Binary tree exercise

src/SUMMARY.md

@@ -121,6 +121,7 @@
 - [Exercises](exercises/day-2/afternoon.md)
   - [Luhn Algorithm](exercises/day-2/luhn.md)
   - [Strings and Iterators](exercises/day-2/strings-iterators.md)
+  - [Binary Tree](exercises/day-2/binary-tree.md)
 
 
 # Day 3: Morning

src/exercises/day-2/binary-tree.md

@@ -0,0 +1,81 @@
+# Binary Tree
+
+A Binary Tree is a tree-type data structure where every node has two children (left and right).
+We want to create a tree where each node would be assigned a variant `Left`, `Right` or `Root`
+depdending on its original position related to its parent. The side is defined in the following enum:
+
+```rust
+#[derive(Debug)]
+enum Side {
+    Left,
+    Right,
+    Root
+}
+```
+
+Using the data structures in the standard library, how can we represent such a Binary Tree in Rust?
+
+<details open=false>
+
+```rust
+#[derive(Debug)]
+struct BinaryTree {
+    value: Side,
+    left: Option<Box<Self>>,
+    right: Option<Box<Self>>
+}
+```
+
+</details>
+
+Let's now write a method to to create a BinaryTree with arbitrary depth:
+
+<details open=false>
+
+```rust
+use Side::*;
+
+impl BinaryTree {
+    fn new_with_depth(depth: i32, side: Side) -> Option<Box<BinaryTree>> {
+        if depth == 0 {
+            return None;
+        }
+        let left = Self::new_with_depth(depth - 1, Left);
+        let right = Self::new_with_depth(depth - 1, Right);
+        Some(Box::new(BinaryTree {
+            value: side,
+            left,
+            right
+        }))
+    }
+}
+```
+
+</details>
+
+Let's now write a method to invert the tree. To make sure that the tree is inverted, 
+left nodes values should now be `Right` and right nodes values should now be `Left`.
+
+
+<details open=false>
+
+```rust
+use Side::*;
+
+impl BinaryTree {
+    fn invert(&mut self) {
+        let mut left = self.left.take();
+        if let Some(left) = &mut left {
+            left.invert();   
+        }
+        let mut right = self.right.take();
+        if let Some(right) = &mut right {
+            right.invert();
+        }
+        self.left = right;
+        self.right = left;
+    }
+}
+```
+
+</details>