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  • How do I find the largest factor of an integer in mysql

    - by Bill H
    I am trying to write a select query that will dynamically determine the minimum number of items that can be packaged together. I am having trouble with one part of the query. ... CASE WHEN (pid.product_id) THEN 1 WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 11 = 0)) THEN CEILING(p.inner_pack / 11) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 7 = 0)) THEN CEILING(p.inner_pack / 7) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 6 = 0)) THEN CEILING(p.inner_pack / 6) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 5 = 0)) THEN CEILING(p.inner_pack / 5) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 4 = 0)) THEN CEILING(p.inner_pack / 4) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 3 = 0)) THEN CEILING(p.inner_pack / 3) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 2 = 0)) THEN CEILING(p.inner_pack / 2) ELSE p.inner_pack END AS min_pack ... What I want to do is find the largest factorial of an integer (p.inner_pack) that is under 12. Is there a better way to do this in mysql?

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  • Need some help understanding this problem

    - by Legend
    I was wondering if someone could help me understand this problem. I prepared a small diagram because it is much easier to explain it visually. Problem I am trying to solve: 1. Constructing the dependency graph Given the connectivity of the graph and a metric that determines how well a node depends on the other, order the dependencies. For instance, I could put in a few rules saying that node 3 depends on node 4 node 2 depends on node 3 node 3 depends on node 5 But because the final rule is not "valuable" (again based on the same metric), I will not add the rule to my system. 2. Execute the request order Once I built a dependency graph, execute the list in an order that maximizes the final connectivity. First and foremost, I am wondering if I constructed the problem correctly and if I should be aware of any corner cases. Secondly, is there a closely related algorithm that I can look at? Currently, I am thinking of something like Feedback Arc Set or the Secretary Problem but I am a little confused at the moment. Any suggestions? PS: I am a little confused about the problem myself so please don't flame on me for that. If any clarifications are needed, I will try to update the question.

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  • Why can't decimal numbers be represented exactly in binary?

    - by Barry Brown
    There have been several questions posted to SO about floating-point representation. For example, the decimal number 0.1 doesn't have an exact binary representation, so it's dangerous to use the == operator to compare it to another floating-point number. I understand the principles behind floating-point representation. What I don't understand is why, from a mathematical perspective, are the numbers to the right of the decimal point any more "special" that the ones to the left? For example, the number 61.0 has an exact binary representation because the integral portion of any number is always exact. But the number 6.10 is not exact. All I did was move the decimal one place and suddenly I've gone from Exactopia to Inexactville. Mathematically, there should be no intrinsic difference between the two numbers -- they're just numbers. By contrast, if I move the decimal one place in the other direction to produce the number 610, I'm still in Exactopia. I can keep going in that direction (6100, 610000000, 610000000000000) and they're still exact, exact, exact. But as soon as the decimal crosses some threshold, the numbers are no longer exact. What's going on? Edit: to clarify, I want to stay away from discussion about industry-standard representations, such as IEEE, and stick with what I believe is the mathematically "pure" way. In base 10, the positional values are: ... 1000 100 10 1 1/10 1/100 ... In binary, they would be: ... 8 4 2 1 1/2 1/4 1/8 ... There are also no arbitrary limits placed on these numbers. The positions increase indefinitely to the left and to the right.

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  • signed angle between two 3d vectors with same origin within the same plane? recipe?

    - by Advanced Customer
    Was looking through the web for an answer but it seems like there is no clear recipe for it. What I need is a signed angle of rotation between two vectors Va and Vb lying within the same 3D plane and having the same origin knowing that: the plane contatining both vectors is an arbitrary and is not parallel to XY or any other of cardinal planes Vn - is a plane normal both vectors along with the normal have the same origin O = { 0, 0, 0 } Va - is a reference for measuring the left handed rotation at Vn The angle should be measured in such a way so if the plane would be XY plane the Va would stand for X axis unit vector of it. I guess I should perform a kind of coordinate space transformation by using the Va as the X-axis and the cross product of Vb and Vn as the Y-axis and then just using some 2d method like with atan2() or something. Any ideas? Formulas?

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  • Solving simultaneous equations

    - by Milo
    Here is my problem: Given x, y, z and ratio where z is known and ratio is known and is a float representing a relative value, I need to find x and y. I know that: x / y == ratio y - x == z What I'm trying to do is make my own scroll pane and I'm figuring out the scrollbar parameters. So for example, If the scrollbar must be able to scroll 100 values (z) and the thumb must consume 80% of the bar (ratio = 0.8) then x would be 400 and y would be 500. Thanks

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  • How would I find all sets of N single-digit, non-repeating numbers that add up to a given sum in PHP

    - by TerranRich
    Let's say I want to find all sets of 5 single-digit, non-repeating numbers that add up to 30... I'd end up with [9,8,7,5,1], [9,8,7,4,2], [9,8,6,4,3], [9,8,6,5,2], [9,7,6,5,3], and [8,7,6,5,4]. Each of those sets contains 5 non-repeating digits that add up to 30, the given sum. Any help would be greatly appreciated. Even just a starting point for me to use would be awesome. I came up with one method, which seems like a long way of going about it: get all unique 5-digit numbers (12345, 12346, 12347, etc.), add up the digits, and see if it equals the given sum (e.g. 30). If it does, add it to the list of possible matching sets. I'm doing this for a personal project, which will help me in solving Kakuro puzzles without actually solving the whole thing at once. Yeah, it may be cheating, but it's... it's not THAT bad... :P

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  • Ruby BigDecimal sanity check (floating point newb)

    - by Andy
    Hello, Hoping to get some feedback from someone more experienced here. I haven't dealt with the dreaded floating-point calculation before... Is my understanding correct that with Ruby BigDecimal types (even with varying precision and scale lengths) should calculate accurately or should I anticipate floating point shenanigans? All my values within a Rails application are BigDecimal type and I'm seeing some errors (they do have different decimal lengths), hoping it's just my methods and not my object types... Thanks!

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  • Moving a Ball on iPhone

    - by Chandan Shetty SP
    I am using below formula to move the ball circular, where accelX and accelY are the values from accelerometer, it is working fine. But the problem in this code is mRadius(I fixed its value to 50), i need to change mRadius according to accelerometer values and also i need bouncing effect when it touches other circles please send your answers ASAP... I am waiting. float degrees = -atan2(accelX, accelY) * 180 / 3.14159; int x = cCentrePoint.x + mRadius * cos(degreesToRadians(degrees)); int y = cCentrePoint.y + mRadius * sin(degreesToRadians(degrees)); Here is the snap of the game i want to develop. http://iphront.com/wp-content/uploads/2009/12/bdece528ea334033.jpg.jpg

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  • C# method to scale values?

    - by John S
    Hello, I have a value range from 0 to 255. There is a method that returns an array with a min and max values within this range, i.e: 13, 15, 20, 27, 50 ... 240 where 13 is the min and 240 is the max I need to scale these values so that 13 becomes 0 and 240 becomes 255 and scale all the other values between them proportionally. Is there any C# method that does that? thanks!

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  • approximating log10[x^k0 + k1]

    - by Yale Zhang
    Greetings. I'm trying to approximate the function Log10[x^k0 + k1], where .21 < k0 < 21, 0 < k1 < ~2000, and x is integer < 2^14. k0 & k1 are constant. For practical purposes, you can assume k0 = 2.12, k1 = 2660. The desired accuracy is 5*10^-4 relative error. This function is virtually identical to Log[x], except near 0, where it differs a lot. I already have came up with a SIMD implementation that is ~1.15x faster than a simple lookup table, but would like to improve it if possible, which I think is very hard due to lack of efficient instructions. My SIMD implementation uses 16bit fixed point arithmetic to evaluate a 3rd degree polynomial (I use least squares fit). The polynomial uses different coefficients for different input ranges. There are 8 ranges, and range i spans (64)2^i to (64)2^(i + 1). The rational behind this is the derivatives of Log[x] drop rapidly with x, meaning a polynomial will fit it more accurately since polynomials are an exact fit for functions that have a derivative of 0 beyond a certain order. SIMD table lookups are done very efficiently with a single _mm_shuffle_epi8(). I use SSE's float to int conversion to get the exponent and significand used for the fixed point approximation. I also software pipelined the loop to get ~1.25x speedup, so further code optimizations are probably unlikely. What I'm asking is if there's a more efficient approximation at a higher level? For example: Can this function be decomposed into functions with a limited domain like log2((2^x) * significand) = x + log2(significand) hence eliminating the need to deal with different ranges (table lookups). The main problem I think is adding the k1 term kills all those nice log properties that we know and love, making it not possible. Or is it? Iterative method? don't think so because the Newton method for log[x] is already a complicated expression Exploiting locality of neighboring pixels? - if the range of the 8 inputs fall in the same approximation range, then I can look up a single coefficient, instead of looking up separate coefficients for each element. Thus, I can use this as a fast common case, and use a slower, general code path when it isn't. But for my data, the range needs to be ~2000 before this property hold 70% of the time, which doesn't seem to make this method competitive. Please, give me some opinion, especially if you're an applied mathematician, even if you say it can't be done. Thanks.

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  • Determining polygon intersection and containment

    - by Victor Liu
    I have a set of simple (no holes, no self-intersections) polygons, and I need to check that they don't intersect each other (one can be entirely contained in another; that is okay). I can check this by simply checking the per-vertex inside-ness of one polygon versus other polygons. I also need to determine the containment tree, which is the set of relationships that say which polygon contains any given polygon. Since no polygon can intersect any other, then any contained polygon has a unique container; the "next-bigger" one. In other words, if A contains B contains C, then A is the parent of B, and B is the parent of C, and we don't consider A the parent of C. The question: How do I efficiently determine the containment relationships and check the non-intersection criterion? I ask this as one question because maybe a combined algorithm is more efficient than solving each problem separately. The algorithm should take as input a list of polygons, given by a list of their vertices. It should produce a boolean B indicating if none of the polygons intersect any other polygon, and also if B = true, a list of pairs (P, C) where polygon P is the parent of child C. This is not homework. This is for a hobby project I am working on.

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  • Extend and Overload MS and Point Types

    - by dr d b karron
    Do I have make my own Point and Vector types to overload them ? Why does this not work ? namespace System . windows { public partial struct Point : IFormattable { public static Point operator * ( Point P , double D ) { Point Po = new Point ( ); return Po; } } } namespace SilverlightApplication36 { public partial class MainPage : UserControl { public static void ShrinkingRectangle ( WriteableBitmap wBM , int x1 , int y1 , int x2 , int y2 , Color C ) { wBM . DrawRectangle ( x1 , y1 , x2 , y2 , Colors . Red ); Point Center = Mean ( x1 , y1 , x2 , y2 ); wBM . SetPixel ( Center , Colors.Blue , 3 ); Point P1 = new Point ( x1 , y1 ); Point P2 = new Point ( x1 , y2 ); Point P3 = new Point ( x1 , y2 ); Point P4 = new Point ( x2 , y1 ); const int Steps = 10; for ( int i = 0 ; i < Steps ; i++ ) { double iF = (double)(i+1) / (double)Steps; double jF = ( 1.0 - iF ); Point P11 = **P1 * jF;** } }

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  • Position elements without overlap

    - by eWolf
    I have a number of rectangular elements that I want to position in a 2D space. I calculate an ideal position for each element. Now my problem is that many elements overlap as very often the ideal positions are concentrated in one region. I want to avoid overlap as much as possible (doesn't have to be perfect, though). How can I do this? I've heard physics simulations are suitable for this - is that correct? And can anyone provide an example/tutorial? By the way: I'm using XNA, if you know any .NET library that does exactly this job - tell me!

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  • If we make a number every millisecond, how much data would we have in a day?

    - by Roger Travis
    I'm a bit confused here... I'm being offered to get into a project, where would be an array of certain sensors, that would give off reading every millisecond ( yes, 1000 reading in a second ). Reading would be a 3 or 4 digit number, for example like 818 or 1529. This reading need to be stored in a database on a server and accessed remotely. I never worked with such big amounts of data, what do you think, how much in terms of MBs reading from one sensor for a day would be?... 4(digits)x1000x60x60x24 ... = 345600000 bits ... right ? about 42 MB per day... doesn't seem too bad, right? therefor a DB of, say, 1 GB, would hold 23 days of info from 1 sensor, correct? I understand that MySQL & PHP probably would not be able to handle it... what would you suggest, maybe some aps? azure? oracle? ... Thansk!

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  • Inverse relationship of two variables

    - by Jam
    this one is maybe pretty stupid.. Or I am just exhausted or something, but I just cant seem to solve it.. Problem : two variables X and Y, value of Y is dependent on value of X. X can have values ranging from some value to some value (lets say from 0 to 250) and y can have different values (lets say from 0.1 to 1.0 or something..) - but it is inverse relatonship (what I mean is: if value of X is e.g. 250, then value of Y would be 0.1 and when X decreases up to 0, value of Y raises up to 1.0.. So how should I do it? lets say I have function: -- double computeValue (double X) { /computation/ return Y; } Also, is there some easy way to somehow make the scaling of the function not so linear? - For example when X raises, Y decreases slower at first but then more rapidly in the end.. (rly dont know how to say it but I hope you guys got it) Thanks in advance for this stupid question :/

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  • How to solve generic algebra using solver/library programmatically? Matlab, Mathematica, Wolfram etc?

    - by DevDevDev
    I'm trying to build an algebra trainer for students. I want to construct a representative problem, define constraints and relationships on the parameters, and then generate a bunch of Latex formatted problems from the representation. As an example: A specific question might be: If y < 0 and (x+3)(y-5) = 0, what is x? Answer (x = -3) I would like to encode this as a Latex formatted problem like. If $y<0$ and $(x+constant_1)(y+constant_2)=0$ what is the value of x? Answer = -constant_1 And plug into my problem solver constant_1 > 0, constant_1 < 60, constant_1 = INTEGER constant_2 < 0, constant_2 > -60, constant_2 = INTEGER Then it will randomly construct me pairs of (constant_1, constant_2) that I can feed into my Latex generator. Obviously this is an extremely simple example with no real "solving" but hopefully it gets the point across. Things I'm looking for ideally in priority order * Solve algebra problems * Definition of relationships relatively straight forward * Rich support for latex formatting (not just writing encoded strings) Thanks!

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  • Express highest floating point quantity that is less than 1

    - by edA-qa mort-ora-y
    I was doing some rounding calculations and happened upon a question. How can I express the highest quantity less than 1 for a given floating point type? That is, how I write/represent value x such that x < 1, x + y >= 1 for any y > 0. In fractions this would be x = (q-1)/q where q is the precision of the type. For example, if you are counting in 1/999 increments then x = 998/999. For a given type (float, double, long double), how could one express the value x in code? I also wonder if such a value actually exists for all values of y. That is, as y's exponent gets smaller perhaps the relation doesn't hold anymore. So an answer with some range restriction on y is also acceptable. (The value of x I want still does exist, the relationship may just not properly express it.)

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  • Detecting periodic repetitions in the data stream

    - by pulegium
    Let's say I have an array of zeros: a = numpy.zeros(1000) I then introduce some repetitive 'events': a[range(0, 1000, 30)] = 1 Question is, how do I detect the 'signal' there? Because it's far from the ideal signal if I do the 'regular' FFT I don't get a clear indication of where my 'true' signal is: f = abs(numpy.fft.rfft(a)) Is there a method to detect these repetitions with some degree of certainty? Especially if I have few of those mixed in, for example here: a[range(0, 1000, 30)] = 1 a[range(0, 1000, 110)] = 1 a[range(0, 1000, 48)] = 1 I'd like to get three 'spikes' on the resulting data...

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  • Learning Basic Mathematics

    - by NeedsToKnow
    I'm going to just come out and say it. I'm 20 and can't do maths. Two years ago I passed the end-of-high-school mathematics exam (but not at school), and did pretty well. Since then, I haven't done a scrap of mathematics. I wondered just how bad I had gotten, so I was looking at some simple algebra problems. You know, the kind you learn halfway through highschool. 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 Couldn't do them. I've got half a year left until I start a Computer Science undergraduate degree. I love designing and creating programs, and I remember I loved mathematics back when I did it. Basically, I've had a pretty bad education, but I want to be knowledgable in these areas. I was thinking of buying some high school textbooks and reading them, but I'm not sure this is the right way to go. I need to start off at some basic level and work towards a greater understanding. My question is: What should I study, how should I study, and what books can you recommend? Thanks!

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  • A simple algorithm for polygon intersection

    - by Elazar Leibovich
    I'm looking for a very simple algorithm for computing the polygon intersection/clipping. That is, given polygons P, Q, I wish to find polygon T which is contained in P and in Q, and I wish T to be maximal among all possible polygons. I don't mind the run time (I have a few very small polygons), I can also afford getting an approximation of the polygons' intersection (that is, a polygon with less points, but which is still contained in the polygons' intersection). But it is really important for me that the algorithm will be simple (cheaper testing) and preferably short (less code). edit: please note, I wish to obtain a polygon which represent the intersection. I don't need only a boolean answer to the question of whether the two polygons intersect.

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  • How to maintain decimal percision in calculations

    - by Blankman
    I need to sum 2 decimal values together, then divide by 2 and convert to string. My calculation currently is trimming to 2 decimal places, but I want to keep as many decimals as I can. city.Latitude = ( (lat.North + lat.South) / 2 ).ToString(); the values for lat.North and lat.Souch are like: 55.32342322

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