Anything to do with intro to algorithms.

Week (NUMBER) contains the lab for set week.

Week XYZ is because i can't be bothered to organize it atm.

The Bs for project contains ideas that can be used for the CA due the 08/04/2024 (WE COOKED)⠀⠀⠀⠀⠀⠀⠀⠀

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Common Definitions:

Linked List:

A linear data structure where each element is a separate object, known as a node. The data field stores the data, and the next field is a reference (link) to the next node in the sequence.

Stack:

Is a data structure that uses last in first out, this means that the most recent piece of data added will be next to be removed

Queue:

Is a data structure that uses first in first out, that means that the oldest piece of data added will be the one next in line to be removed

Binary Search Tree (BST):

Is a tree data structure in which each node has at most two children, referred to as the left child and the right child. For each node, all elements in the left subtree are less than the node, and all elements in the right subtree are greater.

BST Traversal

Given:

3
| \
1   5
|  / \
2  4  6
       \
        7

the pre-order traversal is: 3 1 2 5 4 6 7.
This means that 3 is the root of the tree, 1 and 2 are in the left subtree, and 5 4 6 7 are in the right subtree.
Root then Left to right upwards
Pre-order: 3 1 2 5 4 6 7

In order is all elements in order smallest to biggest
In-order: 1 2 3 4 5 6 7

the post-order traversal is: 2 1 4 7 6 5 3.
This means that 2 and 1 are in the left subtree, 4 7 6 5 are in the right subtree, and 3 is the root of the tree.
left to right downwards then root
Post-order: 2 1 4 7 6 5 3

Aditional Stuff for BST

Perfect:

Is a type of binary tree in which all interior nodes have two children and all leaves have the same depth or same level.
This means that every level of the tree is fully filled.
A Perfect BST will ALWAYS be Balanced and Complete but not necessarily the other way

Perfect means both Balanced and Complete

      4
     / \
   2     6
  / \   / \
 1   3 5   7

Balanced:

Is a binary tree in which the height of the two subtrees of every node never differ by more than one.
A Perfect BST will ALWAYS be Balanced but not necessarily the other way

Balanced and Perfect

      4
     / \
   2     6
  / \   / \
 1   3 5   7

Balanced, NOT Perfect

    3
   / \
  2   5
 /   / \
1   4   6

Complete:

Is a binary tree in which every level, except possibly the last, is completely filled,
and all nodes in the last level are as far left as possible.

Complete

    4
   / \
  2   5
 / \   \
1   3   6

Big O:

A measurement of the worst case time it will take for an algoirhtm to do its job

Orders of Complexity:

Is the measurements used in the Big O such as Constant Time O(1), Linear time O(N) etc

Divide and Conquer:

Is a problem-solving technique that involves breaking down a complex problem into smaller, more manageable subproblems. An example is the merge sort algorithm, which breaks down a big array to smaller arrays to make it easier to sort them.

Algorithm:

A step-by-step procedure or set of rules to be followed in calculations or other problem-solving operations.

4 Key properties:

• Unambiguity
• Finiteness
• Effectivenes
• Input and Output

An example of a real life algorithm is baking a cake: It has an input (ingridients and quantities) a procedure (step by step instructions) output (the cake) Unambiguity (each step is clearly defined) Finiteness (reciepe ends after a number of steps) Effectivenes (practical and can be carried out with common resources)

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Although it's so over for the exam, we ain't making it out.

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