Teaching Kids Programming – N-ary Tree Preorder Traversal Algorithms using Iterations or Recursion

Teaching Kids Programming: Videos on Data Structures and Algorithms

Given the root of an n-ary tree, return the preorder traversal of its nodes’ values.

Nary-Tree input serialization is represented in their level order traversal. Each group of children is separated by the null value (See examples)

n-ary-tree

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

Input: root = [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14]
Output: [1,2,3,6,7,11,14,4,8,12,5,9,13,10]

Recursive Algorithm to Compute the Preorder Traversal Algorithm of a N-ary Tree

The preorder visits the root/current node, then recursively visit the children nodes from left to right. If there is only two children, then we are performing a preorder traversal on a binary tree (NLR).

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"""
# Definition for a Node.
class Node:
    def __init__(self, val=None, children=None):
        self.val = val
        self.children = children
"""
 
class Solution:
    def preorder(self, root: 'Node') -> List[int]:
        if not root:
            return []
        ans = [root.val]
        for x in root.children:
            ans += self.preorder(x)        
        return ans

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

class Solution:
    def preorder(self, root: 'Node') -> List[int]:
        if not root:
            return []
        ans = [root.val]
        for x in root.children:
            ans += self.preorder(x)        
        return ans

Preorder Traversal Algorithm of a N-ary Tree via Iteration

Alternatively, we can use a stack to emulate the Recursion. Pop from the stack, and then add the children in reverse order to the stack.

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class Solution(object):
    def preorder(self, root: 'Node') -> List[int]:
        """
        :type root: Node
        :rtype: List[int]
        """
        if root is None:
            return []
        
        stack, output = [root], []            
        while stack:
            root = stack.pop()
            output.append(root.val)
            stack.extend(root.children[::-1])
                
        return output

class Solution(object):
    def preorder(self, root: 'Node') -> List[int]:
        """
        :type root: Node
        :rtype: List[int]
        """
        if root is None:
            return []
        
        stack, output = [root], []            
        while stack:
            root = stack.pop()
            output.append(root.val)
            stack.extend(root.children[::-1])
                
        return output

Both algorithms have time complexity O(N) and space complexity O(N) where N is the number of the nodes in the given N-ary tree.

See also: Depth First Search Algorithm (Preorder Traversal) to Compute the Kth Smallest in a Binary Search Tree

Also, using GoLang to perform a Recursive Depth First Search Algorithm to Traverse the N-nary Tree in Preorder: GoLang Programming: N-ary Tree Preorder Traversal Algorithm using Depth First Search

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