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• Numeric equivalent of an Excel column name

  - by Vivin Paliath

  The challenge The shortest code by character count that will output the numeric equivalent of an Excel column string. For example, the A column is 1, B is 2, so on and so forth. Once you hit Z, the next column becomes AA, then AB and so on. Test cases: A: 1 B: 2 AD: 30 ABC: 731 WTF: 16074 ROFL: 326676 Code count includes input/output (i.e full program).

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• Fibonacci Code Golf

  - by Claudiu

  Generate the Fibonacci sequence in the fewest amount of characters possible. Any language is OK, except for one that you define with one operator, f, which prints the Fibonacci numbers. Starting point: 25 characters in Haskell: f=0:1:zipWith(+)f(tail f)

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• Calculate the digital root of a number

  - by Gregory Higley

  A digital root, according to Wikipedia, is "the number obtained by adding all the digits, then adding the digits of that number, and then continuing until a single-digit number is reached." For instance, the digital root of 99 is 9, because 9 + 9 = 18 and 1 + 8 = 9. My Haskell solution -- and I'm no expert -- is as follows. digitalRoot n | n < 10 = n | otherwise = digitalRoot . sum . map (\c -> read [c]) . show $ n As a language junky, I'm interested in seeing solutions in as many languages as possible, both to learn about those languages and possibly to learn new ways of using languages I already know. (And I know at least a bit of quite a few.) I'm particularly interested in the tightest, most elegant solutions in Haskell and REBOL, my two principal "hobby" languages, but any ol' language will do. (I pay the bills with unrelated projects in Objective C and C#.) Here's my (verbose) REBOL solution: digital-root: func [n [integer!] /local added expanded] [ either n < 10 [ n ][ expanded: copy [] foreach c to-string n [ append expanded to-integer to-string c ] added: 0 foreach e expanded [ added: added + e ] digital-root added ] ] EDIT: As some have pointed out either directly or indirectly, there's a quick one-line expression that can calculate this. You can find it in several of the answers below and in the linked Wikipedia page. (I've awarded Varun the answer, as the first to point it out.) Wish I'd known about that before, but we can still bend our brains with this question by avoiding solutions that involve that expression, if you're so inclined. If not, Crackoverflow has no shortage of questions to answer. :)

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• Code Golf: Phone Number to Words

  - by Nick Hodges

  Guidelines for code-golf on SO We've all seen phone numbers that are put into words: 1-800-BUY-MORE, etc. What is the shortest amount of code you can write that will produce all the possible combinations of words for a 7 digit US phone number. Input will be a seven digit integer (or string, if that is simpler), and assume that the input is properly formed. Output will be a list of seven character strings that For instance, the number 428-5246 would produce GATJAGM GATJAGN GATJAGO GATJAHM GATJAHN GATJAHO and so on..... Winning criteria will be code from any language with the fewest characters that produce every possible letter combination. Additional Notes: To make it more interesting, words can be formed only by using the letters on a North American Classic Key Pad phone with three letters per number as defined here.That means that Z and Q are excluded. For the number '1', put a space. For the number '0', put a hyphen '-' Bonus points awarded for recognizing output as real English words. Okay, not really. ;-)

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• Code-Golf: Friendly Number Abbreviator

  - by David Murdoch

  Based on this question: Is there a way to round numbers into a friendly format? THE CHALLENGE - UPDATED! (removed hundreds abbreviation from spec) The shortest code by character count that will abbreviate an integer (no decimals). Code should include the full program. Relevant range is from 0 - 9,223,372,036,854,775,807 (the upper limit for signed 64 bit integer). The number of decimal places for abbreviation will be positive. You will not need to calculate the following: 920535 abbreviated -1 place (which would be something like 0.920535M). Numbers in the tens and hundreds place (0-999) should never be abbreviated (the abbreviation for the number 57 to 1+ decimal places is 5.7dk - it is unneccessary and not friendly). Remember to round half away from zero (23.5 gets rounded to 24). Banker's rounding is verboten. Here are the relevant number abbreviations: h = hundred (102) k = thousand (103) M = million (106) G = billion (109) T = trillion (1012) P = quadrillion (1015) E = quintillion (1018) SAMPLE INPUTS/OUTPUTS (inputs can be passed as separate arguments): First argument will be the integer to abbreviate. The second is the number of decimal places. 12 1 => 12 // tens and hundreds places are never rounded 1500 2 => 1.5k 1500 0 => 2k // look, ma! I round UP at .5 0 2 => 0 1234 0 => 1k 34567 2 => 34.57k 918395 1 => 918.4k 2134124 2 => 2.13M 47475782130 2 => 47.48G 9223372036854775807 3 => 9.223E // ect... . . . Original answer from related question (javascript, does not follow spec): function abbrNum(number, decPlaces) { // 2 decimal places => 100, 3 => 1000, etc decPlaces = Math.pow(10,decPlaces); // Enumerate number abbreviations var abbrev = [ "k", "m", "b", "t" ]; // Go through the array backwards, so we do the largest first for (var i=abbrev.length-1; i>=0; i--) { // Convert array index to "1000", "1000000", etc var size = Math.pow(10,(i+1)*3); // If the number is bigger or equal do the abbreviation if(size <= number) { // Here, we multiply by decPlaces, round, and then divide by decPlaces. // This gives us nice rounding to a particular decimal place. number = Math.round(number*decPlaces/size)/decPlaces; // Add the letter for the abbreviation number += abbrev[i]; // We are done... stop break; } } return number; }

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• Code Golf: Spider webs

  - by LiraNuna

  The challenge The shortest code by character count to output a spider web with rings equal to user's input. A spider web is started by reconstructing the center ring: \_|_/ _/ \_ \___/ / | \ Then adding rings equal to the amount entered by the user. A ring is another level of a "spider circles" made from \ / | and _, and wraps the center circle. Input is always guaranteed to be a single positive integer. Test cases Input 1 Output \__|__/ /\_|_/\ _/_/ \_\_ \ \___/ / \/_|_\/ / | \ Input 4 Output \_____|_____/ /\____|____/\ / /\___|___/\ \ / / /\__|__/\ \ \ / / / /\_|_/\ \ \ \ _/_/_/_/_/ \_\_\_\_\_ \ \ \ \ \___/ / / / / \ \ \ \/_|_\/ / / / \ \ \/__|__\/ / / \ \/___|___\/ / \/____|____\/ / | \ Input: 7 Output: \________|________/ /\_______|_______/\ / /\______|______/\ \ / / /\_____|_____/\ \ \ / / / /\____|____/\ \ \ \ / / / / /\___|___/\ \ \ \ \ / / / / / /\__|__/\ \ \ \ \ \ / / / / / / /\_|_/\ \ \ \ \ \ \ _/_/_/_/_/_/_/_/ \_\_\_\_\_\_\_\_ \ \ \ \ \ \ \ \___/ / / / / / / / \ \ \ \ \ \ \/_|_\/ / / / / / / \ \ \ \ \ \/__|__\/ / / / / / \ \ \ \ \/___|___\/ / / / / \ \ \ \/____|____\/ / / / \ \ \/_____|_____\/ / / \ \/______|______\/ / \/_______|_______\/ / | \ Code count includes input/output (i.e full program).

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• What is your favourite cleverly written functional code?

  - by sdcvvc

  What are your favourite short, mind-blowing snippets in functional languages? My two favourite ones are (Haskell): powerset = filterM (const [True, False]) foldl f v xs = foldr (\x g a -> g (f a x)) id xs v -- from Hutton's tutorial (I tagged the question as Haskell, but examples in all languages - including non-FP ones - are welcome as long as they are in functional spirit.)

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• Learning a new language coding 1 program

  - by Steve

  This is not really a programming question Question : Sometimes you have to learn a new language consider this situation for example : you have been programming in C# for some years and then one day you need to code in java. Now being a programmer you already know the programming concepts its just the syntax you need to get used to. Can you think some program to code which covers every(or most) aspect of a programming language? like say you make a desktop search program...it can cover file reading writing, threads maybe interacting with db like sqllite so you get familiar with those topics and the syntax of the new language Just want to know your thoughts about what is the fastest way to go about learning a new language skipping all the basic stuff

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• Factorial Algorithms in different languages

  - by Brad Gilbert

  I want to see all the different ways you can come up with, for a factorial subroutine, or program. The hope is that anyone can come here and see if they might want to learn a new language. Ideas: Procedural Functional Object Oriented One liners Obfuscated Oddball Bad Code Polyglot Basically I want to see an example, of different ways of writing an algorithm, and what they would look like in different languages. Please limit it to one example per entry. I will allow you to have more than one example per answer, if you are trying to highlight a specific style, language, or just a well thought out idea that lends itself to being in one post. The only real requirement is it must find the factorial of a given argument, in all languages represented. Be Creative! Recommended Guideline: # Language Name: Optional Style type - Optional bullet points Code Goes Here Other informational text goes here I will ocasionally go along and edit any answer that does not have decent formatting.

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• Code Golf: Print the entire "12 Days of Christmas" song in the fewest lines of code.

  - by fizzer

  Print all 12 verses of the popular holiday song. By 12 verses I mean the repetition of each line as is sung in the song, ie Verse One: On the first day of Christmas my true love gave to me a partridge in a pear tree. Verse Two On the second day of Christmas my true love gave to me two turtle doves and a partridge in a pear tree. ... Verse N: On the nth day of Christmas my true love gave to me (Verse N-1 without the first line) (line added in verse N)

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• How would you implement a hashtable in language x?

  - by mk

  The point of this question is to collect a list of examples of hashtable implementations using arrays in different languages. It would also be nice if someone could throw in a pretty detailed overview of how they work, and what is happening with each example. Edit: Why not just use the built in hash functions in your specific language? Because we should know how hash tables work and be able to implement them. This may not seem like a super important topic, but knowing how one of the most used data structures works seems pretty important to me. If this is to become the wikipedia of programming, then these are some of the types of questions that I will come here for. I'm not looking for a CS book to be written here. I could go pull Intro to Algorithms off the shelf and read up on the chapter on hash tables and get that type of info. More specifically what I am looking for are code examples. Not only for me in particular, but also for others who would maybe one day be searching for similar info and stumble across this page. To be more specific: If you had to implement them, and could not use built-in functions, how would you do it? You don't need to put the code here. Put it in pastebin and just link it.

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• Create, sort, and print a list of 100 random ints in the fewest chars of code

  - by TheSoftwareJedi

  What is the least amount of code you can write to create, sort (ascending), and print a list of 100 random positive integers? By least amount of code I mean characters contained in the entire source file, so get to minifying. I'm interested in seeing the answers using any and all programming languages. Let's try to keep one answer per language, edit the previous to correct or simplify. If you can't edit, comment?

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• A puzzle - a program printing its own source

  - by mfeingold

  Blast from the past. This is one of the puzzles from my early days: Can you write a method (a function) which when called outputs its own source - literally including all the quotes, indentations, etc? No cheating - no reading from a file

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• Code Golf: Ghost Leg

  - by Anax

  The challenge The shortest code by character count that will output the numeric solution, given a number and a valid string pattern, using the Ghost Leg method. Examples Input: 3, "| | | | | | | | |-| |=| | | | | |-| | |-| |=| | | |-| |-| | |-|" Output: 2 Input: 2, "| | |=| | |-| |-| | | |-| | |" Output: 1 Clarifications Do not bother with input. Consider the values as given somewhere else. Both input values are valid: the column number corresponds to an existing column and the pattern only contains the symbols |, -, = (and [space], [LF]). Also, two adjacent columns cannot both contain dashes (in the same line). The dimensions of the pattern are unknown (min 1x1). Clarifications #2 There are two invalid patterns: |-|-| and |=|=| which create ambiguity. The given input string will never contain those. The input variables are the same for all; a numeric value and a string representing the pattern. Entrants must produce a function. Test case Given pattern: "|-| |=|-|=|LF| |-| | |-|LF|=| |-| | |LF| | |-|=|-|" |-| |=|-|=| | |-| | |-| |=| |-| | | | | |-|=|-| Given value : Expected result 1 : 6 2 : 1 3 : 3 4 : 6 5 : 5 6 : 2

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• Capturing system command output as a string

  - by dreeves

  Perl and PHP do this with backticks. For example: $output = `ls`; This code returns a directory listing into the variable $output. A similar function, system("ls"), returns the operating system return code for the given command. I'm talking about a variant that returns whatever the command prints to stdout. (There are better ways to get the list of files in a directory; the example code is an example of this concept.) How do other languages do this? Is there a canonical name for this function? (I'm going with "backtick"; though maybe I could coin "syslurp".)

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• Generate all the ways to intersperse a list of lists, keeping each list in order.

  - by dreeves

  Given a list of lists like this [[1,2,3],[a,b,c,d],[x,y]] generate all permutations of the flattened list, [1,2,3,a,b,c,d,x,y], such that the elements of each sublist occur in the same order. For example, this one is okay [a,1,b,2,x,y,3,c,d] but this one is not [y,1,2,3,a,b,c,x,d] because y must occur after x, that being how x and y are ordered in the original sublist. I believe the number of such lists is determined by the multinomial coefficient. I.e., if there are k sublists, n_i is the length of the ith sublist, and n is the sum of the n_i's then the number of such permutations is n!/(n_i! * ... * n_k!). The question is how to generate those sublists. Pseudocode is great. An actual implementation in your language of choice is even better!

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• Solving problems with near infinite potential solutions

  - by Zonda333

  Today I read the following problem: Use the digits 2, 0, 1, 1 and the operations +, -, x, ÷, sqrt, ^ , !, (), combinations, and permutations to write equations for the counting numbers 1 through 100. All four digits must be used in each expression. Only the digits 2, 0, 1, 1 may be used, and each must be used exactly once. Decimals may be used, as in .1, .02, etc. Digits may be combined; numbers such as 20 or 101 may be used. Example: 60 = 10*(2+1)!, 54 = ¹¹C2 - 0! Though I was able to quickly find around 50 solutions quite easily in my head, I thought programming it would be a far superior solution. However, I then realized I had no clue how to go about solving a problem like this. I am not asking for complete code for me to copy and paste, but for ideas about how I would solve this problems, and others like it that have nearly infinite potential solutions. As I will be writing it in python, where I have the most experience, I would prefer if the answers were more python based, but general ideas are great too.

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• Code Golf: Connecting the dots

  - by ChristopheD

  Description: The input are multiple lines (terminated by a newline) which describe a 'field'. There are 'numbers' scattered across this field: the numbers always start at 1 they follow the ordering of the natural numbers: every 'next number' is incremented with 1 every number is surrounded by (at least) one whitespace on it's left and right Task: Draw lines between these numbers in their natural order (1 -> 2 -> 3 -> ...N) with the following characteristics: replace a number with a '+' character for horizontal lines: use '-' for vertical lines: use '|' going left and down or right and up: / going left and up or right and down: \ Important note: When drawing lines of type 4 and 5 you can assume that : (given points to connect with coordinates x1, y1 and x2, y2) distance(x1,x2) == distance(y1,y2). Have a look at the examples to see where you should 'attach' the lines. It is important to follow the order in which the dots are connected (newer lines can be drawn over older lines). Sample input 1 9 10 8 7 6 5 11 13 12 3 4 14 15 16 1 2 Sample output 1 /+ / | / | +/ +--+ | +\ | \ | \+ /+ | / | /+-------------+/ +---+ / | +--+ | + | +--------------------------+ Sample input 2 4 2 3 5 6 1 8 7 Sample output 2 /+ / | / | / | /+------------------+/ +--------+\ / \ +/ +--------------------------------------+ Winner: shortest solution (by code count). Input can be read via command line.

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• CodeGolf: Find the Unique Paths

  - by st0le

  Here's a pretty simple idea, in this pastebin I've posted some pair of numbers. These represent Nodes of a directed graph. The input to stdin will be of the form, (they'll be numbers, i'll be using an example here) c d q r a b b c d e p q so x y means x is connected to y (not viceversa) There are 2 paths in that example. a->b->c->d->e and p->q->r. You need to print all the unique paths from that graph The output should be of the format a->b->c->d->e p->q->r Notes You can assume the numbers are chosen such that one path doesn't intersect the other (one node belongs to one path) The pairs are in random order. They are more than 1 paths, they can be of different lengths. All numbers are less than 1000. If you need more details, please leave a comment. I'll amend as required. Shameless-Plug For those who enjoy Codegolf, please Commit at Area51 for its very own site:) (for those who don't enjoy it, please support it as well, so we'll stay out of your way...)

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• using cin and cout in textmate [migrated]

  - by That Guy

  I am usually a Java programmer, and have used textmate for that almost exclusively, but lately I started using C++ with it. but when i use even the most basic programs and incorporate the cin keyword, and run the program, I dont get an oppurtunity to put in anything during runtime and sometimes it inserts random values by itself! for example, if i ran this in textmate: #include <iostream> int stonetolb(int); int main() { using namespace std; int stone; cout << "enter the weight in stone"; cin >> stone; int pounds = stonetolb(stone); cout << stone << "stone = "; cout << pounds <<" pounds."; return 0; } int stonetolb(int sts) { return 14 * sts; } I would come out with the output: enter the weight in stone32767stone = 458738 pounds. Why is this happening, and how do I stop it?

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• Optimization and Saving/Loading

  - by MrPlosion1243

  I'm developing a 2D tile based game and I have a few questions regarding it. First I would like to know if this is the correct way to structure my Tile class: namespace TileGame.Engine { public enum TileType { Air, Stone } class Tile { TileType type; bool collidable; static Tile air = new Tile(TileType.Air); static Tile stone = new Tile(TileType.Stone); public Tile(TileType type) { this.type = type; collidable = true; } } } With this method I just say world[y, x] = Tile.Stone and this seems right to me but I'm not a very experienced coder and would like assistance. Now the reason I doubt this so much is because I like everything to be as optimized as possible and there is a major flaw in this that I need help overcoming. It has to do with saving and loading... well more on loading actually. The way it's done relies on the principle of casting an enumeration into a byte which gives you the corresponding number where its declared in the enumeration. Each TileType is cast as a byte and written out to a file. So TileType.Air would appear as 0 and TileType.Stone would appear as 1 in the file (well in byte form obviously). Loading in the file is alot different though because I can't just loop through all the bytes in the file cast them as a TileType and assign it: for(int x = 0; x < size.X; x++) { for(int y = 0; y < size.Y; y+) { world[y, x].Type = (TileType)byteReader.ReadByte(); } } This just wont work presumably because I have to actually say world[y, x] = Tile.Stone as apposed to world[y, x].Type = TileType.Stone. In order to be able to say that I need a gigantic switch case statement (I only have 2 tiles but you could imagine what it would look like with hundreds): Tile tile; for(int x = 0; x < size.X; x++) { for(int y = 0; y < size.Y; y+) { switch(byteReader.ReadByte()){ case 0: tile = Tile.Air; break; case 1: tile = Tile.Stone; break; } world[y, x] = tile; } } Now you can see how unoptimized this is and I don't know what to do. I would really just like to cast the byte as a TileType and use that but as said before I have to say world[y, x] = Tile.whatever and TileType can't be used this way. So what should I do? I would imagine I need to restructure my Tile class to fit the requirements but I don't know how I would do that. Please help! Thanks.

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• How to display a projectile trajectory in c++? [on hold]

  - by sana

  I am trying to make a game of Gorillas in c++ whose specification is somewhat like....... is : "In this game both players should select their position on a level scaled ground. Scale of the ground should be from 0 to 20 divisions, each division corresponding to 10 meters. Each player will enter an angle and initial velocity (limits of both should be defined) and the player will hurl a stone with this velocity at given angle. Stone will make a projectile and if it hits the other player then shooting player wins. A random effect of air should also be incorporated. Air will support one player and resist other. Velocity of air should be generated randomly, within some limits, and subtracted or added in the horizontal velocity of the stone. An arrow of suitable length shall represent air direction and velocity. The player who hits first wins." How do I display the trajectory of the stone????

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• Experiences with learning Chinese

  - by Greg Low

  I've had a few friends asking me about learning Chinese and what I've found works and doesn't work. I was answering a question on a mailing list today and I thought I should post this info where it might be useful to many. The question that was initially asked was whether Rosetta Stone was useful but I've provided much more info on learning the language here. I’ve used Rosetta Stone with Chinese but it’s really hard to know whether to recommend it or not. Rosetta Stone works the same way in all languages. They show you photos and then let you both see and hear the target language and get you to work out what they’re talking about. The thinking is that that’s how children learn. However, at first, I found it very frustrating. I’d be staring at photos trying to work out what they were really trying to get at. Sometimes it’s far from obvious. I could not have survived without Google Translate open at the same time. The other weird thing is that the photos are from a mixture of countries. While that’s good in a way, it also means that they are endlessly showing pictures of something that would never happen in the target language and culture. For any language, constant interaction with a speaker of the target language is needed. Rosetta Stone has a “Studio” option. That’s the best part of the program. In my case, it lets me connect around twice a week to a live online class from Beijing. Classes usually have the teacher plus two to four students. You get some Studio access with the initial packages but need to purchase it for ongoing use. I find it very inexpensive. It seems to work out to about $70 (AUD/USD) for six months. That’s a real bargain. The other downside to Rosetta Stone is that they tend to teach very formal language, but as with other languages, that’s not how the locals speak. It might have been correct at one point but no-one actually says that. As an example, Rosetta Stone teach Gonggòng qìche (pronounced roughly like “gong gong chee chure” for bus. Most of my friends from areas like Taiwan would just say Gongche. Google Translate says Zongxiàn (pronounced somewhat like “dzong sheean”) instead. Mind you, the Rosetta Stone option isn't really as bad as "omnibus"; it's more like saying "public bus". If you say the option they provide, people would understand you. I also listen to ChinesePod in the car. They also have SpanishPod. Each podcast is about five minutes of spoken conversation. It is very good for providing current language. Another resource I use is local Meetup groups. Most cities have these and for a variety of languages. It’s way less structured (just standard conversation) but good for getting interaction. The obvious challenge for Asian languages is reading/writing. The input editors for Chinese that are part of Windows are excellent. Many of my Chinese friends speak fluently but cannot read or write. I was determined to learn to do both. For writing, I’m talking about on a computer, not with a pen. (Mind you, I can barely write English with a pen nowadays). When using Rosetta Stone, you can choose to have the Chinese words displayed in pinyin (Wo xihuan xuéxí zhongguó) or in Chinese characters (???????) or both. This year, I’ve been forcing myself to just use the Chinese characters. I use a pinyin input editor in Windows though, as it’s very fast.  (The character recognition input in the iPad is also amazing). Notice from the example that I provided above that the pronunciation of the pinyin isn’t that obvious to us at first either.  Since changing to only using characters, I find I can now read many more Chinese characters fluently. It’s a major challenge though. I can read about 300 now and yet you need around 2,500 to be able to read a newspaper fairly well. Tones are a major issue for some Asian languages. Mandarin has four tones (plus a neutral tone) and there is a major difference in meaning between two words that are spelled the same in pinyin but with different tones. For example, Ma (3rd tone?) is a horse, Ma (1st tone?) is like “mom”, and ma (neutral tone?) is a question mark and so on. Clearly you don’t want to mix these up. As in English, they also have words that do sound the same but mean different things in different contexts. What’s interesting is that even though we see two words that differ only by tone as very similar, to a native speaker, if you say the right words with the wrong tone, you might as well have said a completely different word. My wife’s dialect of Chinese has eight tones. It’s much worse. The reason I’m so keen to learn to read/write Chinese is that even though the different dialects are pronounced so differently that speakers of one dialect often cannot understand another dialect, the writing is generally the same. The only difference is that many years ago, the Chinese government created a simplified set of characters for some of the most commonly used ones. Older Chinese and most Cantonese speakers often struggle with the simplified characters. This is the simplified form of “three apples”: ????   This is the traditional form of the same words: ????  Note that two of the characters are the same but the middle two are quite different. For most languages, the best thing is to watch current movies in the target language but to watch them with the target language as subtitles, not your native language. You want to know what they actually said, not what it roughly means (which is what the English subtitle would give you). The difficulty with Asian languages like Chinese is that you have the added challenge of understanding the subtitles when they are written in the target language. I wish there were Mandarin Chinese movies with pinyin subtitles. For learning to read characters, I also recommend HanCard on the iPad. It is targeted at the HSK language proficiency levels. (I’m intending to take the first HSK exam as soon as I’m ready). Hope that info helps someone get started.  

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• How to do the Geometry Wars gravity well effect

  - by Mykel Stone

  I'm not talking about the background grid here, I'm talking about the swirly particles going around the Gravity Wells! I've always liked the effect and decided it'd be a fun experiment to replicate it, I know GW uses Hooke's law all over the place, but I don't think the Particle-to-Well effect is done using springs, it looks like a distance-squared function. Here is a video demonstrating the effect: http://www.youtube.com/watch?v=YgJe0YI18Fg I can implement a spring or gravity effect on some particles just fine, that's easy. But I can't seem to get the effect to look similar to GWs effect. When I watch the effect in game it seems that the particles are emitted in bunches from the Well itself, they spiral outward around the center of the well, and eventually get flung outward, fall back towards the well, and repeat. How does he make the particles spiral outward when spawned? How does he keep the particle bunches together when near the Well but spread away from each other when they're flung outward? How does he keep the particles so strongly attached to the Well?

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• Logarithmic spacing of FFT bins

  - by Mykel Stone

  I'm trying to do the examples within the GameDev.net Beat Detection article ( http://archive.gamedev.net/archive/reference/programming/features/beatdetection/index.html ) I have no issue with performing a FFT and getting the frequency data and doing most of the article. I'm running into trouble though in the section 2.B, Enhancements and beat decision factors. in this section the author gives 3 equations numbered R10-R12 to be used to determine how many bins go into each subband: R10 - Linear increase of the width of the subband with its index R11 - We can choose for example the width of the first subband R12 - The sum of all the widths must not exceed 1024 He says the following in the article: "Once you have equations (R11) and (R12) it is fairly easy to extract 'a' and 'b', and thus to find the law of the 'wi'. This calculus of 'a' and 'b' must be made manually and 'a' and 'b' defined as constants in the source; indeed they do not vary during the song." However, I cannot seem to understand how these values are calculated...I'm probably missing something simple, but learning fourier analysis in a couple of weeks has left me Decimated-in-Mind and I cannot seem to see it.

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