-
Notifications
You must be signed in to change notification settings - Fork 0
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
updated reference links and big o introduction
- Loading branch information
1 parent
b149982
commit 8b90570
Showing
6 changed files
with
256 additions
and
8 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
|
|
@@ -69,7 +69,7 @@ | |
| "source": [ | ||
| "\n", | ||
| "---\n", | ||
| "[next]()" | ||
| "[next](./02-example.ipynb)" | ||
| ] | ||
| } | ||
| ], | ||
|
|
||
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
|
|
@@ -289,7 +289,7 @@ | |
| "source": [ | ||
| "\n", | ||
| "---\n", | ||
| "[next]()" | ||
| "[next](./03-intro-to-big-o.ipynb)" | ||
| ] | ||
| } | ||
| ], | ||
|
|
||
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,241 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "[back](./02-example.ipynb)\n", | ||
| "\n", | ||
| "---\n", | ||
| "## `Introducing Big O`" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "`Big O` notation is a way to formalize fuzzy counting.\n", | ||
| "\n", | ||
| "It provides a way to formally convey the idea of how the runtime of an algorithm grows as the inputs grow." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "### `Big O Definition`" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "We say that an algorithm is $O(f(n))$ if the number of simple operations a computer has to do is eventually less than a constant times $f(n)$, as $n$ increases." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "- $f(n)$ could be linear $(f(n) = n)$\n", | ||
| "- $f(n)$ could be quadratic $(f(n) = n^2)$\n", | ||
| "- $f(n)$ could be constant $(f(n) = 1)$\n", | ||
| "- $f(n)$ could be something entirely different!" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "And when we usually speak of `Big O`, we usually speak of the upper bounds, for example\n", | ||
| "\n", | ||
| "```javascript\n", | ||
| "function addUpTo(n) {\n", | ||
| " return n * (n + 1) / 2;\n", | ||
| "}\n", | ||
| "```\n", | ||
| "\n", | ||
| "This is always three operations, it's constant (in real life, there might be slight variation in the runtime) the overall trend is flat.\n", | ||
| "\n", | ||
| "And this _(Always 3 operations)_ is represented as $O(1)$, meaning as $n$ grows _(the input to the function grows)_, in this case it has no change, it is not reflected in the runtime." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "While we take a look at this one\n", | ||
| "\n", | ||
| "```javascript\n", | ||
| "function addUpTo(n) {\n", | ||
| " let total = 0;\n", | ||
| " for (let i = 1; i <= n; i++) {\n", | ||
| " total += i;\n", | ||
| " }\n", | ||
| " return total;\n", | ||
| "}\n", | ||
| "```\n", | ||
| "\n", | ||
| "Here, the number of operations is (eventually) bounded by a multiple of $n$ (say, $10n$), so it doesn't matter if it's $10n$ or $20n$ or $50n$, it is just $O(n)$ because we simplify by the order of it's magnitude." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "### `Few Examples`" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "#### `01`" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 1, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "function countUpAndDown(n) {\n", | ||
| " console.log('Going up!');\n", | ||
| " for (let i = 0; i < n; i++) {\n", | ||
| " console.log(i);\n", | ||
| " }\n", | ||
| " console.log('At the top!\\nGoing down...');\n", | ||
| " for (let j = n - 1; j >= 0; j--) {\n", | ||
| " console.log(j);\n", | ||
| " }\n", | ||
| " console.log('Back down. Bye!');\n", | ||
| "}" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 6, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "Going up!\n", | ||
| "0\n", | ||
| "1\n", | ||
| "2\n", | ||
| "3\n", | ||
| "4\n", | ||
| "At the top!\n", | ||
| "Going down...\n", | ||
| "4\n", | ||
| "3\n", | ||
| "2\n", | ||
| "1\n", | ||
| "0\n", | ||
| "Back down. Bye!\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "countUpAndDown(5)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "So, we might consider that during the first loop, it's $O(n)$ and again during the second loop it is $O(n)$, so it should be $2n$, but instead it's still $O(n)$" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "#### `02`" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 3, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "function printAllPairs(n) {\n", | ||
| " for (var i = 0; i < n; i++) {\n", | ||
| " for (var j = 0; j < n; j++) {\n", | ||
| " console.log(i, j);\n", | ||
| " }\n", | ||
| " }\n", | ||
| "}" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 5, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "0 0\n", | ||
| "0 1\n", | ||
| "0 2\n", | ||
| "1 0\n", | ||
| "1 1\n", | ||
| "1 2\n", | ||
| "2 0\n", | ||
| "2 1\n", | ||
| "2 2\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "printAllPairs(3)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Here, the first loop is $O(n)$ and the second loop is also $O(n)$, but the difference is that it is nested, so it not the same as $O(2n)$ which simplifies to $O(n)$.\n", | ||
| "\n", | ||
| "So, if an $O(n)$ operation is within another $O(n)$ operation, then it is $O(n * n) => O(n^2)$" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "### `Conclusion`" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "\n", | ||
| "---\n", | ||
| "[next]()" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "JavaScript (Node.js)", | ||
| "language": "javascript", | ||
| "name": "javascript" | ||
| }, | ||
| "language_info": { | ||
| "file_extension": ".js", | ||
| "mimetype": "application/javascript", | ||
| "name": "javascript", | ||
| "version": "18.3.0" | ||
| }, | ||
| "orig_nbformat": 4 | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 2 | ||
| } |