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• Correct permutation cycle for Verhoeff algorithm

  - by James

  Hello, I'm implementing the Verhoeff algorithm for a check digit scheme, but there seems to be some disagreement in web sources as to which permutation cycle should form the basis of the permutation table. Wikipedia uses: (36)(01589427) while apparently, Numerical Recipies uses a different cycle and this book uses: (0)(14)(23)(56789), quoted from a 1990 article by Winters. It also notes that Verhoeff used the one Wikipedia quotes. Now, my number theory is a little rusty, but the Wikipedia cycle clearly will repeat after the 8th power, while the book one will take 10, despite it saying that s^8=s. Table 2.14(b) has other errors in the 2-cycles, so this is dubious anyway. Unfortunately, I don't have copies of the original articles (and am too tight to pay/disgusted that 40-year old knowledge is still being held to ransom by publishers), nor a copy of Numerical Recipes to check (and am loath to install their paranoia-induced copy protection plug-in to view online). So does any one know which is correct? Are they both correct?

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• Algorithm for disordered sequences of strings

  - by Kinopiko

  The Levenshtein distance gives us a way to calculate the distance between two similar strings in terms of disordered individual characters: quick brown fox quikc brown fax The Levenshtein distance = 3. What is a similar algorithm for the distance between two strings with similar subsequences? For example, in quickbrownfox brownquickfox the Levenshtein distance is 10, but this takes no account of the fact that the strings have two similar subsequences, which makes them more "similar" than completely disordered words like quickbrownfox qburiocwknfox and yet the completely disordered version has a Levenshtein distance of eight. What distance measures exist which take the length of subsequences into account, without assuming that the subsequences can be easily broken into distinct words?

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• Algorithm for measuring distance between disordered sequences

  - by Kinopiko

  The Levenshtein distance gives us a way to calculate the distance between two similar strings in terms of disordered individual characters: quick brown fox quikc brown fax The Levenshtein distance = 3. What is a similar algorithm for the distance between two strings with similar subsequences? For example, in quickbrownfox brownquickfox the Levenshtein distance is 10, but this takes no account of the fact that the strings have two similar subsequences, which makes them more "similar" than completely disordered words like quickbrownfox qburiocwknfox and yet this completely disordered version has a Levenshtein distance of eight. What distance measures exist which take the length of subsequences into account, without assuming that the subsequences can be easily broken into distinct words?

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• Graph coloring Algorithm

  - by Amitd

  From wiki In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color. Given 'n' colors and m vertices, how easily can a graph coloring algorithm be implemented? Lan

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• Fast modulo 3 or division algorithm?

  - by aaa

  Hello is there a fast algorithm, similar to power of 2, which can be used with 3, i.e. n%3. Perhaps something that uses the fact that if sum of digits is divisible by three, then the number is also divisible. This leads to a next question. What is the fast way to add digits in a number? I.e. 37 - 3 +7 - 10 I am looking for something that does not have conditionals as those tend to inhibit vectorization thanks

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• Math algorithm question

  - by Senica Gonzalez

  I'm not sure if this can be done without some determining factor....but wanted to see if someone knew of a way to do this. I want to create a shifting scale for numbers. Let's say I have the number 26000. I want the outcome of this algorithm to be 6500; or 25% of the original number. But if I have the number 5000, I want the outcome to be 2500; or 50% of the original number. The percentages don't have to be exact, this is just an example. I just want to have like a sine wave sort of thing. As the input number gets higher, the output number is a lower percentage of the input. Does that make sense?

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• Algorithm for measuring distance between disordered sequences of strings

  - by Kinopiko

  The Levenshtein distance gives us a way to calculate the distance between two similar strings in terms of disordered individual characters: quick brown fox quikc brown fax The Levenshtein distance = 3. What is a similar algorithm for the distance between two strings with similar subsequences? For example, in quickbrownfox brownquickfox the Levenshtein distance is 10, but this takes no account of the fact that the strings have two similar subsequences, which makes them more "similar" than completely disordered words like quickbrownfox qburiocwknfox and yet this completely disordered version has a Levenshtein distance of eight. What distance measures exist which take the length of subsequences into account, without assuming that the subsequences can be easily broken into distinct words?

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• Graph Algorithm To Find All Paths Between N Arbitrary Vertices

  - by russtbarnacle

  I have an graph with the following attributes: Undirected Not weighted Each vertex has a minimum of 2 and maximum of 6 edges connected to it. Vertex count will be < 100 I'm looking for paths between a random subset of the vertices (at least 2). The paths should simple paths that only go through any vertex once. My end goal is to have a set of routes so that you can start at one of the subset vertices and reach any of the other subset vertices. Its not necessary to pass through all the subset nodes when following a route. All of the algorithms I've found (Dijkstra,Depth first search etc.) seem to be dealing with paths between two vertices and shortest paths. Is there a known algorithm that will give me all the paths (I suppose these are subgraphs) that connect these subset of vertices?

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• Simple ranking algorithm in Groovy

  - by Richard Paul

  I have a short groovy algorithm for assigning rankings to food based on their rating. This can be run in the groovy console. The code works perfectly, but I'm wondering if there is a more Groovy or functional way of writing the code. Thinking it would be nice to get rid of the previousItem and rank local variables if possible. def food = [ [name:'Chocolate Brownie',rating:5.5, rank:null], [name:'Pizza',rating:3.4, rank:null], [name:'Icecream', rating:2.1, rank:null], [name:'Fudge', rating:2.1, rank:null], [name:'Cabbage', rating:1.4, rank:null]] food.sort { -it.rating } def previousItem = food[0] def rank = 1 previousItem.rank = rank food.each { item -> if (item.rating == previousItem.rating) { item.rank = previousItem.rank } else { item.rank = rank } previousItem = item rank++ } assert food[0].rank == 1 assert food[1].rank == 2 assert food[2].rank == 3 assert food[3].rank == 3 // Note same rating = same rank assert food[4].rank == 5 // Note, 4 skipped as we have two at rank 3 Suggestions?

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• Average performance of binary search algorithm?

  - by Passonate Learner

  http://en.wikipedia.org/wiki/Binary_search_algorithm#Average_performance BinarySearch(int A[], int value, int low, int high) { int mid; if (high < low) return -1; mid = (low + high) / 2; if (A[mid] > value) return BinarySearch(A, value, low, mid-1); else if (A[mid] < value) return BinarySearch(A, value, mid+1, high); else return mid; } If the integer I'm trying to find is always in the array, can anyone help me write a program that can calculate the average performance of binary search algorithm?

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• Algorithm to fill slots

  - by Peter Lang

  I am searching for an algorithm to fill several slots, which are already filled to some level. The current levels and the available quantity to fill are known Resulting levels should be as equal as possible, but existing level cannot be reduced Slots are filled from left to right, so left slots get higher level if equal level is impossible       The image above shows six examples, each column represents a slot. The grey area is already filled, the blue are is the expected position of the new elements. I could iterate through my slots and increase the quantity on the lowest slot by 1 until the available quantity is consumed, but I wonder about how to actually calculate the new filling levels. I am going to implement this with SQL/PL/SQL, other code is just as welcome though :)

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• Machine Learning Algorithm for Peer-to-Peer Nodes

  - by FreshCode

  I want to apply machine learning to a classification problem in a parallel environment. Several independent nodes, each with multiple on/off sensors, can communicate their sensor data with the goal of classifying an event as defined by a heuristic, training data or both. Each peer will be measuring the same data from their unique perspective and will attempt to classify the result while taking into account that any neighbouring node (or its sensors or just the connection to the node) could be faulty. Nodes should function as equal peers and determine the most likely classification by communicating their results. Ultimately each node should make a decision based on their own sensor data and their peers' data. If it matters, false positives are OK for certain classifications (albeit undesirable) but false negatives would be totally unacceptable. Given that each final classification will receive good or bad feedback, what would be an appropriate machine learning algorithm to approach this problem with if the nodes could communicate with each other to determine the most likely classification?

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• Algorithm - Numbering for TOC (Table of Contents)

  - by belisarius

  I want to implement a VBA function to number Excel rows based upon the grouping depth of the row. But I think a general algorithm for generating TOCs is more interesting. The problem is: Given a list of "indented" lines such as One Two Three Four Five Six (the "indentation level" may be assumed to be known and part of the input data) To generate the following output: 1. One 1.1 Two 1.1.1 Three 1.1.1.1 Four 1.2 Five 2. Six Of course my code is up and running ... and also hidden under THWoS (The Heavy Weight of Shame)

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• Evenly select N elems from array

  - by ninuhadida

  Hi, I need to evenly select n elements from an array. I guess the best way to explain is by example. say I have: array [0,1,2,3,4] and I need to select 3 numbers.. 0,3,4. of course, if the array length <= n, I just need to return the whole array. I'm pretty sure there's a defined algorithm for this, been trying to search, and I took a look at Introduction to algorithms but couldn't find anything that met my needs (probably overlooked it) The problem I'm having is that I can't figure out a way to scale this up to any array [ p..q ], selecting N evenly elements. note: I can't just select the even elements from the example above.. A couple other examples; array[0,1,2,3,4,5,6], 3 elements ; I need to get 0,3,6 array[0,1,2,3,4,5], 3 elements ; I need to get 0, either 2 or 3, and 5

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• Algorithm for finding the smallest power of two that's greater or equal to a given value

  - by Boyan

  I need to find the smallest power of two that's greater or equal to a given value. So far, I have this: int value = 3221; // 3221 is just an example, could be any number int result = 1; while (result < value) result <<= 1; It works fine, but feels kind of naive. Is there a better algorithm for that problem? EDIT. There were some nice Assembler suggestions, so I'm adding those tags to the question.

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• Computation geometry: find where's the triangle after rotation, tranlastion or reflection in a mirro

  - by newba

  Hi, I have a small contest problem in which is given a set of points, in 2D, that form a triangle. This triangle may be subject to an arbitrary rotation, may be subject to an arbitrary translation (both in the 2D plane) and may be subject to a reflection on a mirror, but its dimensions were kept unchanged. Then, they give me a set of points in the plane, and I have to find 3 points that form my triangle after one or more of those geometric operations. Example: 5 15 8 5 20 10 6 5 17 5 20 20 5 10 5 15 20 15 10 I bet that have to apply some known algorithm, but I don't know which. The most common are: convex hull, sweep plane, triangulation, etc. Can someone give a tip? I don't need the code, only a push, please!

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• Need some clarification on Bankers Algorithm

  - by Moonshield

  Hi, just a quick query about safe/unsafe states in Dijkstra's Banker's algorithm... If one of the processes in the snapshot of the system (for example the one below) already has all of its needs fulfilled and there are not sufficient resources available to fulfil the needs of any of the other processes, is the system in a safe state? I know normally we assume that once a process receives its required resources it will terminate soon after and return all resources, but is this assumption factored in when we calculate the state of the system? Allocated Maximum Available | A | B | A | B A | B ---+---+--- ---+---+--- ---+--- P1 | 1 | 2 P1 | 1 | 2 1 | 3 P2 | 5 | 3 P2 | 7 | 8

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• Algorithm to generate a list of unique combinations based on a list of numbers

  - by ross

  I would like to efficiently generate a unique list of combinations of numbers based on a starting list of numbers. example start list = [1,2,3,4,5] but the algorithm should work for [1,2,3...n] result = [1],[2],[3],[4],[5] [1,2],[1,3],[1,4],[1,5] [1,2,3],[1,2,4],[1,2,5] [1,3,4],[1,3,5],[1,4,5] [2,3],[2,4],[2,5] [2,3,4],[2,3,5] [3,4],[3,5] [3,4,5] [4,5] Note. I don't want duplicate combinations, although I could live with them, eg in the above example I don't really need the combination [1,3,2] because it already present as [1,2,3]

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• Machine Learning Algorithm for Parallel Nodes

  - by FreshCode

  I want to apply machine learning to a classification problem in a parallel environment. Several independent nodes, each with multiple on/off sensors, can communicate their sensor data with the goal of classifying an event defined by a heuristic, training data or both. Each peer will be measuring the same data from their unique perspective and will attempt to classify the result while taking into account that any neighbouring node (or its sensors or just the connection to the node) could be faulty. Nodes should function as equal peers and determine the most likely classification by communicating their results. Ultimately each node should make a decision based on their own sensor data and their peers' data. If it matters, false positives are OK (albeit undesirable) but false negatives are totally unacceptable. Given that each final classification will receive good or bad feedback, what would be an appropriate machine learning algorithm to approach this problem with if the nodes could communicate with each other to determine the most likely classification?

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• Algorithm - Pick the best combination of Armor (for a game)

  - by Chu

  I'm designing a piece of a game where the AI needs to determine which combination of armor will give the best overall stat bonus to the character. Each character will have about 10 stats, of which only 3-4 are important, and of those important ones, a few will be more important than the others. Armor will also give a boost to 1 or all stats. For example, a shirt might give +4 to the character's int and +2 stamina while at the same time, a pair of pants may have +7 strength and nothing else. So let's say that a character has a healthy choice of armor to use (5 pairs of pants, 5 pairs of gloves, etc.) We've designated that Int and Perception are the most important stats for this character. How could I write an algorithm that would determine which combination of armor and items would result in the highest of any given stat (say in this example Int and Perception)?

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• Algorithm to aggregate values from child tree nodes

  - by user222164

  I have objects in a tree structure, I would like to aggregate status information from children nodes and update parent node with aggregated status. Lets say node A has children B1, B2, and B1 has C1, C2, C3 as children. Each of the nodes have a status attribute. Now if C1, C2, C3 are all complete then I would like to mark B1 as completed. And if C4, C5,C6,C7 are complete make B2 as complete. When B1 and B2 are both complete mark A as complete. I can go through these nodes in brute force method and make updates, could someone suggest an efficient algorithm to do it. A { B1 { C1, C2, C3}, B2 { C4, C5, C6, C7} }

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• Matrix Comparison algorithm

  - by SysAdmin

  If you have 2 Matrices of dimensions N*M. what is the best way to get the difference Rect? Example: 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 4 5 4 3 2 3 <---> 2 3 2 3 2 3 2 3 2 3 4 5 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 | | \ / Rect([2,2] , [3,4]) 4 5 4 4 5 2-> A (2 x 3 Matrix) The best I could think of is to scan from Top-Left hit the point where there is difference. Then scan from Bottom Right and hit the point where there is a difference. But In worst case, this is O(N*M). is there a better efficient algorithm?

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• Redundancy algorithm for reading noisy bitstream

  - by Tedd Hansen

  I'm reading a lossy bit stream and I need a way to recover as much usable data as possible. There can be 1's in place of 0's and 0's in palce of 1's, but accuracy is probably over 80%. A bonus would be if the algorithm could compensate for missing/too many bits as well. The source I'm reading from is analogue with noise (microphone via FFT), and the read timing could vary depending on computer speed. I remember reading about algorithms used in CD-ROM's doing this in 3? layers, so I'm guessing using several layers is a good option. I don't remember the details though, so if anyone can share some ideas that would be great! :) Edit: Added sample data Best case data: in: 0000010101000010110100101101100111000000100100101101100111000000100100001100000010000101110101001101100111000101110000001001111011001100110000001001100111011110110101011100111011000100110000001000010111 out: 0010101000010110100101101100111000000100100101101100111000000100100001100000010000101110101001101100111000101110000001001111011001100110000001001100111011110110101011100111011000100110000001000010111011 Bade case (timing is off, samples are missing): out: 00101010000101101001011011001110000001001001011011001110000001001000011000000100001011101010011011001 in: 00111101001011111110010010111111011110000010010000111000011101001101111110000110111011110111111111101 Edit2: I am able to controll the data being sent. Currently attempting to implement simple XOR checking (though it won't be enough).

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• Algorithm to classify a list of products?

  - by Martin

  I have a list representing products which are more or less the same. For instance, in the list below, they are all Seagate hard drives. Seagate Hard Drive 500Go Seagate Hard Drive 120Go for laptop Seagate Barracuda 7200.12 ST3500418AS 500GB 7200 RPM SATA 3.0Gb/s Hard Drive New and shinny 500Go hard drive from Seagate Seagate Barracuda 7200.12 Seagate FreeAgent Desk 500GB External Hard Drive Silver 7200RPM USB2.0 Retail For a human being, the hard drives 3 and 5 are the same. We could go a little bit further and suppose that the products 1, 3, 4 and 5 are the same and put in other categories the product 2 and 6. We have a huge list of products that I would like to classify. Does anybody have an idea of what would be the best algorithm to do such thing. Any suggestions? I though of a Bayesian classifier but I am not sure if it is the best choice. Any help would be appreciated! Thanks.

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• Optimal sorting algorithm with modified cost... [closed]

  - by David

  The numbers are in a list that is not sorted and supports only one type of operation. The operation is defined as follows: Given a position i and a position j the operation moves the number at position i to position j without altering the relative order of the other numbers. If i j, the positions of the numbers between positions j and i - 1 increment by 1, otherwise if i < j the positions of the numbers between positions i+1 and j decreases by 1. This operation requires i steps to find a number to move and j steps to locate the position to which you want to move it. Then the number of steps required to move a number of position i to position j is i+j. Design an algorithm that given a list of numbers, determine the optimal(in terms of cost) sequence of moves to rearrange the sequence.

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