how to create 5-dimensional array ?
in [JavaScript]
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From: Dr J R Stockton on 27 Apr 2010 12:12 In comp.lang.javascript message <7fe7b790-e599-4592-a83d-8526174bacfe(a)y3 0g2000yqh.googlegroups.com>, Mon, 26 Apr 2010 04:28:58, Sean Kinsey <okinsey(a)gmail.com> posted: >On Apr 26, 4:09�am, Stefan Weiss <krewech...(a)gmail.com> wrote: ><snip> >> I swear, one of these days I'm going to learn Russian. There's a huge >> part of the web that I don't have access to, and that bugs me. > >Haven't you tried Google Chrome with its translation feature? There is no *need* to use Chrome for that; one can go to <http://translate.google.com/?langpair=it|en#> directly, and remove or adjust the language pair. I don't know what the hash is for. -- (c) John Stockton, nr London, UK. ?@merlyn.demon.co.uk Turnpike v6.05 IE 7. Web <URL:http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, & links. MiniTrue is good for viewing/searching/altering files, at a DOS / CMD prompt; free, DOS/Win/UNIX, new via <URL:http://www.merlyn.demon.co.uk/pc-links.htm>.
From: Michael Wojcik on 29 Apr 2010 13:00 Dr J R Stockton wrote: > In comp.lang.javascript message <7fe7b790-e599-4592-a83d-8526174bacfe(a)y3 > 0g2000yqh.googlegroups.com>, Mon, 26 Apr 2010 04:28:58, Sean Kinsey > <okinsey(a)gmail.com> posted: >> On Apr 26, 4:09 am, Stefan Weiss <krewech...(a)gmail.com> wrote: >> <snip> >>> I swear, one of these days I'm going to learn Russian. There's a huge >>> part of the web that I don't have access to, and that bugs me. >> Haven't you tried Google Chrome with its translation feature? > > There is no *need* to use Chrome for that; one can go to > <http://translate.google.com/?langpair=it|en#> directly, and remove or > adjust the language pair. I don't know what the hash is for. The hash is the delimiter for an empty fragment identifier. An empty fragment ID is a no-op for an HTTP URL, but it appears that Google Translate's URL canonicalization will add it if you omit it. You can also add "&text=[URL-encoded text in source language]" to the URL, and have the page appear with the translation: http://translate.google.com/?langpair=it|en&text=ciao# in which case, at least if you have a small viewport, the "#autotrans" fragment identifier might be useful: http://translate.google.com/?langpair=it|en&text=ciao#autotrans -- Michael Wojcik Micro Focus Rhetoric & Writing, Michigan State University
From: Spamless on 30 Apr 2010 22:06 On 2010-04-26, VK <schools_ring(a)yahoo.com> wrote: > While trying to port the promised Shannon's Clairvoyant code to > Javascript, I am having real troubles to figure out what that would be > in Javascript: 5-dimensional array ... I wouldn't. Suppose you want to have five dimension, let me index them from 0 through 4 and want to hold data with index (a,b,c,d,e) where the first index has A possible values (from 0 throut A-1), the second has B values (from 0 through B-1), etc. I would construct a one dimensional array of size A*B*C*D*E, say MYARRAY and use the function: _indexer(a,b,c,d,e) = {return ((((e*D+d)*C+c)*B+b)*A+a)} as MYARRAY[_indexer(a,b,c,d,e)] It is easy enough to calculate _indexer. It gives a single number from five and that number is unique (once you know it, take the result mod(A) to find a mod A, but as a can only vary from 0 through A-1, you know A. Subtract to get (((e*D+d)*C+c)*B+b)*A, divide by A to get ((e*D+d)*C+c)*B+b and take that mod B to get b mod B. But b can only vary from 0 through B-1 so you know b ... in short, once you have that single number it gives the five numbers which are used to create it). This one-one mapping maps to the range 0 through A*B*C*D*E-1, A*B*C*D*E consecutive integers to hold just that many elements (which would be required by the five dimensional array). There *are* ways to do it if you don't know A,B,C,D,E, but they can be inefficient (find some one-one mappying from five non-negative integers into the integers) in that it may not map to all consecutive integers in the smallest range.
From: VK on 1 May 2010 00:13 On May 1, 6:06 am, Spamless <Spaml...(a)Nil.nil> wrote: > On 2010-04-26, VK <schools_r...(a)yahoo.com> wrote: > > > While trying to port the promised Shannon's Clairvoyant code to > > Javascript, I am having real troubles to figure out what that would be > > in Javascript: 5-dimensional array ... > > I wouldn't. Suppose you want to have five dimension, let me index them > from 0 through 4 and want to hold data with index (a,b,c,d,e) where the > first index has A possible values (from 0 throut A-1), the second has > B values (from 0 through B-1), etc. I would construct a one dimensional > array of size A*B*C*D*E, say MYARRAY and use the function: > _indexer(a,b,c,d,e) = {return ((((e*D+d)*C+c)*B+b)*A+a)} > as MYARRAY[_indexer(a,b,c,d,e)] > > It is easy enough to calculate _indexer. It gives a single number from > five and that number is unique (once you know it, take the result mod(A) > to find a mod A, but as a can only vary from 0 through A-1, you know A. > Subtract to get (((e*D+d)*C+c)*B+b)*A, divide by A to get ((e*D+d)*C+c)*B+b > and take that mod B to get b mod B. But b can only vary from 0 through B-1 > so you know b ... in short, once you have that single number it gives the > five numbers which are used to create it). > > This one-one mapping maps to the range 0 through A*B*C*D*E-1, A*B*C*D*E > consecutive integers to hold just that many elements (which would be > required by the five dimensional array). You just answered it before I got ready to post myself :-( :-) Indeed I was getting nuts by trying to visualize that "5-dimensional array of 72 elements" because I hate to use things I do not "see" even if they work properly. Finally I realized that numOfNodes-dimensional real array just unnecessarily obfuscates the otherwise simple picture. In fact we have a symmetrical binary tree with 5 node steps and 64 leaves. On each of five steps we have to either turn left or turn right. Let's denote left turn as zero and right turn as 1. This way the path to each leaf is one of permutations between 00000 (all left turns) and 11111 (all right turns). Let's look at these permutations as binary numbers. Let's also introduce the "holding bit" on the left to prevent zeros collapsing if we ever need to stringify the path. The set of paths to each leaf is then the set of binary numbers 100000 - 111111 (decimal 32 - 63). The universal init algorithm then is as simple as: function initTree(numOfNodes) { var Tree = new Array(); // var Tree = new Object(); var lBound = ''; var uBound = ''; do { lBound+= '0'; } while (lBound.length < numOfNodes); lBound = parseInt('1'+lBound, 2); do { uBound+= '1'; } while (uBound.length < numOfNodes); uBound = parseInt('1'+uBound, 2); for (var i = lBound; i<uBound; i++) { Tree[i] = 0; // or another init value } return Tree; } The algorithm can be further improved of course. For instance it is highly tempting to use binary logical operators AND, OR, XOR instead of string manipulations in order to get paths and later to match the given path to the leaf value. It is tempting as it would be first ever practical and logical use of binary logical operators in JavaScript I would ever saw. The beauty of this approach is that it works for ternary and higher orders trees as well. One just need to think for say ternary tree (left, straight, right choice on each node) as a set of two wrong choices and one right choice. By denoting wrong with 0 and right with 1 we are getting 001, 010, 100 and respectively the full set of paths will be found in a range of base-3 numbers with the right choice for each node being a trit in that number. So on for base-4, base-5 etc. I am sure that all that is already written in tree books but I arrived to that completely by my own so cannot resist to state how proud I am of myself :-) P.S. I am wondering if it would be more effective or equal for storing paths: to use properties of Object instance or to use sparse Array instance?
From: VK on 1 May 2010 04:20
On May 1, 8:13 am, VK <schools_r...(a)yahoo.com> wrote: > The beauty of this approach is that it works for ternary and higher > orders trees as well. One just need to think for say ternary tree > (left, straight, right choice on each node) as a set of two wrong > choices and one right choice. By denoting wrong with 0 and right with > 1 we are getting 001, 010, 100 and respectively the full set of paths > will be found in a range of base-3 numbers with the right choice for > each node being a trit in that number. The latter means that it is possible to build an analog of neural quantum network and entanglement states using tools of JavaScript. Just each trit has to be a qubit like function Qubit(entangledQubit) { this.superposition = true; this.entangledQubit = entangledQubit || null; this.state = -1; this.mesure = Qubit.mesure; } Quibit.mesure = function() { this.superposition = false; var n = Math.floor(Math.random()*2); this.state = (n==2) ? 1 : 0; this.entangledQubit.state = !this.state; } It's all highly sketchy and not even sure if practically applicable but hell, I have to think of it immediately... - |