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+#+TITLE: Data Structures
+#+AUTHOR: Christopher James Hayward
+
+#+HUGO_BASE_DIR: ~/.local/source/website
+#+HUGO_SECTION: notes
+
++ Built on primitive data types
++ Organization and management format
++ Forms the basis of abstract data types
+
+* Binary Tree
+
+#+begin_example
+    a
+   / \
+  b   c
+ / \ / \
+d   e   f
+#+end_example
+
++ Hierarchical data structure
++ Different from Arrays, Lists, Stacks & Queues
+
+| Node    | Type | Description                       |
+|---------+------+-----------------------------------|
+| a       | Root | Topmost node of the tree          |
+| b, c    | Node | Children of a, parents of d, e, f |
+| d, e, f | Node | Leaves (nothing below)            |
+
+** Example
+
+Using =C++=, we begin by including the ~stdc++~ header and the ~std~ namespace.
+
+#+begin_src cpp
+#include <bits/stc++.h>
+using namespace std;
+#+end_src
+
+We then define the data structure to represent a =Node= within the tree, including a constructor method for creating new instances easily.
+
+#+begin_src cpp
+struct Node {
+  int data;
+  struct Node* left;
+  struct Node* right;
+
+  Node(int d) {
+    this->data = d;
+    this->left = NULL;
+    this->right = NULL;
+  }
+};
+#+end_src
+
+We begin by initializing the root of the tree, leaving us with something like this:
+
+#+begin_example
+  1
+ / \
+?   ?
+#+end_example
+
+Initialize it with the value of ~1~.
+
+#+begin_src cpp
+struct Node* node = new Node(1);
+#+end_src
+
+Creating children for nodes ~2~ and ~3~ will expand the tree outwards in both directions, leaving us with something like this:
+
+#+begin_example
+    1
+   / \
+  2   3
+ / \ / \
+?   ?   ?
+#+end_example
+
+This is done by adding the children to the root.
+
+#+begin_src cpp
+root->left = new Node(2);
+root->right = new Node(3);
+#+end_src
+
+Expanding down the left side only. 
+
+#+begin_example
+      1
+     / \
+    2   3
+   / \ / \
+  4   ?   ?
+ / \
+?   ?
+#+end_example
+
+Adding a branch of ~4~ to ~2~ gives us the final result.
+
+#+begin_src cpp
+root->left->left = new Node(4);
+#+end_src
+
+** Inverting
+
+#+begin_quote
+Google: 90% of our engineers use the software you wrote (homebrew), but you can't invert a binary tree on a whiteboard? F*** off!
+#+end_quote
+
+It's actually not as daunting a task as you may think, given the hype around past statements like that. But what is the process of inverting a binary tree? Starting with the given input:
+
+#+begin_example
+  1
+ / \
+2   5
+   / \
+  3   4
+#+end_example
+
+We expect to produce an output matching:
+
+#+begin_example
+    1
+   / \
+  5   2
+ / \
+4   3
+#+end_example
+
+Using a recursive approach, we can operate on the tree as to produce the expected result.
+
+#+begin_src cpp
+Node* invert(Node* root) {
+  if (root == NULL) {
+    return NULL;
+  }
+
+  Node* left = invert(root->left);
+  Node* right = invert(root->right);
+
+  root->left = right;
+  root->right = left;
+
+  return root;
+}
+#+end_src