Insertion in n-ary tree in given order and Level order traversal

Given a set of parent nodes where the index of the array is the child of each Node value, the task is to insert the nodes as a forest(multiple trees combined together) where each parent could have more than two children. After inserting the nodes, print each level in a sorted format.

Example:

Input: arr[] = {5, 3, -1, 2, 5, 3}
Output:
-1
2
3
1 5

Input: arr[] = {-1, -1, -1, -1, -1, 1}
Output:
-1
0 1 2 3 4
5

Below is the explanation of the above examples:



  1. Example 1:
    • In this given array, the elements of the array will be the parent node and the array index will be the child nodes.
    • Initially, we set the root of the forest to be -1 for reference.
    • Now on traversing the array, we insert the nodes into the forest structure.
    • Initially we identify the roots of the individual trees in the forest and insert them into the root of the forest.
    • The index of -1 is 2. Print -1 and append 2 as child node.
    • Now search the list for list value as 2. Index 3 has value 2. Therefore 3 becomes the child of 2.
    • Now the indexes having value 3 are 1 and 5. So 1 and 5 are the children of 3.
      • The list does not contain 1 so ignore 1.
      • The index that contains 5 are 0 and 4. So they become the child.
            -1 ---------- root of the forest
           /
          2    ---------- level (0) 
         /
        3       ---------- level (1)
       / \
      1   5     ---------- level (2)
     /     \
    0       4       ---------- level (3)
    
    Note: level (0) contains roots of each tree
    
  2. Example 2:
    • In this case, the tree will be of the format
    
         -1        -------- root of the forest
      / | | | \
     0  1 2 3  4   -------- level (0)
        |
        5          -------- level (1)
    Note: level (0) contains roots of each tree
    

Prerequisite: Level order traversal.
Approach: The idea is to recursively insert nodes in a tree. However the tree structure is quite different, usually in the case of binary tree there will be a maximum of two child nodes for any node but in this case the root node can have N number of child nodes.’-1′ is considered as the root and the index of the root will be considered as child nodes.

Example:
If -1 is present in index 3 then 3 will be the child node of -1.

     -1
    / 
   3

Insert -1 into the queue. Now if the root is empty then -1 node becomes the root. Now dequeue and queue the child nodes of -1. Create nodes and append them with the root. Continue this till all the child nodes have been inserted.

Level order Traversal:
     -1
   3   5
 2 4 6   9
The output for level order traversal will be: -1 3 5 2 4 6 9

Same enqueue and dequeue approach is followed for traversing by level order.

Below is the implementation of the above approach:

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# Python3 implementation of the approach
  
# Node creation
class Node:
  
    # Constructor
    def __init__(self, data):  
          
        self.val = data
          
        # Since n children are possible for a root.
        # A list created to store all the children.
        self.child = []   
  
  
# Function to insert
def insert(root, parent, node):
      
    # Root is empty then the node will become the root
    if root is None:
        root = node               
  
    else:
        if root.val == parent:
            root.child.append(node)             
        else:
  
            # Recursive approach to 
            # insert the child
            l = len(root.child)
              
            for i in range(l):
                if root.child[i].val == parent:
                    insert(root.child[i], parent, node)
                else:
                    insert(root.child[i], parent, node)
  
# Function that calls levelorder method to 
# perform level order traversal
def levelorder_root(root):
    if root:
        level = []
        level.append(root)
        print(root.val)
        levelorder(level)
  
# Function to perform level order traversal
def levelorder(prev_level):
  
    cur_level = []
    print_data = []
    l = len(prev_level)
  
    if l == 0:
        exit()
  
    for i in range(l):    
        prev_level_len = len(prev_level[i].child)
  
        for j in range(prev_level_len):
              
            # enqueue all the children
            # into cur_level list
            cur_level.append(
                   prev_level[i].child[j])  
  
            # Copies the entire cur_level
            # list into prev_level
            print_data.append(
                   prev_level[i].child[j].val)
  
    prev_level = cur_level[:]                 
    print(*print_data)
    levelorder(prev_level)
  
  
# Driver code
  
# -1 is the root element    
arr = [-1, -1, -1, -1, -1]
root = Node(-1)
l = len(arr)
que = []
  
# Inserting root element to the queue
que.append(-1)
  
while 1:
    temp = []
    for i in range(l):
        if arr[i] in que:
              
            # Insert elements into the tree
            insert(root, arr[i], Node(i)) 
            temp.append(i)
  
    # Append child nodes into the queue
    # and insert the child
    que = temp[:]                      
      
    if len(que)== 0:
        break
  
levelorder_root(root)    
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Output:
-1
0 1 2 3 4

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