This document discusses Big O notation and time complexity of algorithms. It introduces common time complexities like O(n) linear time, O(log n) logarithmic time, and O(n^2) quadratic time. Examples are given of linear search which is O(n) and binary search which is O(log n). Common sorting algorithms are also listed like insertion sort, bubble sort, quick sort, merge sort, and selection sort along with their time complexities.

1. Big O Notation
Asymptotic analysis is the process of of describing the
efficiency of algorithms as their input size (n) grows
Asymptotics are usually expressed in a common format
known as Big O Notation

2. O(n) - Linear Time
var input = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
function linearSearch(key) {
for (var i = 0; i < input.length; i++) {
if (input[i] === key) return i
}
return null
}

3. O(log n) - Logarithmic Time
var input = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
function binarySearch(key, imin, imax) {
var midIndex = (imin + imax) / 2
var midNumber = input[midIndex]
if (midNumber > key) {
binarySearch(key, imin, midIndex - 1)
} else if (midNumber < key ) {
binarySearch(key, midIndex + 1, imax)
} else {
return midIndex
}
}

4. • O(n) - Linear Time
• O(log n) - Logarithmic time
• O(1) - Constant time
• O(n^2)

6. Sorting
• Invariant - http://en.wikipedia.org/wiki/
Invariant_(computer_science)
• Insertion Sort - http://en.wikipedia.org/wiki/Insertion_sort
• Bubble Sort - http://en.wikipedia.org/wiki/Bubble_sort
• Quick Sort - http://en.wikipedia.org/wiki/Quicksort
• Merge Sort - http://en.wikipedia.org/wiki/Merge_sort
• Selection Sort - http://en.wikipedia.org/wiki/Selection_sort