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• question about missing element in array

  - by davit-datuashvili

  i have following problem from book introduction algorithm second edition by MIT university problem is following An array A[1 . . n] contains all the integers from 0 to n except one. It would be easy to determine the missing integer in O(n) time by using an auxiliary array B[0 . . n] to record which numbers appear in A. In this problem, however, we cannot access an entire integer in A with a single operation. The elements of A are represented in binary, and the only operation we can use to access them is “fetch the j th bit of A[i],” which takes constant time. Show that if we use only this operation, we can still determine the missing inte- ger in O(n) time please help

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• Color generation based on random number

  - by Mikulas Dite

  I would like to create a color generator based on random numbers, which might differ just slightly, but I need colors to be easily recognizable from each other. I was thinking about generation then in a rgb format which would be probably easiest. I'm afraid simply multiplying given arguments wouldn't do very well. What algorithm do you suggest using? Also, second generated color should not be the same as previous one, but I don't want to store them - nor multiplying with (micro)time would do well since the scripts' parts are usually faster.

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• Finding the heaviest of N objects using M scales

  - by cpprulez

  We have N objects and M scales. It's up to us what the objects are, and we need to position the objects on the scales so that it is undoubtful which is the heaviest object. For example, if we have 3 objects: "a", "b", "c" and 2 scales, one possible solution is "a" "b", "b" = "c" (here "a" is the heaviest). I need an algorithm which generates such solutions given N and M. Also let's assume that "a" is always the heaviest object. I've lost a few hours figuring out how to do it, but no matter what I figure out, there's always cases which I miss. For example, another solution is: "a" + "c" = 2 * "b", "a" "c".

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• Do "if" statements affect in the time complexity analysis?

  - by FranXh

  According to my analysis, the running time of this algorithm should be N2, because each of the loops goes once through all the elements. I am not sure whether the presence of the if statement changes the time complexity? for(int i=0; i<N; i++){ for(int j=1; j<N; j++){ System.out.println("Yayyyy"); if(i<=j){ System.out.println("Yayyy not"); } } }

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• Partition a rectangle into near-squares of given areas

  - by Marko Dumic

  I have a set of N positive numbers, and a rectangle of dimensions X and Y that I need to partition it in N smaller rectangles such that: the surface area of each smaller rectangle is proportional to it's corresponding number in given set all space of big rectangle is occupied and there is no leftover space between smaller rectangles each small rectangle should be shaped as close to square as feasible the execution time should be reasonably small I need directions on this. Do you know of such algorithm described on the web? Do you have any ideas (pseudo-code is fine)? Thanks.

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• Is it faster to loop through a Python set of number or a set of letters?

  - by Scott Bartell

  Is it faster to loop through a Python set of numbers or a Python set of letters given that each set is the exact same length and each item within each set is the same length? Why? I would think that there would be a difference because letters have more possible characters [a-zA-Z] than numbers [0-9] and therefor would be more 'random' and likely affect the hashing to some extent. numbers = set([00000,00001,00002,00003,00004,00005, ... 99999]) letters = set(['aaaaa','aaaab','aaaac','aaaad', ... 'aaabZZ']) # this is just an example, it does not actually end here for item in numbers: do_something() for item in letters: do_something() where len(numbers) == len(letters) Update: I am interested in Python's specific hashing algorithm and what happens behind the scenes with this implementation.

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• Modify a given number to find the required sum?

  - by Gaurav

  A friend of mine sent me this question. I haven't really been able to come up with any kind of algorithm to solve this problem. You are provided with a no. say 123456789 and two operators * and +. Now without changing the sequence of the provided no. and using these operators as many times as you wish, evaluate the given value: eg: given value 2097 Solution: 1+2+345*6+7+8+9 Any ideas on how to approach problems like these?

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• Simple prime number program - Weird issue with threads C#

  - by Para

  Hi! This is my code: using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading; namespace FirePrime { class Program { static bool[] ThreadsFinished; static bool[] nums; static bool AllThreadsFinished() { bool allThreadsFinished = false; foreach (var threadFinished in ThreadsFinished) { allThreadsFinished &= threadFinished; } return allThreadsFinished; } static bool isPrime(int n) { if (n < 2) { return false; } if (n == 2) { return true; } if (n % 2 == 0) { return false; } int d = 3; while (d * d <= n) { if (n % d == 0) { return false; } d += 2; } return true; } static void MarkPrimes(int startNumber,int stopNumber,int ThreadNr) { for (int j = startNumber; j < stopNumber; j++) nums[j] = isPrime(j); lock (typeof(Program)) { ThreadsFinished[ThreadNr] = true; } } static void Main(string[] args) { int nrNums = 100; int nrThreads = 10; //var threadStartNums = new List<int>(); ThreadsFinished = new bool[nrThreads]; nums = new bool[nrNums]; //var nums = new List<bool>(); nums[0] = false; nums[1] = false; for(int i=2;i<nrNums;i++) nums[i] = true; int interval = (int)(nrNums / nrThreads); //threadStartNums.Add(2); //int aux = firstStartNum; //int i = 2; //while (aux < interval) //{ // aux = interval*i; // i=i+1; // threadStartNums.Add(aux); //} int startNum = 0; for (int i = 0; i < nrThreads; i++) { var _thread = new System.Threading.Thread(() => MarkPrimes(startNum, Math.Min(startNum + interval, nrNums), i)); startNum = startNum + interval; //set the thread to run in the background _thread.IsBackground = true; //start our thread _thread.Start(); } while (!AllThreadsFinished()) { Thread.Sleep(1); } for (int i = 0; i < nrNums; i++) if(nums[i]) Console.WriteLine(i); } } } This should be a pretty simple program that is supposed to find and output the first nrNums prime numbers using nrThreads threads working in parallel. So, I just split nrNums into nrThreads equal chunks (well, the last one won't be equal; if nrThreads doesn't divide by nrNums, it will also contain the remainder, of course). I start nrThreads threads. They all test each number in their respective chunk and see if it is prime or not; they mark everything out in a bool array that keeps a tab on all the primes. The threads all turn a specific element in another boolean array ThreadsFinished to true when they finish. Now the weird part begins: The threads never all end. If I debug, I find that ThreadNr is not what I assign to it in the loop but another value. I guess this is normal since the threads execute afterwards and the counter (the variable i) is already increased by then but I cannot understand how to make the code be right. Can anyone help? Thank you in advance. P.S.: I know the algorithm is not very efficient; I am aiming at a solution using the sieve of Eratosthenes also with x given threads. But for now I can't even get this one to work and I haven't found any examples of any implementations of that algorithm anywhere in a language that I can understand.

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• How to calculate median of a Map<Int,Int>?

  - by Chris

  For a map where the key represents a number of a sequence and the value the count how often this number appeared in the squence, how would an implementation of an algorithm in java look like to calculate the median? For example: 1,1,2,2,2,2,3,3,3,4,5,6,6,6,7,7 in a map: Map<Int,Int> map = ... map.put(1,2) map.put(2,4) map.put(3,3) map.put(4,1) map.put(5,1) map.put(6,3) map.put(7,2) double median = calculateMedian(map); print(median); would result in: > print(median); 3 > So what i am looking for is a java implementation of calculateMedian.

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• Simple integer encryption

  - by tloflin

  Is there a simple algorithm to encrypt integers? That is, a function E(i,k) that accepts an n-bit integer and a key (of any type) and produces another, unrelated n-bit integer that, when fed into a second function D(i,k) (along with the key) produces the original integer? Obviously there are some simple reversible operations you can perform, but they all seem to produce clearly related outputs (e.g. consecutive inputs lead to consecutive outputs). Also, of course, there are cryptographically strong standard algorithms, but they don't produce small enough outputs (e.g. 32-bit). I know any 32-bit cryptography can be brute-forced, but I'm not looking for something cryptographically strong, just something that looks random. Theoretically speaking it should be possible; after all, I could just create a dictionary by randomly pairing every integer. But I was hoping for something a little less memory-intensive.

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• How to generate all permutations of a string in PHP ?

  - by Johan

  I need an algorithm that return all possible combination of all characters in one string. I've tried: $langd = strlen($input); for($i = 0;$i < $langd; $i++){ $tempStrang = NULL; $tempStrang .= substr($input, $i, 1); for($j = $i+1, $k=0; $k < $langd; $k++, $j++){ if($j > $langd) $j = 0; $tempStrang .= substr($input, $j, 1); } $myarray[] = $tempStrang; } But that only returns the same amount combination as the length of the string. Say the $input is = "hey", the result would be: hey, hye, eyh, ehy, yhe, yeh.

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• How to test if an array contains a pair of numbers whose product is odd?

  - by John

  How can I write a function that takes an array of integers and returns true if their exists a pair of numbers whose product is odd? What are the properties of odd integers? And of course, how do you write this function in Java? Also, maybe a short explanation of how you went about formulating an algorithm for the actual implementation. Yes, this is a function out of a textbook. No, this is not homework—I'm just trying to learn, so please no "do your own homework comments."

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• How to turn this simple 10 digit hex number back into 8 digits?

  - by Babil

  The algorithm to convert input 8 digit hex number into 10 digit are following: Given that the 8 digit number is: '12 34 56 78' x1 = 1 * 16^8 * 2^3 x2 = 2 * 16^7 * 2^2 x3 = 3 * 16^6 * 2^1 x4 = 4 * 16^4 * 2^4 x5 = 5 * 16^3 * 2^3 x6 = 6 * 16^2 * 2^2 x7 = 7 * 16^1 * 2^1 x8 = 8 * 16^0 * 2^0 Final 10 digit hex is: = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 = '08 86 42 98 E8' The problem is - how to go back to 8 digit hex from a given 10 digit hex (for example: 08 86 42 98 E8 to 12 34 56 78) Some sample input and output are following: input output 11 11 11 11 08 42 10 84 21 22 22 33 33 10 84 21 8C 63 AB CD 12 34 52 D8 D0 88 64 45 78 96 32 21 4E 84 98 62 FF FF FF FF 7B DE F7 BD EF

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• Who owes who money optimisation problem

  - by Francis

  Say you have n people, each who owe each other money. In general it should be possible to reduce the amount of transactions that need to take place. i.e. if X owes Y £4 and Y owes X £8, then Y only needs to pay X £4 (1 transaction instead of 2). This becomes harder when X owes Y, but Y owes Z who owes X as well. I can see that you can easily calculate one particular cycle. It helps for me when I think of it as a fully connected graph, with the nodes being the amount each person owes. Problem seems to be NP-complete, but what kind of optimisation algorithm could I make, nevertheless, to reduce the total amount of transactions? Doesn't have to be that efficient, as N is quite small for me.

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• Draw arrow on line

  - by Pete

  Hi, I have this code: CGPoint arrowMiddle = CGPointMake((arrowOne.x + arrowTo.x)/2, (arrowOne.y + arrowTo.y)/2); CGPoint arrowLeft = CGPointMake(arrowMiddle.x-40, arrowMiddle.y); CGPoint arrowRight = CGPointMake(arrowMiddle.x, arrowMiddle.y + 40); [arrowPath addLineToScreenPoint:arrowLeft]; [arrowPath addLineToScreenPoint:arrowMiddle]; [arrowPath addLineToScreenPoint:arrowRight]; [[mapContents overlay] addSublayer:arrowPath]; [arrowPath release]; with this output: http://yfrog.com/edschermafbeelding2010032p What have i to add to get the left and right the at same degree of the line + 30°. If someone has the algorithm of drawing an arrow on a line, pleas give it. It doesn't matter what programming language it is... Thanks

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• python parallel computing: split keyspace to give each node a range to work on

  - by MatToufoutu

  My question is rather complicated for me to explain, as i'm not really good at maths, but i'll try to be as clear as possible. I'm trying to code a cluster in python, which will generate words given a charset (i.e. with lowercase: aaaa, aaab, aaac, ..., zzzz) and make various operations on them. I'm searching how to calculate, given the charset and the number of nodes, what range each node should work on (i.e.: node1: aaaa-azzz, node2: baaa-czzz, node3: daaa-ezzz, ...). Is it possible to make an algorithm that could compute this, and if it is, how could i implement this in python? I really don't know how to do that, so any help would be much appreciated

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• 3D Mesh Joining

  - by morlst

  I have 2 (or more) intersecting meshes, which require joining into 1 mesh object. I want to have some control over the resulting seam vertex insertion, so looking to write myself rather than use a library. Has anyone come across some open source code to base the algorithm on / ideas on the process? Initial impressions are: 1. Present in every 3D modelling program - mostly reinventing existing process (hence search for examples) 2. Potential for fiddly-ness around the polygon face direction and just touching conditions. (see above point)

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• How to detect if breaking an edge will make a graph disjoint?

  - by the_graph_guy

  I have a graph that starts off with a single, root node. Nodes are added one by one to the graph. At node creation time, they have to be linked either to the root node, or to another node, by a single edge. Edges can also be created and deleted (one by one, between any two nodes). Nodes can be deleted one at a time. Node and edge creation, deletion operations can happen in any arbitrary order. OK, so here's my question: When an edge is deleted, is it possible do determine, in constant time (i.e. with an O(1) algorithm), if doing this will divide the graph into two disjoint subgraphs? If it will, then which side of the edge will the root node belong? I'm willing to maintain, within reasonable limits, any additional data structure that can facilitate the derivation of this information. Maybe it is not possible to do it in O(1), if so any pointers to literature will be appreciated.

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• Help with algorithm to determine phrase occurrence in string in PHP

  - by Will M.

  I have an array of phrases (max 2 words) like $words = array('barack obama', 'chicago', 'united states'); and then I have a string like: $sentence = "Barack Obama is from Chicago. Barack Obama's favorite food it pizza."; I want to find/create an efficient algorithm that would return the number of occurrences of the words in the array $words in the string $sentence. In this case it would be: 'barack obama' => 2 'chicago' => 0 How can I built this?

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• Make any posible combination of one string with php

  - by Johan

  I need an algorithm that return all possible combination of all characters in one string. I've tried: $langd = strlen($input); for($i = 0;$i < $langd; $i++){ $tempStrang = NULL; $tempStrang .= substr($input, $i, 1); for($j = $i+1, $k=0; $k < $langd; $k++, $j++){ if($j > $langd) $j = 0; $tempStrang .= substr($input, $j, 1); } $myarray[] = $tempStrang; } But that only returns the same amount combination as the length of the string. Say the $input is = "hey", the result would be: hey, hye, eyh, ehy, yhe, yeh.

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• Divide people into teams for most satisfaction

  - by Jweede

  Just a curiosity question. Remember when in class groupwork the professor would divide people up into groups of a certain number (n)? Some of my professors would take a list of n people one wants to work with and n people one doesn't want to work with from each student, and then magically turn out groups of n where students would be matched up with people they prefer and avoid working with people they don't prefer. To me this algorithm sounds a lot like a Knapsack problem, but I thought I would ask around about what your approach to this sort of problem would be.

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• merge three file into one big file

  - by davit-datuashvili

  suppose that we have three array int a[]=new int[]{4,6,8,9,11,12}; int b[]=new int[]{3,5,7,13,14}; int c[]=new int[]{1,2,15,16,17}; and we want to merge it into one big d array where d.length=a.length+b.length+c.length but we have memory problem it means that we must need use only this d array where we should merge these these three array of course we can use merge sort but can we use merge algorithm without sorting method? like two sorted array we can merge in one sorted array what about three or more array?

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• Randomly generating sequence of ints in a specific range

  - by vvv

  Hi, I am unsure how to put this and my math skills aren't that strong. But here's what I need. I want to generate a list of all the 16bit integers (0-65535). But everytime I do so I want to seed the algorithm randomly that each time the list starts with a different integer and all the subsequent integers will be generated once but also in random order. small example (1-5): ... 1, 5, 3, 2, 4 4, 3, 1, 5, 2 2, 1, 4, 5, 3 ... Any help?

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• Arrange 0's & 1's in a array

  - by Ganesh M

  This is one of an interview question which I had recently. I would like to know others perception of approach for this problem. Question: You are given a structure which holds an employee details with two elements as int Deptartment and string Name. struct Employee { string Name; int Dept; } You are given details of N Employees among which there are N/2 employees Dept are 0's and N/2 employees dept are 1's arranged in some random order. You need to sort the employee details based on their Dept value and it should be stable i.e., the order of 1s and 0s in the original record should be maintained. For example, given the following sample data: Name Dept X1 0 X2 1 X3 0 X4 1 X5 0 after sorting the result should be: Name Dept X2 1 X4 1 X1 0 X3 0 X5 0 The algorithm should be stable and the complexity should be o(N), with constant space for additional variables (which means sorting should be done in-place).

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• How do I pick the most beneficial combination of items from a set of items?

  - 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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