CS50x Helpers is a website built by students of CS50 course to help other students having issues.

CS50x is Harvard College's introduction to the intellectual enterprises of computer science and the art of programming
for majors and non-majors alike, with or without prior programming experience.
An entry-level course taught by David J. Malan, CS50x teaches students how to think algorithmically and solve problems efficiently.

**Topics** include abstraction, algorithms, data structures, encapsulation, resource management, security, software engineering, and web development.

**Languages** include C, PHP, and JavaScript plus SQL, CSS, and HTML.
Problem sets inspired by real-world domains of biology, cryptography, finance, forensics, and gaming.

Anyone who’s read Programming Pearls or any other Computer Science books and doesn’t have a grounding in Mathematics will have hit a wall when they reached chapters that mention O(N log N) or other seemingly crazy syntax. Hopefully this article will help you gain an understanding of the basics of Big O and Logarithms.

A nice guide to Big O nottion is provided by Rob Bell in his paper at A beginner's guide to Big O nottion

The result of the analysis of an algorithm is usually a formula giving the amount of time, in terms of seconds, number of memory accesses, number of comparisons or some other metric, that the algorithm takes.

In its simplest form, a logarithm answers the question: "How many of one number do we multiply to get another number?"

Example: How many 2s do we multiply to get 8?

Answer: 2 × 2 × 2 = 8, so we needed to multiply 3 of the 2s to get 8

So the logarithm is 3

We write "the number of 2s we need to multiply to get 8 is 3" as:

log_{2}(8) = 3

The number we are multiplying is called the "base", so we can say:

"the logarithm of 8 with base 2 is 3"

or "log base 2 of 8 is 3"

or "the base-2 log of 8 is 3"

Notice we are dealing with three numbers:

the base: the number we are multiplying (a "2" in the example above)

how many times to use it in a multiplication (3 times, which is the logarithm)

The number we want to get (an "8")

A basic explaination can be found here

A more detailed and strict description is here

These are words. Can you show me a table where these values are compared?

Sure! Note that the natural logarithm has been used for the example.

n = | log(n) | n | nlog(n) | n^2 | n^2log(n) | n^3 | e^n | n^n | n! |
---|---|---|---|---|---|---|---|---|---|

1 | 0.0 | 1 | 0 | 1 | 0 | 1 | 2.7 | 1 | 1 |

5 | 1.6 | 5 | 8 | 25 | 40 | 125 | 148.4 | 3125 | 120 |

10 | 2.3 | 10 | 23 | 100 | 2300 | 10000 | 22026.5 | 1.0x10^20 | 3.6x10^6 |

50 | 3.9 | 50 | 195 | 2500 | 9750 | 125000 | 5,2×10^21 | 8.9x10^84 | 3.0x10^64 |

100 | 4.6 | 100 | 460 | 10000 | 46000 | 1000000 | 2.7x10^43 | 1.0x10^200 | 9.3x10^157 |

200 | 5.3 | 200 | 1060 | 40000 | 212000 | 8000000 | 7.2x10^86 | 1.6x10^460 | 7.9x10^374 |

500 | 6.2 | 500 | 3100 | 250000 | 1550000 | 125000000 | 1.4x10^217 | 3.0x10^1349 | 1.2x10^1134 |

1000 | 6.9 | 1000 | 6900 | 1000000 | 6900000 | 1000000000 | 2.0x10^434 | 1.0x10^3000 | 4.0x10^2567 |

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