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Big O

Big O(oh) **notation is used to describe the efficiency of an algorithm or function.**This efficiency is evaluated based on 2 factors:

  1. Running Time (also known as time efficiency / complexity) The amount of time a function needs to complete.

  2. Memory Space (also known as space efficiency / complexity) The amount of memory resources a function uses to store data and instructions.

Overview

Big O’s role in algorithm efficiency is to describe the Worst Case of efficiency an algorithm can have in performing it’s job. It specifically looks at the factors mentioned above, which we often refer to as Space and Time. In order to analyze these limiting factors, we should consider 4 Key Areas for analysis:

  • Input Size
  • Units of Measurement
  • Orders of Growth
  • Best Case, Worst Case, and Average Case

Input size

Input Size refers to the size of the parameter values that are read by the algorithm. This does not simply refer to the number of parameters an algorithm reads, but takes into account the size of each parameter value as well.

We will use the letter n to refer to the Input Size value.

The higher this number, the more likely there will be an increase to Running Time and Memory Space.

linked list

A Linked List is a sequence of Nodes that are connected/linked to each other. The most defining feature of a Linked List is that each Node references the next Node in the link.

There are two types of Linked List - Singly and Doubly. We will be implementing a Singly Linked List in this implementation.

Terminology:

  • linked list - a data structure that contained nodes that links/points to the next node in the list.

  • Singly - Singly refers to the number of references the node has. A Singly linked list means that there is only one reference, and the reference points to the Next node in a linked list.

  • Doubly - Doubly refers to there being two (double) references within the node. A Doubly linked list means that there is a reference to both the Next and Previous node.

  • Node - Nodes are the individual items/links that live in a linked list. Each node contains the data for each link.

  • Next - Each node contains a property called Next. This property contains the reference to the next node.

  • Head - The Head is a reference of type Node to the first node in a linked list.

  • Current - The Current is a reference of type Node to the node that is currently being looked at. When traversing, you create a new Current variable at the Head to guarantee you are starting from the beginning of the linked list.