DataStructures_Algorithms

Runtime Analysis

Big O Notation

• Big O Notation is used to describe the upper bound of a particular algorithm. Big O is used to describe worst case scenarios

Little O Notation

• Little O Notation is also used to describe an upper bound of a particular algorithm; however, Little O provides a bound that is not asymptotically tight

Big Ω Omega Notation

• Big Omega Notation is used to provide an asymptotic lower bound on a particular algorithm

Little ω Omega Notation

• Little Omega Notation is used to provide a lower bound on a particular algorithm that is not asymptotically tight

Theta Θ Notation

• Theta Notation is used to provide a bound on a particular algorithm such that it can be "sandwiched" between two constants (one for an upper limit and one for a lower limit) for sufficiently large values

Data Structures

Linked List

• A Linked List is a linear collection of data elements, called nodes, each pointing to the next node by means of a pointer. It is a data structure consisting of a group of nodes which together represent a sequence.
• Singly-linked list: linked list in which each node points to the next node and the last node points to null
• Doubly-linked list: linked list in which each node has two pointers, p and n, such that p points to the previous node and n points to the next node; the last node's n pointer points to null
• Circular-linked list: linked list in which each node points to the next node and the last node points back to the first node
• Time Complexity:
  • Access: O(n)
  • Search: O(n)
  • Insert: O(1)
  • Remove: O(1)

Stack

• A Stack is a collection of elements, with two principle operations: push, which adds to the collection, and pop, which removes the most recently added element
• Last in, first out data structure (LIFO): the most recently added object is the first to be removed
• Time Complexity:
  • Access: O(n)
  • Search: O(n)
  • Insert: O(1)
  • Remove: O(1)

Queue

• A Queue is a collection of elements, supporting two principle operations: enqueue, which inserts an element into the queue, and dequeue, which removes an element from the queue
• First in, first out data structure (FIFO): the oldest added object is the first to be removed
• Time Complexity:
  • Access: O(n)
  • Search: O(n)
  • Insert: O(1)
  • Remove: O(1)