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  • Given a number N, find the number of ways to write it as a sum of two or more consecutive integers

    - by hilal
    Here is the problem (Given a number N, find the number of ways to write it as a sum of two or more consecutive integers) and example 15 = 7+8, 1+2+3+4+5, 4+5+6 I solved with math like that : a + (a + 1) + (a + 2) + (a + 3) + ... + (a + k) = N (k + 1)*a + (1 + 2 + 3 + ... + k) = N (k + 1)a + k(k+1)/2 = N (k + 1)*(2*a + k)/2 = N Then check that if N divisible by (k+1) and (2*a+k) then I can find answer in O(N) time Here is my question how can you solve this by dynamic-programming ? and what is the complexity (O) ? P.S : excuse me, if it is a duplicate question. I searched but I can find

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  • How to detect if a certain range resides (partly) within an other range?

    - by Tom
    Lets say I've got two squares and I know their positions, a red and blue square: redTopX; redTopY; redBotX; redBotY; blueTopX; blueTopY; blueBotX; blueBotY; Now, I want to check if square blue resides (partly) within (or around) square red. This can happen in a lot of situations, as you can see in this image I created to illustrate my situation better: Note that there's always only one blue and one red square, I just added multiple so I didn't have to redraw 18 times. My original logic was simple, I'd check all corners of square blue and see if any of them are inside square red: if ( ((redTopX >= blueTopX) && (redTopY >= blueTopY) && (redTopX <= blueBotX) && (redTopY <= blueBotY)) || //top left ((redBotX >= blueTopX) && (redTopY >= blueTopY) && (redBotX <= blueBotX) && (redTopY <= blueBotY)) || //top right ((redTopX >= blueTopX) && (redBotY >= blueTopY) && (redTopX <= blueBotX) && (redBotY <= blueBotY)) || //bottom left ((redBotX >= blueTopX) && (redBotY >= blueTopY) && (redBotX <= blueBotX) && (redBotY <= blueBotY)) //bottom right ) { //blue resides in red } Unfortunately, there are a couple of flaws in this logic. For example, what if red surrounds blue (like in situation 1)? I thought this would be pretty easy but am having trouble coming up with a good way of covering all these situations.. can anyone help me out here? Regards, Tom

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  • Formula for popularity? (based on "like it", "comments", "views")

    - by paullb
    I have some pages on a website and I have to create an ordering based on "popularity"/"activity" The parameters that I have to use are: views to the page comments made on the page (there is a form at the bottom where uses can make comments) clicks made to the "like it" icon Are there any standards for what a formula for popularity would be? (if not opinions are good too) (initially I thought of views + 10*comments + 10*likeit)

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  • Can my tortoise vs. hare race be improved?

    - by FredOverflow
    Here is my code for detecting cycles in a linked list: do { hare = hare.next(); if (hare == back) return; hare = hare.next(); if (hare == back) return; tortoise = tortoise.next(); } while (tortoise != hare); throw new AssertionError("cyclic linkage"); Is there a way to get rid of the code duplication inside the loop? Am I right in assuming that I don't need a check after making the tortoise take a step forward? As I see it, the tortoise can never reach the end of the list before the hare (contrary to the fable). Any other ways to simplify/beautify this code?

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  • Picking apples off a tree

    - by John Retallack
    I have the following problem: I am given a tree with N apples, for each apple I am given it's weight and height. I can pick apples up to a given height H, each time I pick an apple the height of every apple is increased with U. I have to find out the maximum weight of apples I can pick. 1 = N = 100000 0 < {H, U, apples' weight and height, maximum weight} < 231 Example: N=4 H=100 U=10 height weight 82 30 91 10 93 5 94 15 The answer is 45: first pick the apple with the weight of 15 then the one with the weight of 30. Could someone help me approach this problem?

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  • maximum of given function

    - by davit-datuashvili
    first of all i am doing programs in java language this code is merely taken from web site i have not question about divide and conqurer but about function and it's argument here is code of ternary search def ternarySearch(f, left, right, absolutePrecision): #left and right are the current bounds; the maximum is between them if (right - left) < absolutePrecision: return (left + right)/2 leftThird = (2*left + right)/3 rightThird = (left + 2*right)/3 if f(leftThird) < f(rightThird): return ternarySearch(f, leftThird, right, absolutePrecision) return ternarySearch(f, left, rightThird, absolutePrecision) i am not asking once again how implement it in java i am asking for example how define function?for example let y=x^+3 yes we can determine it as public static int y(int x){ return x*x+3; } but here return ternarySearch(f, leftThird, right, absolutePrecision) function f does not have argument and how do such?please help me

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  • What are some practical uses of generating all permutations of a list, such as ['a', 'b', 'c'] ?

    - by Jian Lin
    I was asked by somebody in an interview for web front end job, to write a function that generates all permutation of a string, such as "abc" (or consider it ['a', 'b', 'c']). so the expected result from the function, when given ['a', 'b', 'c'], is abc acb bac bca cab cba Actually in my past 20 years of career, I have never needed to do something like that, especially when doing front end work for web programming. What are some practical use of this problem nowadays, in web programming, front end or back end, I wonder? As a side note, I kind of feel that expecting a result in 3 minutes might be "either he gets it or he doesn't", especially I was thinking of doing it by a procedural, non-recursive way at first. After the interview, I spent another 10 minutes and thought of how to do it using recursion, but expecting it to be solved within 3 minutes... may not be a good test of how qualified he is, especially for front end work.

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  • A quick way to map unordered list of longs to buffer location ?

    - by alhazen
    I have a large number of points (indexed by long) that are processed by multiple threads and I'm using a buffer to hold the output results in order. As the number of points processed is huge, what would be an efficient way to map the indexes of the points to the corresponding ordered position in the buffer ? Example: long bufferIndex bufferIndex index (if BufferSize = 2) (if BufferSize = 4) ---------------------------------------------- 2938 0 0 2939 1 1 2941 1 3 2940 0 2 Thanks.

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  • Creating objects makes the VM faster?

    - by Sudhir Jonathan
    Look at this piece of code: MessageParser parser = new MessageParser(); for (int i = 0; i < 10000; i++) { parser.parse(plainMessage, user); } For some reason, it runs SLOWER (by about 100ms) than for (int i = 0; i < 10000; i++) { MessageParser parser = new MessageParser(); parser.parse(plainMessage, user); } Any ideas why? The tests were repeated a lot of times, so it wasn't just random. How could creating an object 10000 times be faster than creating it once?

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  • Javascript plugins design pattern like jQuery

    - by Marco Demaio
    Could someone write down a very simple basic example in javascript to conceptualize (and hopefully make me understand) how the jQuery plugin design pattern is done and how it works? I'm not interested in how creating plugin for jQuery (so no jQuery code here at all). I'm interested in a simple explanation (maybe with a bit of Javascript code) to explain how it is done the plugin concept. Plz do not reply me to go and read jQuery code, I tried, but I it's too complex, otherwise I would have not post a question here.

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  • What's the best way to implement one-dimensional collision detection?

    - by cyclotis04
    I'm writing a piece of simulation software, and need an efficient way to test for collisions along a line. The simulation is of a train crossing several switches on a track. When a wheel comes within N inches of the switch, the switch turns on, then turns off when the wheel leaves. Since all wheels are the same size, and all switches are the same size, I can represent them as a single coordinate X along the track. Switch distances and wheel distances don't change in relation to each other, once set. This is a fairly trivial problem when done through brute force by placing the X coordinates in lists, and traversing them, but I need a way to do so efficiently, because it needs to be extremely accurate, even when the train is moving at high speeds. There's a ton of tutorials on 2D collision detection, but I'm not sure the best way to go about this unique 1D scenario.

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  • What is the optimum way to select the most dissimilar individuals from a population?

    - by Aaron D
    I have tried to use k-means clustering to select the most diverse markers in my population, for example, if we want to select 100 lines I cluster the whole population to 100 clusters then select the closest marker to the centroid from each cluster. The problem with my solution is it takes too much time (probably my function needs optimization), especially when the number of markers exceeds 100000. So, I will appreciate it so much if anyone can show me a new way to select markers that maximize diversity in my population and/or help me optimize my function to make it work faster. Thank you # example: library(BLR) data(wheat) dim(X) mdf<-mostdiff(t(X), 100,1,nstart=1000) Here is the mostdiff function that i used: mostdiff <- function(markers, nClust, nMrkPerClust, nstart=1000) { transposedMarkers <- as.array(markers) mrkClust <- kmeans(transposedMarkers, nClust, nstart=nstart) save(mrkClust, file="markerCluster.Rdata") # within clusters, pick the markers that are closest to the cluster centroid # turn the vector of which markers belong to which clusters into a list nClust long # each element of the list is a vector of the markers in that cluster clustersToList <- function(nClust, clusters) { vecOfCluster <- function(whichClust, clusters) { return(which(whichClust == clusters)) } return(apply(as.array(1:nClust), 1, vecOfCluster, clusters)) } pickCloseToCenter <- function(vecOfCluster, whichClust, transposedMarkers, centers, pickHowMany) { clustSize <- length(vecOfCluster) # if there are fewer than three markers, the center is equally distant from all so don't bother if (clustSize < 3) return(vecOfCluster[1:min(pickHowMany, clustSize)]) # figure out the distance (squared) between each marker in the cluster and the cluster center distToCenter <- function(marker, center){ diff <- center - marker return(sum(diff*diff)) } dists <- apply(transposedMarkers[vecOfCluster,], 1, distToCenter, center=centers[whichClust,]) return(vecOfCluster[order(dists)[1:min(pickHowMany, clustSize)]]) } }

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  • deteminant of matrix

    - by davit-datuashvili
    suppose there is given two dimensional array int a[][]=new int[4][4]; i am trying to find determinant of matrices please help i know how find it mathematical but i am trying to find it in programaticaly

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  • How to do "map chunks", like terraria or minecraft maps?

    - by O'poil
    Due to performance issues, I have to cut my maps into chunks. I manage the maps in this way: listMap[x][y] = new Tile (x,y); I tried in vain to cut this list for several "chunk" to avoid loading all the map because the fps are not very high with large map. And yet, when I update or Draw I do it with a little tile range. Here is how I proceed: foreach (List<Tile> list in listMap) { foreach (Tile leTile in list) { if ((leTile.Position.X < screenWidth + hero.Pos.X) && (leTile.Position.X > hero.Pos.X - tileSize) && (leTile.Position.Y < screenHeight + hero.Pos.Y) && (leTile.Position.Y > hero.Pos.Y - tileSize) ) { leTile.Draw(spriteBatch, gameTime); } } } (and the same thing, for the update method). So I try to learn with games like minecraft or terraria, and any two manages maps much larger than mine, without the slightest drop of fps. And apparently, they load "chunks". What I would like to understand is how to cut my list in Chunk, and how to display depending on the position of my character. I try many things without success. Thank you in advance for putting me on the right track! Ps : Again, sorry for my English :'( Pps : I'm not an experimented developer ;)

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  • sloving Algorithm notation

    - by neednewname
    Use big-O notation to classify the traditional grade school algorithms for addition and multiplication. That is, if asked to add two numbers each having N digits, how many individual additions must be performed? If asked to multiply two N-digit numbers, how many individual multiplications are required Suppose f is a function that returns the result of reversing the string of symbols given as its input, and g is a function that returns the concatenation of the two strings given as its input. If x is the string hrwa, what is returned by g(f(x),x)? Explain your answer - don't just provide the result!

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  • Counting bits set in a .Net BitArray Class

    - by Sam
    I am implementing a library where I am extensively using the .Net BitArray class and need an equivalent to the Java BitSet.Cardinality() method, i.e. a method which returns the number of bits set. I was thinking of implementing it as an extension method for the BitArray class. The trivial implementation is to iterate and count the bits set (like below), but I wanted a faster implementation as I would be performing thousands of set operations and counting the answer. Is there a faster way than the example below? count = 0; for (int i = 0; i < mybitarray.Length; i++) { if (mybitarray [i]) count++; }

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  • Sort string based upon the count of characters Options

    - by prp
    Sample Data : input : "abcdacdc" Output : "cadb" here we have to sort strings in order of count of characters. If the count is same for characters. maintain the original order of the characters from input string. my approach: i have used array of 26 for maintaining occurrence of all characters and sort it then print it.But while doing so i am not able to maintain order in case if two characters have same count. please suggest any improvement or any other algo.

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  • Setting last N bits in an array

    - by Martin
    I'm sure this is fairly simple, however I have a major mental block on it, so I need a little help here! I have an array of 5 integers, the array is already filled with some data. I want to set the last N bits of the array to be random noise. [int][int][int][int][int] set last 40 bits [unchanged][unchanged][unchanged][24 bits of old data followed 8 bits of randomness][all random] This is largely language agnostic, but I'm working in C# so bonus points for answers in C#

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  • parsing of mathematical expressions

    - by gcc
    (in c90) (linux) input: sqrt(2 - sin(3*A/B)^2.5) + 0.5*(C*~(D) + 3.11 +B) a b /*there are values for a,b,c,d */ c d input: cos(2 - asin(3*A/B)^2.5) +cos(0.5*(C*~(D)) + 3.11 +B) a b /*there are values for a,b,c,d */ c d input: sqrt(2 - sin(3*A/B)^2.5)/(0.5*(C*~(D)) + sin(3.11) +ln(B)) /*max lenght of formula is 250 characters*/ a b /*there are values for a,b,c,d */ c /*each variable with set of floating numbers*/ d As you can see infix formula in the input depends on user. My program will take a formula and n-tuples value. Then it calculate the results for each value of a,b,c and d. If you wonder I am saying ;outcome of program is graph. /sometimes,I think i will take input and store in string. then another idea is arise " I should store formula in the struct" but i don't know how I can construct the code on the base of structure./ really, I don't know way how to store the formula in program code so that I can do my job. can you show me? /* a,b,c,d is letters cos,sin,sqrt,ln is function*/

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