# Exercise: Binary Tree

A binary tree is a tree-type data structure where every node has two children (left and right). We will create a tree where each node stores a value. For a given node N, all nodes in a N's left subtree contain smaller values, and all nodes in N's right subtree will contain larger values.

Implement the following types, so that the given tests pass.

Extra Credit: implement an iterator over a binary tree that returns the values in order.

``````/// A node in the binary tree.
#[derive(Debug)]
struct Node<T: Ord> {
value: T,
left: Subtree<T>,
right: Subtree<T>,
}

/// A possibly-empty subtree.
#[derive(Debug)]
struct Subtree<T: Ord>(Option<Box<Node<T>>>);

/// A container storing a set of values, using a binary tree.
///
/// If the same value is added multiple times, it is only stored once.
#[derive(Debug)]
pub struct BinaryTree<T: Ord> {
root: Subtree<T>,
}

impl<T: Ord> BinaryTree<T> {
fn new() -> Self {
Self { root: Subtree::new() }
}

fn insert(&mut self, value: T) {
self.root.insert(value);
}

fn has(&self, value: &T) -> bool {
self.root.has(value)
}

fn len(&self) -> usize {
self.root.len()
}
}

// Implement `new`, `insert`, `len`, and `has` for `Subtree`.

#[cfg(test)]
mod tests {
use super::*;

#[test]
fn len() {
let mut tree = BinaryTree::new();
assert_eq!(tree.len(), 0);
tree.insert(2);
assert_eq!(tree.len(), 1);
tree.insert(1);
assert_eq!(tree.len(), 2);
tree.insert(2); // not a unique item
assert_eq!(tree.len(), 2);
}

#[test]
fn has() {
let mut tree = BinaryTree::new();
fn check_has(tree: &BinaryTree<i32>, exp: &[bool]) {
let got: Vec<bool> =
(0..exp.len()).map(|i| tree.has(&(i as i32))).collect();
assert_eq!(&got, exp);
}

check_has(&tree, &[false, false, false, false, false]);
tree.insert(0);
check_has(&tree, &[true, false, false, false, false]);
tree.insert(4);
check_has(&tree, &[true, false, false, false, true]);
tree.insert(4);
check_has(&tree, &[true, false, false, false, true]);
tree.insert(3);
check_has(&tree, &[true, false, false, true, true]);
}

#[test]
fn unbalanced() {
let mut tree = BinaryTree::new();
for i in 0..100 {
tree.insert(i);
}
assert_eq!(tree.len(), 100);
assert!(tree.has(&50));
}
}``````