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Exercise 1

Write an algorithm for finding a node in a binary search tree.

In this problem, like in other binary tree problems, where depth-first search is possible, the easiest solution will be the recursive one, and for the recursive solution, we know what we need, a base case and a recursive definition.

Solution

Base Case

What is our base case in this problem? Of course, if we find the node with a target value, we can return true. Is that sufficient? What happens when we reach null. This is also a base case, but what should we return? It doesn't make much sense to return true, as null is certainly not the node with the target value. If we reach null, that means the space that could potentially house our value has run out, and we can return false.

Base Case: If the node is null return false. Otherwise, if the node's value is the target value, return true.

Recursive Definition

The recursive definition is more straightforward in this case. If the node's value is greater than the target, we have to find the node on the left side. Otherwise, if it's less, we must find the node on the right side. Whenever we say "find the node," we mean invoking the recursive function with that particular side (either the left or right child).

Recursive Definition: If the node's value is greater than the target, find the node in the BST on the left side. Otherwise, find the node in the BST on the right side.

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