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• Brackets matching using BIT

  - by amit.codename13

  edit: I was trying to solve a spoj problem. Here is the link to the problem : http://spoj.pl/problems/BRCKTS I can think of two possible data structures for solving the problem one using segment tree and the other using a BIT. I have already implemented the solution using a segment tree. I have read about BIT but i can't figure out how to do a particular thing with it(which i have mentioned below) I am trying to check if brackets are balanced in a given string containing only ('s or )'s. I am using a BIT(Binary indexed tree) for solving the problem. The procedure i am following is as follows: I am taking an array of size equal to the number of characters in the string. I am assigning -1 for ) and 1 for ( to the corresponding array elements. Brackets are balanced in the string only if the following two conditions are true. The cumulative sum of the whole array is zero. Minimum cumulative sum is non negative. i.e the minimum of cumulative sums of all the prefixes of the array is non-negative. Checking condition 1 using a BIT is trivial. I am facing problem in checking condition 2.

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• I am trying to build a list of limitations of all graph algorithms

  - by Jack

  Single Source shortest Path Dijkstra's - directed and undirected - works only for positive edge weights - cycles ?? Bellman Ford - directed - no cycles should exist All source shortest path Floyd Warshall - no info Minimum Spanning Tree ( no info about edge weights or nature of graph or cycles) Kruskal's Prim's - undirected Baruvka's

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• RSA Factorization problem

  - by dada

  At class we found this programming problem, and currently, we have no idea how to solve it. The positive integer n is given. It is known that n = p * q, where p and q are primes, p<=q and |q-k*p|<10^5 for some given positive integer k. You must find p and q. Input: 35 1 121 1 1000730021 9 Output: 5 * 7 11 * 11 10007 * 100003 It's not a homework, we are just trying to solve some interesting problems. If you have some ideas, please post them here so we can try something, thanks.

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• CMYK + CMYK = ? CMYK / 2 = ?

  - by Pete

  Suppose there are two colors defined in CMYK: color1 = 30, 40, 50, 60 color2 = 50, 60, 70, 80 If they were to be printed what values would the resulting color have? color_new = min(cyan1 + cyan2, 100), min(magenta1 + magenta2, 100), min(yellow1 + yellow2, 100), min(black1 + black2, 100)? Suppose there is a color defined in CMYK: color = 40, 30, 30, 100 It is possible to print a color at partial intensity, i.e. as a tint. What values would have a 50% tint of that color? color_new = cyan / 2, magenta / 2, yellow / 2, black / 2? I'm asking this to better understand the "tintTransform" function in PDF Reference 1.7, 4.5.5 Special Color Spaces, DeviceN Color Spaces Update: To better clarify: I'm not entirely concerned with human perception or how the CMYK dyies react to the paper. If someone specifies 90% tint which, when printed, looks like full intensity colorant, that's ok. In other words, if I asking how to compute 50% of cmyk(40, 30, 30, 100) I'm asking how to compute the new values, regardless of whether the result looks half-dark or not. Update 2: I'm confused now. I checked this in InDesign and Acrobat. For example Pantone 3005 has CMYK 100, 34, 0, 2, and its 25% tint has CMYK 25, 8.5, 0, 0.5. Does it mean I can "monkey around in a linear way"?

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• Project euler problem 45

  - by Peter

  Hi, I'm not yet a skilled programmer but I thought this was an interesting problem and I thought I'd give it a go. Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: Triangle T_(n)=n(n+1)/2 1, 3, 6, 10, 15, ... Pentagonal P_(n)=n(3n-1)/2 1, 5, 12, 22, 35, ... Hexagonal H_(n)=n(2n-1) 1, 6, 15, 28, 45, ... It can be verified that T_(285) = P_(165) = H_(143) = 40755. Find the next triangle number that is also pentagonal and hexagonal. Is the task description. I know that Hexagonal numbers are a subset of triangle numbers which means that you only have to find a number where Hn=Pn. But I can't seem to get my code to work. I only know java language which is why I'm having trouble finding a solution on the net womewhere. Anyway hope someone can help. Here's my code public class NextNumber { public NextNumber() { next(); } public void next() { int n = 144; int i = 165; int p = i * (3 * i - 1) / 2; int h = n * (2 * n - 1); while(p!=h) { n++; h = n * (2 * n - 1); if (h == p) { System.out.println("the next triangular number is" + h); } else { while (h > p) { i++; p = i * (3 * i - 1) / 2; } if (h == p) { System.out.println("the next triangular number is" + h); break; } else if (p > h) { System.out.println("bummer"); } } } } } I realize it's probably a very slow and ineffecient code but that doesn't concern me much at this point I only care about finding the next number even if it would take my computer years :) . Peter

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• Chain call in clojure?

  - by Konrad Garus

  I'm trying to implement sieve of Eratosthenes in Clojure. One approach I would like to test is this: Get range (2 3 4 5 6 ... N) For 2 <= i <= N Pass my range through filter that removes multiplies of i For i+1th iteration, use result of the previous filtering I know I could do it with loop/recur, but this is causing stack overflow errors (for some reason tail call optimization is not applied). How can I do it iteratively? I mean invoking N calls to the same routine, passing result of ith iteration to i+1th.

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• total number of magic square from 9 numbers

  - by Peeyush

  9 numbers need to be arranged in a magic number square. A magic number square is a square of numbers that is arranged such that every row and column has the same sum.(condition for diagonal has been relaxed) For example: 1 2 3 3 2 1 2 2 2 How do we calculate total number of distinct magic square from 9 numbers. Two magic number squares are distinct if they differ in value at one or more positions. For example, there is only one magic number square that can be made of 9 instances of the same number. e.g. for these 9 numbers { 4, 4, 4, 4, 4, 4, 4, 4, 4 }, answer should be 1. Also the complexity should be optimal. Do we need to iterate through all the permutations , discarding if a[0]+a[1]+a[2] %3!=0 such combinations ? moreover how do we remove duplicate magic square?

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• Zoom image to pixel level

  - by zaf

  For an art project, one of the things I'll be doing is zooming in on an image to a particular pixel. I've been rubbing my chin and would love some advice on how to proceed. Here are the input parameters: Screen: sw - screen width sh - screen height Image: iw - image width ih - image height Pixel: px - x position of pixel in image py - y position of pixel in image Zoom: zf - zoom factor (0.0 to 1.0) Background colour: bc - background colour to use when screen and image aspect ratios are different Outputs: The zoomed image (no anti-aliasing) The screen position/dimensions of the pixel we are zooming to. When zf is 0 the image must fit the screen with correct aspect ratio. When zf is 1 the selected pixel fits the screen with correct aspect ratio. One idea I had was to use something like povray and move the camera towards a big image texture or some library (e.g. pygame) to do the zooming. Anyone think of something more clever with simple pseudo code? To keep it more simple you can make the image and screen have the same aspect ratio. I can live with that. I'll update with more info as its required.

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• Accenture interview question - Find the only unpaired element in the array

  - by karank

  You have been given an array of size 2n+1 that have n pair of integers(can be +ve, -ve or 0) and one unpaired element. How would you find the unpaired element. Pair means duplicate. So (3,3) is a pair and (3,-3) is not a pair.

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• MATLAB: Reading floating point numbers and strings from a file

  - by xsound

  I am using the following functions for writing and reading 4098 floating point numbers in MATLAB: Writing: fid = fopen(completepath, 'w'); fprintf(fid, '%1.30f\r\n', y) Reading: data = textread(completepath, '%f', 4098); where y contains 4098 numbers. I now want to write and read 3 strings at the end of this data. How do I read two different datatypes? Please help me. Thanks in advance.

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• Grouping php array items based on user and created time

  - by Jim

  This is an array of objects showing a user uploading photos: Array ( [12] => stdClass Object ( [type] => photo [created] => 2010-05-14 23:36:41 [user] => stdClass Object ( [id] => 760 [username] => mrsmith ) [photo] => stdClass Object ( [id] => 4181 ) ) [44] => stdClass Object ( [type] => photo [created] => 2010-05-14 23:37:15 [user] => stdClass Object ( [id] => 760 [username] => mrsmith ) [photo] => stdClass Object ( [id] => 4180 ) ) ) However instead of showing: mr smith uploaded one photo mr smith uploaded one photo I'd like to display: mr smith uploaded two photos by grouping similar items, grouping by user ID and them having added them within, let's say 15 minutes of each other. So I'd like to get the array in this sort of shape: Array ( [12] => stdClass Object ( [type] => photo [created] => 2010-05-14 23:36:41 [user] => stdClass Object ( [id] => 760 [username] => mrsmith ) [photos] => Array ( [0] => stdClass Object ( [id] => 4181 ) [1] => stdClass Object ( [id] => 4180 ) ) ) ) preserving the first item of the group and it's created time, and supplementing it with any other groupable photos and then unsetting any items that were grouped (so the final array doesn't have key 44 anymore as it was grouped in with 12). The array contains other actions than just photos, hence the original keys of 12 and 44. I just can't figure out a way to do this efficiently. I used to use MySQL and PHP to do this but am trying to just use pure PHP for caching reasons. Can anyone shed any insights? I thought about going through each item and seeing if I can group it with the previous one in the array but the previous one might not necessarily be relevant or even a photo. I've got total brain freeze :(

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• A shortest path problem with superheroes and intergalactic journeys

  - by Dman

  You are a super-hero in the year 2222 and you are faced with this great challenge: starting from your home planet Ilop you must try to reach Acinhet or else your planet will be destroyed by evil green little monsters. To do this you are given a map of the universe: there are N planets and M inter-planetary connections ( bidirectional ) that bind these planets. Each connection requires a certain time and a certain amount of fuel in order for you to cover the connection from one planet to another. The total time spent going from one planet to another is obtained by multiplying the time past to cover each connection between all the planets you go through. There are some "key planets", that allow you to refuel if you arrive on those certain "key planets". A "key planet" is the planet with the property that if it disappears the road between at least two planets would be lost.(In the example posted below with the input/output files such a "key planet" is 2 because without it the road to 7 would be lost) When you start your mission you are given the possibility of choosing between K ships each with its own maximum fuel capacity. The goal is to find the SHORTEST TIME CONSUMING path but also choose the ship with the minimum fuel capacity that can cover that shortest path(this means that if more ships can cover the shortest path you choose the one with the minimum fuel capacity). Because the minimum time can be a rather large number (over long long int) you are asked to provide only the last 6 digits of the number. For a better understanding of the task, here is an example of input/output files: INPUT: mission.in 7 8 6 1 4 6 5 9 8 7 10 1 2 7 8 1 4 14 9 1 5 3 1 2 3 1 2 2 7 7 1 3 4 2 2 4 6 4 1 5 6 3 7 On the first line (in order): N M K On the second line :the number for the starting planet and the finishing planet On the third line :K numbers that represent the capacities of the ships you can choose from Then you have M lines, all of them have the same structure: Xi Yi Ti Fi-which means that there is a connection between Xi and Yi and you can cover the distance from Xi to Yi in Ti time and with a Fi fuel consumption. OUTPUT:mission.out 000014 8 1 2 3 4 On the first line:the minimum time and fuel consumption; On the second line :the path Restrictions: 2 = N = 1 000 1 = M = 30 000 1 = K = 10 000 Any suggestions or ideas of how this problem might be solved would be most welcomed.

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• Easiest way of checking if a string consists of unique characters?

  - by serg555

  I need to check in Java if a word consists of unique letters (case insensitive). As straight solution is boring, I came up with: For every char in a string check if indexOf(char) == lastIndexOf(char). Add all chars to HashSet and check if set size == string length. Convert a string to a char array, sort it alphabetically, loop through array elements and check if c[i] == c[i+1]. Currently I like #2 the most, seems like the easiest way. Any other interesting solutions?

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• Finding a small image in a bigger one

  - by tur1ng

  Given an image with a large dimension ( 1.000 x 1.000). What is a good approach to find a small image (e.g. 50 x 50) in the big one? The smaller image can be rotated and differ in the size, but only with a 1:1 ratio. It's not related to any programming language - I'm just interested in pattern recognition. Thank you.

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• Find three numbers appeared only once

  - by shilk

  In a sequence of length n, where n=2k+3, that is there are k unique numbers appeared twice and three numbers appeared only once. The question is: how to find the three unique numbers that appeared only once? for example, in sequence 1 1 2 6 3 6 5 7 7 the three unique numbers are 2 3 5. Note: 3<=n<1e6 and the number will range from 1 to 2e9 Memory limits: 1000KB , this implies that we can't store the whole sequence. Method I have tried(Memory limit exceed): I initialize a tree, and when read in one number I try to remove it from the tree, if the remove returns false(not found), I add it to the tree. Finally, the tree has the three numbers. It works, but is Memory limit exceed. I know how to find one or two such number(s) using bit manipulation. So I wonder if we can find three using the same method(or some method similar)? Method to find one/two number(s) appeared only once: If there is one number appeared only once, we can apply XOR to the sequence to find it. If there are two, we can first apply XOR to the sequence, then separate the sequence into 2 parts by one bit of the result that is 1, and again apply XOR to the 2 parts, and we will find the answer.

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• comparison of sorting algorithms

  - by hash5

  When do we prefer a) bucket sort, and b) radix sort over comparison sorts like bubble sort insertion sort selection sort merge sort quick sort?

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• Recommend an algorithms exercise book?

  - by Parappa

  I have a little book called Problems on Algorithms by Ian Parberry which is chock full of exercises related to the study of algorithms. Can anybody recommend similar books? What I am not looking for are recommendations of good books related to algorithms or the theory of computation. Introduction to Algorithms is a good one, and of course there's the Knuth stuff. Ideally I want to know of any books that are light on instructional material and heavy on sample problems. In a nutshell, exercise books. Preferably dedicated to algorithms rather than general logic or other math problems. By the way, the Parberry book does not seem to be in print, but it is available as a PDF dowload.

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• Could a truly random number be generated using pings to psuedo-randomly selected IP addresses?

  - by _ande_turner_

  The question posed came about during a 2nd Year Comp Science lecture while discussing the impossibility of generating numbers in a deterministic computational device. This was the only suggestion which didn't depend on non-commodity-class hardware. Subsequently nobody would put their reputation on the line to argue definitively for or against it. Anyone care to make a stand for or against. If so, how about a mention as to a possible implementation?

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• How to check if a integer is sum of given integers?

  - by p3trix

  Lets say I have a integer result and an array of integers, lets say [a,b,c] (not a fixed length). I need to detect if result=a*i +b*j + c*k, with i,j,k=0. I prefer a solution in C/C# if it is possible. PS The problem is from a reservation system, a trip can be sold if its durations is a combination of given durations. Thanks!

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• Test if single linked list is circular by traversing it only once

  - by user1589754

  I am a fresher and I was asked this question in a recent interview I gave. The question was --- By traversing each element of linked list just once find if the single linked list is circular at any point. To this I answered that we will store reference of each node while traversing the list in another linked list and for every node in the list being tested we will find if the reference exists in the list I am storing the references. The interviewer said that he needs a more optimized way to solve this problem. Can anyone please tell me what would be a more optimized method to solve this problem.

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• What is the best emulator for MIX and/or MMIX?

  - by CrashCodes

  MIX is the hypothetical computer outlined by Donald Knuth in the Art of Computer Programming. I guess when I say best, I mean most suitable for working with the algorithms and problems in the Art of Computer Programming.

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• Fastest primality test

  - by Grigory Javadyan

  Hi. Could you suggest a fast, deterministic method that is usable in practice, for testing if a large number is prime or not? Also, I would like to know how to use non-deterministic primality tests correctly. For example, if I'm using such a method, I can be sure that a number is not prime if the output is "no", but what about the other case, when the output is "probably"? Do I have to test for primality manually in this case? Thanks in advance.

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• nth smallest number among two databases of size n each using divide and conquer

  - by urfriend

  we have two databases of size n containing numbers without repeats. So, in total we have 2n elements. They can be accessed through a query to one database at a time. The query is such that you give it a k and it returns kth smallest entry in that database. we need to find nth smallest entry among all the 2n elements in O(logn) queries. the idea is to use divide and conquer but i need some help thinking through this. thanks!

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• what is the idea behind scaling an image using lanczos?

  - by banister

  Hi, I'm interested in image scaling algorithms and have implemented the bilinear and bicubic methods. However, I have heard of the lanczos and other more sophisticated methods for even higher quality image scaling and I am very curious how they work. Could someone here explain the basic idea behind scaling an image using lanczos (both upscaling and downscaling) and why it results in higher quality? I do have a background in fourier analysis and have done some signal processing stuff in the past, but not with relation to image processing, so don't be afraid to use terms like "frequency response" and such in your answer :) EDIT: I guess what i really want to know is the concept and theory behind using a convolution filter for interpolation. (Note: i have already read the wikipedia article on lanczos resampling but it didn't have nearly enough detail for me) thanks alot!

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• Why do some questions get closed for no reason? [closed]

  - by IVlad

  Recently there was a question asking about generating all subsets of a set using a stack and a queue, which was closed (and now deleted it seems) as not a real question for no good reason, since it didn't fit into any of these conditions: It's difficult to tell what is being asked here. No, it was clear what was being asked. This question is ambiguous, vague, incomplete, or rhetorical and cannot be reasonably answered in its current form. Not ambiguous, not vague, not incomplete, definitely not rhetorical and could easily be answered if one knew the solution. Now, the exact same thing has happened with this question: http://stackoverflow.com/questions/2791982/a-shortest-path-problem-with-superheroes-and-intergalactic-journeys/2793746#2793746 I am interested in hearing a logical argument for why that question is either ambiguous, vague, incomplete, rhetorical or cannot reasonably be answered in its current form. It seems that (the same bunch of) people like to close questions that they think are homework questions, especially when they think people want to be served the solution on a platter, which is also not the case: Any suggestions or ideas of how this problem might be solved would be most welcomed. Most of the time the people asking these questions are very reasonable and appreciate even the most vague idea, yet their question is closed. Let's go further and assume that it IS a homework problem. So what? When I registered here I didn't see any rule that said not to post homework problems, nor do I see such a rule now. What is wrong with posting homework problems that makes people hunt them down with a passion to close them without even reading the entire question body? This site is full of questions asked by people who get paid to know the things they are asking, yet their questions are considered fine. How is solving someone's homework problem worse? In some places (like where I live), computer science is a mandatory high school subject, and not everyone is interested in it. How is helping at least those people worse than doing someone's JOB? Not answering homework questions is fine and it's everyone's choice, but I consider closing them to be an act of power abuse, selfishness, and an insult to the fellow community members who are also interested in a solution or want feedback on their proposed solution. So my questions are: - Why do questions like the above get closed for reasons that do not apply? Why do you close them? Why don't you? - Why doesn't a vote to reopen a question reopen it automatically? Needing 5 votes for a reopen takes too long, and it's not fair because one reopen vote basically cancels out a close vote, making it 4 close votes (or 5 to 1, which is the same as only 4 people wanting to close the question), which isn't enough to close the question. I think a question should only be closed when CloseVotes - ReopenVotes >= 5. I'm hoping this will stay up, but I realize it probably won't. In either case, I think this is worth saying and discussing, since it IS community-related.

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