From 0ed86b2cc2ec2f85a13255b742fd401e38215594 Mon Sep 17 00:00:00 2001
From: Ciro Santilli <ciro.santilli@gmail.com>
Date: Mon, 21 Jul 2014 23:10:52 +0200
Subject: [PATCH] btree img, hash function properties.

---
 README.md   | 488 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 btree.png   | Bin 0 -> 21970 bytes
 crypto.md   |  22 ++-
 funny.md    |  27 ---
 graph.md    | 125 ++++++++++----
 index.md    | 470 --------------------------------------------------
 licenses.md |  23 +--
 7 files changed, 607 insertions(+), 548 deletions(-)
 create mode 100644 btree.png
 delete mode 100644 funny.md
 delete mode 100644 index.md

diff --git a/README.md b/README.md
index b56d0d2..647d2c2 100644
--- a/README.md
+++ b/README.md
@@ -1 +1,489 @@
 Computer science topics.
+
+#Tips
+
+##Operating system choice
+
+Use Linux because it is free and open source and better than windows for programming.
+
+##Make cheatsheets
+
+Everything you learn, write it down! You will forget it later.
+
+If there is a good link or book, save the link or the book page!
+
+If possible make assertions like C, Java or python `assert` statements, so you can be sure that what you think is right is right.
+
+Publish your cheats so that others can use them too.
+
+##Build your CV
+
+Keep a list of:
+
+- open source contributions with importance of each contribution. Example: <http://www.cirosantilli.com/contrib>
+- a self evaluation of what you know about programming. Example: <http://www.cirosantilli.com/self-evaluation>
+
+##How to type
+
+- user four fingers
+- use closes finger
+- look at the screen
+- use keyboard shortcuts and good programs that have them (ex: vim)
+
+Saves time and preserves your arm.
+
+##Standards matter
+
+The first thing you should ask yourself when learning a new language or other interfaces is: what are the standards?
+
+Is there a dominating standard?
+
+What is the state of implementations? Are they consistent with one another? Are they updated. Example:
+
+- standard: W3C HTML or CSS
+- semi compatible implementations: browsers: Firefox, Chrome, IE
+
+What are the most important extensions to the standard? How portable are they? Example:
+
+- standard: ANSI C vs POSIX vs GNU Extensions
+
+##Download and read the docs
+
+First start with tutorials which are easier to understand and find the most interesting things in.
+
+As soon as you can handle the docs, download and read the official docs, since those are more precise and up to date than tutorials.
+
+#Language
+
+##Programming
+
+-   Most popular? Hard to say
+
+-   Niches matter. Some languages dominate certain application spaces.
+
+    - PHP, Ruby, Javascript == web
+    - Fortran == numerical
+
+-   All programming languages the same (theoretical)
+
+-   Categories:
+
+    - compiled vs interpreted (virtual machine) non compiled languages
+
+        speed vs multiplataform, quick test, prototyping
+
+        there is no hard distiction: any compiled language could also be interpreted and vice versa
+
+        it is mainly a question of design: some langs are designed to be interpreted
+
+        hakell for example can be compiled but also comes with a standard [REPL] interface
+
+    - objects oriented vs non object oriented
+
+    - type systems
+
+        - statically vs dynamically typed
+        - weakly vs strongly typed
+
+-   Languages are easy, libraries are hard.
+
+    Languages are easy to learn because they are all very similar.
+
+    Library interfaces however are not, because they involve completely different concepts between one another.
+
+    Therefore: if a project does what you want in a language you don't know
+
+    - learn that language!
+    - **don't** recode the project!
+
+My languages of choice:
+
+- C
+- C++
+- Java
+- Python
+
+##Data languages
+
+- XML
+- Json
+
+##Markup languages
+
+- HTML
+- LaTeX
+- Markdown
+
+##Web development
+
+-   HTML
+-   HTTP
+-   CGI
+-   apache configuration
+-   CSS
+-   JS
+-   MySQL
+
+-   PHP
+-   the other interpreted CGI languages:
+    - Python
+    - Ruby
+    - Perl
+
+- real deployment
+
+    - ftp
+    - deal with permissions you lack on server
+    - ssh
+
+##Multiple browsers
+
+Have at least two browsers, one main where you are logged in all your websites,
+and one secondary, which you will use to see how other users see your profiles.
+
+Same goes for web development: have multiple browsers to quickly switch users.
+Also good practice as it lets you see often how the website renders under different browsers.
+
+For websites that allow you limited unsigned entry, have a third browser to test as unsigned.
+
+E.g. on Ubuntu 12.04 I run Firefox (primary), Chromium (secondary) and Chrome (unsigned).
+
+#Filesystem
+
+One of the first things you should understand better as a programmer is your filesystem.
+
+-   home dir
+
+-   upper vs lower case
+
+-   naming conventions
+
+    - bin
+
+    - `~` and `.bak`
+
+    - doc
+
+    - dot hidden
+
+    - lib
+
+    - src
+
+    - include
+
+    - share
+
+    - local
+
+    - and the rest of the Linux Filesystem Hierarchy Standard
+        <http://www.tuxfiles.org/linuxhelp/linuxdir.html>
+
+-   do not start with hyphen
+
+-   symlinks/hardlinks
+
+-   magic folders ala Windows library/documents
+
+-   inner workings: how is data actually stored/retreived on disk?
+
+#Database
+
+- MySQL
+- SQLite
+
+#Important programs for life
+
+- dropdown terminal emulator: Guake.
+
+- Vim
+
+    Text editor.
+
+- Krusader
+
+    File manager.
+
+- Source version control.
+
+    you need to contribute with others
+
+    Most commonly used:
+
+    - Git. Entirely dominates web development.
+    - SVN
+
+- make (Makefile)
+
+    automate compilations
+
+    <http://www.jfranken.de/homepages/johannes/vortraege/make_inhalt.en.html>
+
+- bugrackers, like GitHub built-in one. **Always** use one for your project!
+
+- virtual machines. VirtualBox + Vagrant are game changing.
+
+- Ack (find/grep replacement)
+
+    Find in files.
+
+##shell
+
+- language:
+
+    - Linux: bash
+    - windows: cmd
+
+- terminal:
+
+    - pro: reproduce commands easily
+    - con: cannot do graphs
+
+    The terminal allows you to interact with the shell interpreter.
+
+- bash:
+
+    - pro: super easy file/pipe/process handling
+    - con: insane, slow
+
+    Use for one liners only. replacements:
+
+    - Perl is dead, but golfs really well.
+    - Python! Also useful for other things, so worth learning
+
+- --help (how to read, [], ..., ), man, version
+
+- directory structure, homedir, fake vs real dirs
+
+- options, ls, cd, mkdir, cp, rm, rmdir, control z, bg, find, grep
+
+- stdin/stderr/stdout
+
+    - three holes
+    - pipes > to file, | grep, 1>&2
+
+- exit status
+
+- pipe (help grep example)
+
+- interactive vs. non-interactive
+
+#algorithm
+
+See [this](algorithm.md).
+
+#assembler
+
+Understand exactly what operations a processor can do.
+
+<http://www.bottomupcs.com/>
+
+#data representation
+
+##character representation
+
+- ascii
+- unicode
+- utf8
+
+##integer representation
+
+- binary, hexa
+- signed
+
+    - one's complement
+    - 2-complement
+
+##float representation
+
+TODO
+
+#operating systems
+
+You must learn how your operating system works.
+
+The only operating system you can really understand is Linux since it is open source,
+so understand Linux.
+
+Topics which you should look into:
+
+##program memory space
+
+address, operational system division
+
+- <www.dirac.org/linux/gdb/02a-Memory_Layout_And_The_Stack.php>
+
+    tutorial to gdb
+
+##driver programming
+
+- <http://www.linuxjournal.com/article/7353>
+    #5/5
+    #control a lamp. contains c code.
+
+- <http://www.freesoftwaremagazine.com/articles/drivers_linux>
+
+##executable files
+
+ELF files, including libraries
+
+#hardware
+
+- memory: registers vs caches vs RAM vs ROM (BIOS) vs VRAM vs HD
+
+    <http://arstechnica.com/gadgets/2002/07/caching/2/>
+
+    deep explanaition
+
+- busses
+    <http://computer.howstuffworks.com/pci1.htm>
+
+#multithreading concurrency IPC
+
+    - thread vs process
+
+        a process can contain many threads
+
+        threads share a memory space, process don't
+
+    - ipc
+
+        - pipes : same machine
+        - sockets : different machines
+            - internet
+            - pci
+            - usb
+
+#Formal languages
+
+Important if you ever want to create a computer language.
+
+- Backus-Naur form: <http://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form>
+
+#Optimizing code
+
+More important than those are to first:
+
+- use best algorithm
+
+- compile instead of interpret
+
+A few important ones are:
+
+- cache: <http://en.wikipedia.org/wiki/CPU_cache>
+
+- speculative execution <http://en.wikipedia.org/wiki/Speculative_execution>
+
+- loop unwinding: <http://en.wikipedia.org/wiki/Loop_unwinding>
+
+- out of order execution: <http://en.wikipedia.org/wiki/Out-of-order_execution>
+
+- register renaming: <http://en.wikipedia.org/wiki/Register_renaming>
+
+#automatic optimization
+
+- branch prediction
+
+    <http://en.wikipedia.org/wiki/Branch_predictor>
+
+    An example of perceptible branch prediction:
+
+    <http://stackoverflow.com/questions/11227809/why-is-processing-a-sorted-array-faster-than-an-unsorted-array>
+
+#design patterns
+
+See [this](design-patterns).
+
+#GPU programming
+
+TODO
+
+#stragegy
+
+artistic level
+
+- coworkers
+- clients
+- market
+
+- <http://www.joelonsoftware.com/>
+
+    quite a few strategy articles
+
+    ex microsoft employee, lots of exp
+
+#Philosophy
+
+##What computers do
+
+Manipulate information:
+
+- copy and move information around
+- reaching new information from old
+
+In a way that is *very*:
+
+- fast
+- cheap
+- without errors
+
+##Programming and ideas
+
+    ideas (that can be programmed)
+    +
+    programming
+    ------------------------------
+    *power*
+
+- without ideas, programming is useless!
+- without programming, some ideas are useless!
+
+##Imperfection
+
+It is the work of a programmer to search perfection, while accepting that imperfection is inevitable.
+
+When in doubt, look, decide, and follow your decision all the time,
+knowing that all other choices are also imperfect.
+
+#semver
+
+#Semantic versioning
+
+Popular standard for program versioning <http://semver.org/> by Tom Preston-Werner.
+
+#Sources
+
+##Free
+
+- [stack overflow](http://stackoverflow.com/)
+
+    Great QA site with gamification. Huge programming community.
+
+    Also check related sites maintained by the same enterprise: [stack exchange](http://stackexchange.com/).
+
+    Reasonable way to show your knowledge to enterpreises.
+
+- [top coder algorithm contests](http://community.topcoder.com/tc?module=ProblemArchive&sr=1&er=50&sc=&sd=&class=&cat=&div1l=&div2l=&mind1s=&mind2s=&maxd1s=&maxd2s=&wr=)
+
+    Hosts timed programming contests online.
+
+    Lost of programming problems available with solutions proposed by contestants.
+
+    Good way to show your knowledge to enterpreises.
+    Very popular as of 2013, lots of employers looking there.
+
+    Also worth checking their tutorials: <http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=alg_index>
+
+    Must use a annoying Java program to run in the contests, and hard to find the problems in the site in the first place.
+
+- [spoj contests](http://www.spoj.com/problems/classical/)
+
+    Much like top coder.
+
+    Problems can be solved any time.
+
+    Solutions can be submitted any time for online tests.
+
+    Does time and memory tests, and ranks algorithms accordingly.
+
+    It is not possible to view submitted solutions.
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diff --git a/crypto.md b/crypto.md
index 678f9c5..50d4c90 100644
--- a/crypto.md
+++ b/crypto.md
@@ -1,4 +1,6 @@
-#public key cryptography
+# Cryptography
+
+## Public key cryptography
 
 Public key cryptography is a way to do cryptography so that it is not necessary
 to exchange secret data before the actual data is transferred:
@@ -16,14 +18,28 @@ but too slow to inverse.
 
 Main algorithms are:
 
-- RSA
+-   RSA
 
     Multiplication / Factorization problem.
 
     Both secrecy and signature.
 
-- Diffie-Hellman
+-   Diffie-Hellman
 
     Discrete Exponent mod n / Discrete logarithm mod n problem.
 
     Only provides secrecy.
+
+## Cryptographic hash function
+
+<http://en.wikipedia.org/wiki/checksum_algorithm>
+
+Used in cryptography as well as other applications,
+e.g. Git SHA to identify objects uniquely.
+
+Desired properties:
+
+- it is easy to compute the hash value for any given message
+- it is infeasible to generate a message that has a given hash
+- it is infeasible to modify a message without changing the hash
+- it is infeasible to find two different messages with the same hash.
diff --git a/funny.md b/funny.md
deleted file mode 100644
index 6a8c675..0000000
--- a/funny.md
+++ /dev/null
@@ -1,27 +0,0 @@
-Stuff which only comp-sci nerds might find funny.
-
-[Perl poetry](http://www.perlmonks.org/?node=Perl%20Poetry). That entire website is funny actually.
-
-[Fork Bomb](http://en.wikipedia.org/wiki/Fork_bomb) Type of DnS attack.
-
-[Standard proliferation](http://xkcd.com/927/) Amazing insights and visualization.
-
-[Any key](http://en.wikipedia.org/wiki/Any_key)
-
-"Do you pine for the nice days of Minix-1.1, when men were men and wrote their own device drivers?" Linus Torvalds
-
-[Spaghetti code](http://en.wikipedia.org/wiki/Spaghetti_code)
-
-[Esoteric language](http://en.wikipedia.org/wiki/Esoteric_programming_language)
-
-[Sockpuppet](http://en.wikipedia.org/wiki/Sockpuppet_%28Internet%29)
-
-[Heisenbug](http://en.wikipedia.org/wiki/heisenbug)
-
-[REPL]: http://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop
-
-[BMP C++ program](http://stackoverflow.com/a/5509538/895245)
-
-[w3schools](https://chrome.google.com/webstore/detail/w3schools-hider/igiahejkpbnbnekdaefddmdceocmjpll). The site is considered so bad, but has such huge Google Rating, that a Google Chrome extension was created to block it from Google searches.
-
-[Godwin's Law](http://en.wikipedia.org/wiki/Godwin%27s_law)
diff --git a/graph.md b/graph.md
index 157940b..36bba22 100644
--- a/graph.md
+++ b/graph.md
@@ -21,7 +21,8 @@ Trees are special cases of directed connected graphs that have the properties:
 - no loops
 - root: there is a distinguished node from which every other node is reachable
 
-This immediately implies that E = V - 1, and simplifies search procedures since you don't need to check if you have already visited some nodes.
+This immediately implies that E = V - 1, and simplifies search procedures
+since you don't need to check if you have already visited some nodes.
 
 ##BST
 
@@ -29,11 +30,14 @@ This immediately implies that E = V - 1, and simplifies search procedures since
 
 Each node has 2 children.
 
-Not necessarily balanced, so bounds for all operations is $O(n)$, although average times are $long(n)$.
+Not necessarily balanced, so bounds for all operations is $O(n)$,
+although average times are $long(n)$.
 
-There are balanced search trees such as [RB-tree](red-black-tree) which actually have $O(ln)$ for all operations.
+There are balanced search trees such as [RB-tree](red-black-tree)
+which actually have $O(ln)$ for all operations.
 
-The only complicated operation is delete, visualize it here: <http://www.algolist.net/Data_structures/Binary_search_tree/Removal>
+The only complicated operation is delete, visualize it here:
+<http://www.algolist.net/Data_structures/Binary_search_tree/Removal>
 
 ##RB-tree.
 
@@ -41,42 +45,75 @@ The only complicated operation is delete, visualize it here: <http://www.algolis
 
 Balanced binary search tree.
 
-Red black tree are binary search trees that support element query, insertion and deletion in $log(n)$ time.
+Red black tree are binary search trees that support element query,
+insertion and deletion in $log(n)$ time.
 
 All that is needed is to store one extra bit per node: red or black.
 
 It must have the following properties:
 
-- A node is either red or black.
-- The root is black.
-- All leaves (NIL) are black.
-- Both children of every red node are black.
+-   A node is either red or black.
+
+-   The root is black.
+
+-   All leaves (NIL) are black.
+
+-   Both children of every red node are black.
 
     Children of a black node can have any color.
 
-- Every simple path from a given node to any of its descendant leaves contains the same number of black nodes.
+-   Every simple path from a given node to any of its descendant leaves
+    contains the same number of black nodes.
 
-A leaf is not a node and a node is not a leaf in this context. Nodes contain the actual numbers that are being indexed, leafs don't contain any information, except indicating that there are no more nodes below.
+A leaf is not a node and a node is not a leaf in this context.
+Nodes contain the actual numbers that are being indexed,
+leafs don't contain any information, except indicating that there are no more nodes below.
 
 Leafs in this context are also called sentinels.
 
-Operations are $log(n)$ because the properties imply that the tree is balanced in the sense that the deepest leaf from a node can only be twice as deep as the shallowest one.
+Operations are $log(n)$ because the properties imply that the tree is balanced
+in the sense that the deepest leaf from a node can only be twice as deep as the shallowest one.
 
 The key to using the tree is keeping it balanced after insertion or deletion.
 
-Live Java applet demo: <http://www.ece.uc.edu/~franco/C321/html/RedBlack/>. Requires a bit too many clicks, but really cool.
+Live Java applet demo: <http://www.ece.uc.edu/~franco/C321/html/RedBlack/>.
+Requires a bit too many clicks, but really cool.
 
 TODO visualize insert
 
+##B-tree
+
+*Not* binary tree: <http://en.wikipedia.org/wiki/B-tree>.
+
+Like a binary tree with many values per node:
+
+![btree](bree.png)
+
+Same complexity as RB-tree, but with slower in theory by a constant factor.
+
+Default data structure for MySQL InnoDB `INDEX`.
+
+In practice: way faster for accessing trees saved in slow storage like hard disks.
+
+- to go down each level, you must traverse all values of a node
+- less memory efficient
+
+Advantage:
+
+- less nodes need to be retrieved. Huge practical gains here to read data from slow media.
+
 #DFS
 
 DFS can be done either recursively or not with a stack.
 
-The only key difference is that the recursive version uses the system's call stack, while the non-recursive version uses an explicit stack
+The only key difference is that the recursive version uses the system's call stack,
+while the non-recursive version uses an explicit stack
 
 #BFS
 
-BFS cannot be done recursively naturaly, since the non-recursive impementation uses a queue, and not a stack like DFS.
+BFS cannot be done recursively naturally,
+since the non-recursive implementation uses a queue,
+and not a stack like DFS.
 
 <http://stackoverflow.com/questions/2549541/performing-breadth-first-search-recursively>
 
@@ -84,23 +121,32 @@ BFS cannot be done recursively naturaly, since the non-recursive impementation u
 
 Both are methods to search vertexes on unordered graphs.
 
-On a general graph, you must keep track of which nodes you have already looked into not to go on loops, so you need to add a search bit to each vertex.
+On a general graph, you must keep track of which nodes you have already looked into not to go on loops,
+so you need to add a search bit to each vertex.
 
 On trees (specific type of graph) this is not needed since trees have no loops by definition.
 
 Advantages of DFS:
 
-- if the searched solutions are guaranteed to be at the greatest depths (ex leaves of a tree) then DFS will certainly be faster.
+- if the searched solutions are guaranteed to be at the greatest depths
+    (e.g. leaves of a tree) then DFS will certainly be faster.
 
-- if the graph is somehow balanced (nodes of maximum depth are at similar depths), then DFS will certainly use less memory than BFS, since BFS must store a FIFO of each level ($2^depth$ vertexes on a balanced binary tree) while BFS stores at most the maximum depth sequence of parents ($depth$ elements).
+- if the graph is somehow balanced (nodes of maximum depth are at similar depths),
+    then DFS will certainly use less memory than BFS
+    since BFS must store a FIFO of each level ($2^depth$ vertexes on a balanced binary tree)
+    while BFS stores at most the maximum depth sequence of parents ($depth$ elements).
 
 Advantages of BFS:
 
-- it is the obvious choice when looking for minimum distances, since you want to keep as close as possible to the start and not go too deep.
+- it is the obvious choice when looking for minimum distances,
+    since you want to keep as close as possible to the start and not go too deep.
 
-- if the depth can be too long, or even infinite, it is simpler to look breadth first, and limit the descent, or the process could take forever or too long.
+- if the depth can be too long, or even infinite,
+    it is simpler to look breadth first, and limit the descent,
+    or the process could take forever or too long.
 
-    It also makes more sense to use heuristics with BFS, looking around the current position, and then deciding where to descend further.
+    It also makes more sense to use heuristics with BFS,
+    looking around the current position, and then deciding where to descend further.
 
 #Dijkstra
 
@@ -108,7 +154,8 @@ Advantages of BFS:
 
 Find the shortest path between two given nodes.
 
-Only works if all weights are positive. If negative weights are possible, consider using the [bellman ford algorithm](http://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm).
+Only works if all weights are positive. If negative weights are possible,
+consider using the [bellman ford algorithm](http://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm).
 
 ##Dijkstra complexity
 
@@ -116,15 +163,15 @@ Time worst case: $O(|E| + |V| log |V|)$, so $O(|V|^2)$ on a dense graph.
 
 In the worst case we have a dense graph and we must visit all the nodes giving:
 
-- `FOR_VERTEX`: for each vertex ($|V|$):
+-   `FOR_VERTEX`: for each vertex ($|V|$):
 
-    - `MARK_VISITED`: mark vertex as visited.
+    -   `MARK_VISITED`: mark vertex as visited.
 
-    - `FOR_NEIGHBOUR`: for each neighbour: $|O(\sqrt(|E|))|$, $|V|$ for a dense graph.
+    -   `FOR_NEIGHBOUR`: for each neighbour: $|O(\sqrt(|E|))|$, $|V|$ for a dense graph.
 
-        - UPDATE_WEIGHT: update the weights of that neighbour
+        - `UPDATE_WEIGHT`: update the weights of that neighbour
 
-    - FIND_MIN: find the minimum adjacent element to determine the next vertex
+    -   `FIND_MIN`: find the minimum adjacent element to determine the next vertex
 
 Lets consider two data structure possibilities for storing node distances and if it was visited or not:
 
@@ -153,24 +200,25 @@ operations.
 
 We order the vertexes on a min heap that takes the distance into account.
 
-The complexity will depend on the type of min heap used. We consider there the two most commmon and efficient min heaps for practical data sizes:
+The complexity will depend on the type of min heap used.
+We consider there the two most common and efficient min heaps for practical data sizes:
 
 - binary heap
 - Fibonacci heap
 
 TODO get this right
 
-- `MARK_VISITED`    means that we have to remove the root element from the min heap:
+-   `MARK_VISITED`: means that we have to remove the root element from the min heap:
 
     - Binary heap:    `log`
     - Fibonacci heap: `n` worst case, `log` amortized
 
-- `UPDATE_WEIGHT`  this critical operation depends on the type of min heap used.
+-   `UPDATE_WEIGHT`:  this critical operation depends on the type of min heap used.
 
     - Binary heap:    `log`
     - Fibonacci heap: `log` worst case, `1`
 
-- `FIND_MIN`        always $O(1)$ since we are using heaps
+-   `FIND_MIN`: always $O(1)$ since we are using heaps
 
 Therefore for the binary heap:
 
@@ -180,7 +228,7 @@ $$
     V^2 log(V)
 $$
 
-and for fibonacci amortized time:
+and for Fibonacci amortized time:
 
 $$
     FOR_VERTEX * ( MARK_VISITED + ( ( FOR_NEIGHBOUR * UPDATE_WEIGHTS ) + FIND_MIN ) =
@@ -192,14 +240,15 @@ $$
 
 The final choice of the data structure will depend on the expected density of the graph:
 
-- if the graph is expected to be dense, use an unordered array, as it has the best wort time for that case, while a Fibonacci heap offers only
-
-- if the graph is known to be sparse, $degree(v) <<< V/log(V)$, then the ordered approch starts being better.
+-   if the graph is expected to be dense, use an unordered array,
+    as it has the best wort time for that case, while a Fibonacci heap offers only
 
-- If amortized time can be taken into account and it is not clear if the graph is dense or not, the Fibonnaci Heap implementation  is the best option, as it:
+-   if the graph is known to be sparse, $degree(v) <<< V/log(V)$, then the ordered approch starts being better.
 
-    - works as well as the unordered array implementation
-    - for dense graphs, and better if the graph is not dense (often the case).
+-   If amortized time can be taken into account and it is not clear if the graph is dense or not,
+    the Fibonnaci Heap implementation is the best option, as it:
+    works as well as the unordered array implementation
+    for dense graphs, and better if the graph is not dense (often the case).
 
 #A star
 
diff --git a/index.md b/index.md
deleted file mode 100644
index 8bb47cc..0000000
--- a/index.md
+++ /dev/null
@@ -1,470 +0,0 @@
-This contains general tips to become a good programmer.
-
-#Tips
-
-##Operating system choice
-
-Use Linux because it is free and open source and better than windows for programming.
-
-##Make cheatsheets
-
-Everything you learn, write it down! You will forget it later.
-
-If there is a good link or book, save the link or the book page!
-
-If possible make assertions like C, Java or python `assert` statements, so you can be sure that what you think is right is right.
-
-Publish your cheats so that others can use them too.
-
-##Build your CV
-
-Keep a list of:
-
-- open source contributions with importance of each contribution. Example: <http://www.cirosantilli.com/contrib>
-- a self evaluation of what you know about programming. Example: <http://www.cirosantilli.com/self-evaluation>
-
-##How to type
-
-- user four fingers
-- use closes finger
-- look at the screen
-- use keyboard shortcuts and good programs that have them (ex: vim)
-
-Saves time and preserves your arm.
-
-##standards matter
-
-The first thing you should ask yourself when learning a new language or other interfaces is: what are the standards?
-
-Is there a dominating standard?
-
-What is the state of implementations? Are they consistent with one another? Are they updated. Example:
-
-- standard: W3C HTML or CSS
-- semi compatible implementations: browsers: Firefox, Chrome, IE
-
-What are the most important extensions to the standard? How portable are they? Example:
-
-- standard: ANSI C vs POSIX vs GNU Extensions
-
-##Download and read the docs
-
-First start with tutorials which are easier to understand and find the most interesting things in.
-
-As soon as you can handle the docs, download and read the official docs, since those are more precise and up to date than tutorials.
-
-#Language
-
-##Programming
-
-- most popular? Hard to say
-
-- niches matter. Some languages dominate certain application spaces.
-
-    - PHP, Ruby, Javascript == web
-    - Fortran == numerical
-
-- all programming languages the same (theoretical)
-
-- categories:
-
-    - compiled vs interpreted (virtual machine) non compiled languages
-
-        speed vs multiplataform, quick test, prototyping
-
-        there is no hard distiction: any compiled language could also be interpreted and vice versa
-
-        it is mainly a question of design: some langs are designed to be interpreted
-
-        hakell for example can be compiled but also comes with a standard [REPL] interface
-
-    - objects oriented vs non object oriented
-
-    - type systems
-
-        - statically vs dynamically typed
-        - weakly vs strongly typed
-
-- lang easy, lib hard
-
-    Languages are easy to learn because they are all very similar.
-
-    Library interfaces however are not, because they involve completely different concepts between one another.
-
-    Therefore: if a project does what you want in a language you don't know
-
-    - learn that language!
-    - **don't** recode the project!
-
-My languages of choice:
-
-- C
-- C++
-- Java
-- Python
-
-##Data languages
-
-- XML
-- Json
-
-##Markup languages
-
-- HTML
-- LaTeX
-- Markdown
-
-##Web development
-
-- HTML
-- HTTP
-- CGI
-- apache configuration
-- CSS
-- JS
-- MySQL
-
-- PHP
-- the other interpreted CGI languages:
-    - Python
-    - Ruby
-    - Perl
-
-- real deployment
-
-    - ftp
-    - deal with permissions you lack on server
-    - ssh
-
-##Multiple browsers
-
-Have at least two browsers, one main where you are logged in all your websites, and one secondary, which you will use to see how other users see your profiles.
-
-Same goes for web development: have multiple browsers to quickly switch users. Also good practice as it lets you see often how the website renders under different browsers.
-
-#Filesystem
-
-One of the first things you should understand better as a programmer is your filesystem.
-
-- home dir
-
-- upper vs lower case
-
-- naming conventions
-
-    - bin
-
-    - ~ and .bak
-
-    - doc
-
-    - dot hidden
-
-    - lib
-
-    - src
-
-    - include
-
-    - share
-
-    - local
-
-    - and the rest of the Linux Filesystem Hierarchy Standard
-        <http://www.tuxfiles.org/linuxhelp/linuxdir.html>
-
-- do not start with hyphen
-
-- symlinks/hardlinks
-
-- magic folders ala Windows library/documents
-
-- inner workings: how is data actually stored/retreived on disk?
-
-#Database
-
-- MySQL
-- SQLite
-
-#Important programs for life
-
-- dropdown terminal emulator: Guake.
-
-- Vim
-
-    Text editor.
-
-- Krusader
-
-    File manager.
-
-- Source version control.
-
-    you need to contribute with others
-
-    Most commonly used:
-
-    - Git. Entirely dominates web development.
-    - SVN
-
-- make (makefile)
-
-    automate compilations
-
-    <http://www.jfranken.de/homepages/johannes/vortraege/make_inhalt.en.html>
-
-- bugrackers, like GitHub built-in one. **Always** use one for your project!
-
-- virtual machines. VirtualBox + Vagrant are game changing.
-
-- ack (find/grep replacement)
-
-    Find in files.
-
-##shell
-
-- language:
-
-    - Linux: bash
-    - windows: cmd
-
-- terminal:
-
-    - pro: reproduce commands easily
-    - con: cannot do graphs
-
-    The terminal allows you to interact with the shell interpreter.
-
-- bash:
-
-    - pro: super easy file/pipe/process handling
-    - con: insane, slow
-
-    Use for one liners only. replacements:
-
-    - Perl is dead, but golfs really well.
-    - Python! Also useful for other things, so worth learning
-
-- --help (how to read, [], ..., ), man, version
-
-- directory structure, homedir, fake vs real dirs
-
-- options, ls, cd, mkdir, cp, rm, rmdir, control z, bg, find, grep
-
-- stdin/stderr/stdout
-
-    - three holes
-    - pipes > to file, | grep, 1>&2
-
-- exit status
-
-- pipe (help grep example)
-
-- interactive vs. non-interactive
-
-#algorithm
-
-See [this](algorithm.md).
-
-#assembler
-
-Understanc exactly what operations a processor can do.
-
-<http://www.bottomupcs.com/>
-
-#data representation
-
-##character representation
-
-- ascii
-- unicode
-- utf8
-
-##integer representation
-
-- binary, hexa
-- signed
-
-    - one's complement
-    - 2-complement
-
-##float representation
-
-TODO
-
-#operating systems
-
-You must learn how your operating system works.
-
-The only operating system you can really understand is Linux since it is open source,
-so understand Linux.
-
-Topics which you should look into:
-
-##program memory space
-
-address, operational system division
-
-- <www.dirac.org/linux/gdb/02a-Memory_Layout_And_The_Stack.php>
-
-    tutorial to gdb
-
-##driver programming
-
-- <http://www.linuxjournal.com/article/7353>
-    #5/5
-    #control a lamp. contains c code.
-
-- <http://www.freesoftwaremagazine.com/articles/drivers_linux>
-
-##executable files
-
-ELF files, including libraries
-
-#hardware
-
-- memory: registers vs caches vs RAM vs ROM (BIOS) vs VRAM vs HD
-
-    <http://arstechnica.com/gadgets/2002/07/caching/2/>
-
-    deep explanaition
-
-- busses
-    <http://computer.howstuffworks.com/pci1.htm>
-
-#multithreading concurrency IPC
-
-    - thread vs process
-
-        a process can contain many threads
-
-        threads share a memory space, process don't
-
-    - ipc
-
-        - pipes : same machine
-        - sockets : different machines
-            - internet
-            - pci
-            - usb
-
-#formal languages
-
-Important if you ever want to create a computer language.
-
-- backus naur form: http://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form
-
-#optimizing code
-
-more important than those are to first:
-
-- use best algorithm
-
-- compile instead of interpret
-
-a few important ones are:
-
-- cache: http://en.wikipedia.org/wiki/CPU_cache
-
-- speculative execution http://en.wikipedia.org/wiki/Speculative_execution
-
-- loop unwinding: http://en.wikipedia.org/wiki/Loop_unwinding
-
-- out of order execution: http://en.wikipedia.org/wiki/Out-of-order_execution
-
--register renaming: http://en.wikipedia.org/wiki/Register_renaming
-
-#automatic optimization
-
-- branch prediction
-
-    <http://en.wikipedia.org/wiki/Branch_predictor>
-
-    An example of perceptible branch prediction:
-
-    <http://stackoverflow.com/questions/11227809/why-is-processing-a-sorted-array-faster-than-an-unsorted-array>
-
-#design patterns
-
-See [this](design-patterns).
-
-#GPU programming
-
-TODO
-
-#stragegy
-
-artistic level
-
-- coworkers
-- clients
-- market
-
-- <http://www.joelonsoftware.com/>
-
-    quite a few strategy articles
-
-    ex microsoft employee, lots of exp
-
-#phylosophy
-
-##what computers do
-
-Manipulate information:
-
-- copy and move information around
-- reaching new information from old
-
-In a way that is *very*:
-
-- fast
-- cheap
-- without errors
-
-##programming and ideas
-
-    ideas (that can be programmed)
-    +
-    programming
-    ------------------------------
-    *power*
-
-- without ideas, programming is useless!
-- without programming, some ideas are useless!
-
-#sources
-
-##free
-
-- [stack overflow](http://stackoverflow.com/)
-
-    Great QA site with gamification. Huge programming community.
-
-    Also check related sites maintained by the same enterprise: [stack exchange](http://stackexchange.com/).
-
-    Reasonable way to show your knowledge to enterpreises.
-
-- [top coder algorithm contests](http://community.topcoder.com/tc?module=ProblemArchive&sr=1&er=50&sc=&sd=&class=&cat=&div1l=&div2l=&mind1s=&mind2s=&maxd1s=&maxd2s=&wr=)
-
-    Hosts timed programming contests online.
-
-    Lost of programming problems available with solutions proposed by contestants.
-
-    Good way to show your knowledge to enterpreises.
-    Very popular as of 2013, lots of employers looking there.
-
-    Also worth checking their tutorials: <http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=alg_index>
-
-    Must use a annoying Java program to run in the contests, and hard to find the problems in the site in the first place.
-
-- [spoj contests](http://www.spoj.com/problems/classical/)
-
-    Much like top coder.
-
-    Problems can be solved any time.
-
-    Solutions can be submitted any time for online tests.
-
-    Does time and memory tests, and ranks algorithms accordingly.
-
-    It is not possible to view submitted solutions.
diff --git a/licenses.md b/licenses.md
index 4b8a2cc..78c198e 100644
--- a/licenses.md
+++ b/licenses.md
@@ -1,19 +1,22 @@
-# gpl
+# Licenses
+
+## MIT
 
 - you can use, study, share (copy), and modify the software
 
-- you *cannot* use it in non gpl projects (copyleft),
-	meaning that you cannot make a closed source project that uses it.
+- every substantial reproduction of the software must maintain the copyright note
+
+Basically like GPL except you *can* use in commercial projects,
+so you can basically do anything you want, except remove the license from sub products
 
-# mit liscence
+## GPL
 
-- like gpl
+Like MIT< but you *cannot* use it in non GPL PROJECTS (COPYLEFT),
+meaning that you cannot make a closed source project that uses it.
 
-- except you *can* use in commercial projects,
-	so you can basically do anyting you want,
-	except remove the license from subproducts
+This makes the project useless for closed source projects to build upon.
 
-# dual
+## Dual
 
-some licenses are called dual X/Y (ex: dual BSD/GPL), meaning that you can
+Some licenses are called dual X/Y (ex: dual BSD/GPL), meaning that you can
 take either one of them.