child[i], k);
        document.write(root.key + " ");
    }

    ind = 0;
    let k = 3, n = 10;
    let preorder = [ 1, 2, 5, 6, 7, 3, 8, 9, 10, 4 ];
    let root = BuildKaryTree_1(preorder, n, k, ind);
    document.write("Postorder traversal of " +
                       "constructed full k-ary" + "</br>" + "tree is: ");
    postord(root, k);
    document.write("</br>");

</script>

Output

Postorder traversal of constructed full k-ary tree is: 5 6 7 2 8 9 10 3 4 1 

Time Complexity: O(n),the time complexity of this algorithm is O(n) where n is the number of elements in the given array. We traverse the given array once and create a k-ary tree from it, which takes linear time.

Auxiliary Space: O(n),the space complexity of this algorithm is also O(n) as we need to create a k-ary tree with the given elements in the array. We also need to store intermediate nodes in the function stack frame.

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