Recursion for Tree Traversal 101

Mastering Recursion: A Guide to Solving Tree Traversal Problems

Recursion can be a daunting concept, especially when it comes to solving complex problems. However, with the right approach and techniques, it can be a powerful tool in your programming arsenal. In this article, we’ll explore how to use recursion to solve tree traversal problems.

When to Use Recursion

Recursion is particularly useful when dealing with problems that can be broken down into smaller sub-problems of the same type. This is known as a recursive data structure. A classic example of a recursive data structure is a tree, where each node has child nodes that are themselves trees.

The Three-Part Approach

To solve a tree traversal problem using recursion, we need to consider three cases:

1. Base Case: This is the smallest possible input that our function can handle. It’s usually an empty list or a single element.
2. Node Case: This is when we’re dealing with a single node in the tree. We need to decide what to do with the node and its children.
3. List Case: This is when we’re dealing with a list of nodes. We need to recursively call our function on each node in the list.

Finding Items in a Tree

Let’s say we have a tree of neighborhoods in New York City, and we want to find a specific neighborhood. We can use recursion to traverse the tree and find the neighborhood.

javascript
function includes(tree, item) {
if (isEmpty(tree)) { // Base Case
return false;
} else if (isNode(tree)) { // Node Case
if (tree.value === item) {
return true;
} else {
return includes(tree.children, item);
}
} else { // List Case
return includes(first(tree), item) || includes(rest(tree), item);
}
}


Removing Items from a Tree

Now let’s say we want to remove a specific neighborhood from the tree. We can use recursion to traverse the tree and remove the neighborhood.

javascript
function remove(tree, item) {
if (isEmpty(tree)) { // Base Case
return [];
} else if (isNode(tree)) { // Node Case
if (tree.value === item) {
return tree.children;
} else {
return [tree].concat(remove(tree.children, item));
}
} else { // List Case
return remove(first(tree), item).concat(remove(rest(tree), item));
}
}


Exercise: Counting Occurrences

Can you write a function that counts the number of occurrences of a specific neighborhood in the tree?

Tips and Tricks

• Always define your base case first.
• Use recursive calls to break down the problem into smaller sub-problems.
• Remember to handle the node and list cases separately.
• Use concat to combine the results of recursive calls.

By following these tips and practicing with different examples, you’ll become proficient in using recursion to solve tree traversal problems. Happy coding!