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Exercise 1

Write a recursive definition for pre-order traversal of a binary tree, including the base case and the recursive step.

Solution

Base Case

Let's start with the base case. As in the previous problems, the base case occurs when the node is null. In this scenario, we simply return from the function to prevent accessing the val property of null, which would raise an error.

Base Case: Return from the function if the node is null.

Recursive Definition

In this case, we don't have to follow a template; instead, we can follow the NLR pattern we learned in the previous assignment. We first want to process the node, then go left, and then go right. When we say go left, we mean we want to perform the preorder traversal on the left child, which means calling the function recursively and passing the left child to it. When we say go right, we mean we want to perform the preorder traversal on the right child, which means calling the function recursively and passing the right child to it.

Recursive Definition: Add the node's value to the result array, then perform a preorder traversal by recursively calling the function on the current node's left child, followed by recursively calling the function on current node's right child.

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