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  • Convert a post-order binary tree traversal index to an level-order (breadth-first) index

    - by strfry
    Assuming a complete binary tree, each node can be adressed with the position it appears in a given tree traversal algorithm. For example, the node indices of a simple complete tree with height 3 would look like this: breadth first (aka level-order): 0 / \ 1 2 / \ / \ 3 4 5 6 post-order dept first: 6 / \ 2 5 / \ / \ 0 1 3 4 The height of the tree and an index in the post-order traversal is given. How can i calculate the breadth first index from this information?

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  • Divide sequence elements into pairs

    - by alex
    I have a sequence of 16 elements: 1,2,3,..., 16 ( or 2*n elements). Sequence elements always goes from 1 to length(sequence) that is sequence of 4 elements is 1,2,3,4. I want to write an algorithm which divide elements into pairs. For Example, 1-15 2-16 3-13 4-9 5-14 6-10 7-11 8-12 PS: no linq please :)

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  • Image in Image Algorithm

    - by Paul
    I need an algorithm written in any language to find an image inside of an image, including at different scales. Does anyone know a starting point to solving a problem like this? For example: I have an image of 800x600 and in that image is a yellow ball measuring 180 pixels in circumference. I need to be able to find this image with a search pattern of a yellow ball having a circumference of 15 pixels. Thanks

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  • Interesting task using random numbers only

    - by psihodelia
    Given any number of the random real numbers from the interval [0,1] is there exist any method to construct a floating point number with zero decimal part? Your algorithm can use only random() function calls and no variables or constants. No constants and variables are allowed, no type casting is allowed. You can use for/while, if/else or any other programming language operands.

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  • Code Golf: Countdown Number Game

    - by Noldorin
    Challenge Here is the task, inspired by the well-known British TV game show Countdown. The challenge should be pretty clear even without any knowledge of the game, but feel free to ask for clarifications. And if you fancy seeing a clip of this game in action, check out this YouTube clip. It features the wonderful late Richard Whitely in 1997. You are given 6 numbers, chosen at random from the set {1, 2, 3, 4, 5, 6, 8, 9, 10, 25, 50, 75, 100}, and a random target number between 100 and 999. The aim is to make use the six given numbers and the four common arithmetic operations (addition, subtraction, multiplication, division; all over the rational numbers) to generate the target - or as close as possible either side. Each number may only be used once at most, while each arithmetic operator may be used any number of times (including zero.) Note that it does not matter how many numbers are used. Write a function that takes the target number and set of 6 numbers (can be represented as list/collection/array/sequence) and returns the solution in any standard numerical notation (e.g. infix, prefix, postfix). The function must always return the closest-possible result to the target, and must run in at most 1 minute on a standard PC. Note that in the case where more than one solution exists, any single solution is sufficient. Examples: {50, 100, 4, 2, 2, 4}, target 203 e.g. 100 * 2 + 2 + (4 / 4) e.g. (100 + 50) * 4 * 2 / (4 + 2) {25, 4, 9, 2, 3, 10}, target 465 e.g. (25 + 10 - 4) * (9 * 2 - 3) {9, 8, 10, 5, 9, 7), target 241 e.g. ((10 + 9) * 9 * 7) + 8) / 5 Rules Other than mentioned in the problem statement, there are no further restrictions. You may write the function in any standard language (standard I/O is not necessary). The aim as always is to solve the task with the smallest number of characters of code. Saying that, I may not simply accept the answer with the shortest code. I'll also be looking at elegance of the code and time complexity of the algorithm! My Solution I'm attempting an F# solution when I find the free time - will post it here when I have something! Format Please post all answers in the following format for the purpose of easy comparison: Language Number of characters: ??? Fully obfuscated function: (code here) Clear (ideally commented) function: (code here) Any notes on the algorithm/clever shortcuts it takes.

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  • Cuboid inside generic polyhedron

    - by DOFHandler
    I am searching for an efficient algorithm to find if a cuboid is completely inside or completely outside or (not-inside and not-outside) a generic (concave or convex) polyhedron. The polyhedron is defined by a list of 3D points and a list of facets. Each facet is defined by the subset of the contour points ordinated such as the right-hand normal points outward the solid. Any suggestion? Thank you

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  • Find a regular expression that matches a string?

    - by Mirai
    I need a model for finding all of the regular expressions that would match a particular string. Basically, I need an algorithm for doing what I do to generate a regex search string from some pattern. My purpose for this to create a list of potential regular expressions from a selection of text and order that list from least specific (i.e. string of characters with abitrary length) to most specific (i.e. the string itself) to be used in text editor.

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  • faster strlen ?

    - by Jack
    Typical strlen() traverse from first character till it finds \0. This requires you to traverse each and every character. In algorithm sense, its O(N). Is there any faster way to do this where input is vaguely defined. Like: length would be less than 50, or length would be around 200 characters. I thought of lookup blocks and all but didn't get any optimization.

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  • What should students be taught first when first learning sorting algorithms?

    - by Johan
    If you were a programming teacher and you had to choose one sorting algorithm to teach your students which one would it be? I am asking for only one because I just want to introduce the concept of sorting. Should it be the bubble sort or the selection sort? I have noticed that these two are taught most often. Is there another type of sort that will explain sorting in an easier to understand way?

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  • Big Oh Notation - formal definition.

    - by aloh
    I'm reading a textbook right now for my Java III class. We're reading about Big-Oh and I'm a little confused by its formal definition. Formal Definition: "A function f(n) is of order at most g(n) - that is, f(n) = O(g(n)) - if a positive real number c and positive integer N exist such that f(n) <= c g(n) for all n = N. That is, c g(n) is an upper bound on f(n) when n is sufficiently large." Ok, that makes sense. But hold on, keep reading...the book gave me this example: "In segment 9.14, we said that an algorithm that uses 5n + 3 operations is O(n). We now can show that 5n + 3 = O(n) by using the formal definition of Big Oh. When n = 3, 5n + 3 <= 5n + n = 6n. Thus, if we let f(n) = 5n + 3, g(n) = n, c = 6, N = 3, we have shown that f(n) <= 6 g(n) for n = 3, or 5n + 3 = O(n). That is, if an algorithm requires time directly proportional to 5n + 3, it is O(n)." Ok, this kind of makes sense to me. They're saying that if n = 3 or greater, 5n + 3 takes less time than if n was less than 3 - thus 5n + n = 6n - right? Makes sense, since if n was 2, 5n + 3 = 13 while 6n = 12 but when n is 3 or greater 5n + 3 will always be less than or equal to 6n. Here's where I get confused. They give me another example: Example 2: "Let's show that 4n^2 + 50n - 10 = O(n^2). It is easy to see that: 4n^2 + 50n - 10 <= 4n^2 + 50n for any n. Since 50n <= 50n^2 for n = 50, 4n^2 + 50n - 10 <= 4n^2 + 50n^2 = 54n^2 for n = 50. Thus, with c = 54 and N = 50, we have shown that 4n^2 + 50n - 10 = O(n^2)." This statement doesn't make sense: 50n <= 50n^2 for n = 50. Isn't any n going to make the 50n less than 50n^2? Not just greater than or equal to 50? Why did they even mention that 50n <= 50n^2? What does that have to do with the problem? Also, 4n^2 + 50n - 10 <= 4n^2 + 50n^2 = 54n^2 for n = 50 is going to be true no matter what n is. And how in the world does picking numbers show that f(n) = O(g(n))? Please help me understand! :(

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  • Fastest way to find the largest power of 10 smaller than x

    - by peoro
    Is there any fast way to find the largest power of 10 smaller than a given number? I'm using this algorithm, at the moment, but something inside myself dies anytime I see it: 10**( int( math.log10(x) ) ) # python pow( 10, (int) log10(x) ) // C I could implement simple log10 and pow functions for my problems with one loop each, but still I'm wondering if there is some bit magic for decimal numbers.

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  • Flip Vertices Array

    - by James
    Hi, I have an array of position vertices that make up a 2D polygon. Vector2[] _chassisConcaveVertices = { new Vector2(5.122f, 0.572f), new Vector2(3.518f, 0.572f), new Vector2(3.458f, 0.169f), new Vector2(2.553f, 0.169f), new Vector2(2.013f, 0.414f), new Vector2(0.992f, 0.769f), new Vector2(0.992f, 1.363f), new Vector2(5.122f, 1.363f), }; What algorithm can I use to modify the positions so the resultant polygon is flipped? I need to flip the polygon both horizontally and vertically.

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  • resampling a series of points

    - by clamp
    hello, i have an array of points in 3d (imagine the trajectory of a ball) with X samples. now, i want to resample these points so that i have a new array with positions with y samples. y can be bigger or smaller than x but not smaller than 1. there will always be at least 1 sample. how would an algorithm look like to resample the original array into a new one? thanks!

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  • Adding to a bit array

    - by Martin
    In my program, I am using BitArrays to represent 160 bit numbers. I want to be able to add, subtract, increment and decrement these numbers, what is the algorithm for doing this? At the moment I'm not interested in multiplication and division, but I might be in the future so bonus points for that. I'm implementing in C#, but pseudocode is fine if you're not familiar with the language

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  • effective functonal sort

    - by sreservoir
    I'm programming a function for a ti-nspire, so I can't use the builtins from inside a function. what is the most generally efficient algorithm for sorting a list of numbers without modifying the list itself? (recursion and list-splitting are fair game, as is general use of math.)

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