Complexity Analysis of Level Order Binary Tree Traversal
Although this method works differently from the queue method, the time and space complexity of this method is same as that of the queue method.
Time Complexity
In the above program, we start from the root node and then go to the left and right child using recursion. This goes on till we find the NULL. It shows that we are accessing a node only once leading to the,
Time complexity of Level Order Binary Tree Traversal using Recursion O(N).
where, N is the total number of nodes.
Auxiliary Space Complexity
The auxiliary space complexity have to consider two element. One is the call stack space due to recursion and other is due the 2D array that stores the level order values.
In the program, the left child recursive call will go on till we get the NULL value for the node, which is possible for the nodes with no left child. It will then go for the right child and same will continue till we encounter the node which does not have any children (i.e. leaf node). It infers that the number of stack required will be equal to the number of nodes for the given path from root node to the leaf node. And the max number of stack space will be required for the longest path which is the height of the tree.
So the worst case auxiliary space complexity for the recursive function is O(N). (for skew trees)
Now, for 2D array, it will always have the N number of elements at the end of execution. So, considering both requirements,
Auxiliary Space Complexity of Level Order Binary Tree Traversal using Recursion is O(N)
Binary Tree Level Order Traversal in C++
Trees are the type of data structure that stores the data in the form of nodes having a parent or children or both connected through edges. It leads to a hierarchical tree-like structure that can be traversed in multiple ways such as —preorder, inorder, postorder, and level order. A binary tree is a tree data structure a node can only have 2 children at max.
In this article, we will learn about level order binary tree traversal in C++, how to implement it using a C++ program and analyze its time and space complexity.