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  • Weakly connected balanced digraph

    - by user1074557
    How can I prove that if a balanced digraph is weakly connected, then it is also strongly connected? (balanced digraph means that for every node, it's indegree and outdegree is the same and weakly connected means the non-directed version of this graph is connected). What I can think of so far is: if the graph is balanced, it means it is a union of directed cycles. So if I remove any cycle, it will stay balanced. Also each vertex in the cycle has one edge coming into it and one edge leading out of it.. Then I guess I need to use some contradiction or induction to prove that the graph is strongly connected.. That's where I confused.

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  • Given the lat/lon of 2 close points on earth (<10m), How do I calculate the distance in metres?

    - by Rory
    I have the lat/lon of 2 points on the earth. They are really close together, <10m. Let's assume the earth is flat. How do I calculate the distance between them in metres? I know about tools (PostGIS, etc.) that can do this correctly, however I'm just doing a rough and ready type, and I'm OK with low accuracy. At such small sizes a difference of 1% is only 10cm, which is fine for me. I'm doing this in stock python. I'm OK with a standard Euclidean distance thing.

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  • Minimizing distance to a weighted grid

    - by Andrew Tomazos - Fathomling
    Lets suppose you have a 1000x1000 grid of positive integer weights W. We want to find the cell that minimizes the average weighted distance.to each cell. The brute force way to do this would be to loop over each candidate cell and calculate the distance: int best_x, best_y, best_dist; for x0 = 1:1000, for y0 = 1:1000, int total_dist = 0; for x1 = 1:1000, for y1 = 1:1000, total_dist += W[x1,y1] * sqrt((x0-x1)^2 + (y0-y1)^2); if (total_dist < best_dist) best_x = x0; best_y = y0; best_dist = total_dist; This takes ~10^12 operations, which is too long. Is there a way to do this in or near ~10^8 or so operations?

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  • Search inside dynamic array in python

    - by user2091683
    I want to implement a code that loops inside an array that its size is set by the user that means that the size isn't constant. for example: A=[1,2,3,4,5] then I want the output to be like this: [1],[2],[3],[4],[5] [1,2],[1,3],[1,4],[1,5] [2,3],[2,4],[2,5] [3,4],[3,5] [4,5] [1,2,3],[1,2,4],[1,2,5] [1,3,4],[1,3,5] and so on [1,2,3,4],[1,2,3,5] [2,3,4,5] [1,2,3,4,5] Can you help me implement this code?

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  • Loop through different sets of unique permutations

    - by user558610
    Hi I'm having a hard time getting started to layout code for this problem. I have a fixed amount of random numbers, in this case 8 numbers. R[] = { 1, 2, 3, 4, 5, 6, 7, 8 }; That are going to be placed in 3 sets of numbers, with the only constraint that each set contain minimum one value, and each value can only be used once. For example: R1[] = { 1, 4 } R2[] = { 2, 8, 5, 6 } R3[] = { 7, 4 } I need to loop through all possible combinations of a set R1, R2, R3. Order is not important, so if the above example happened, I don't need R1[] = { 4, 1 } R2[] = { 2, 8, 5, 6 } R3[] = { 7, 4 } NOR R1[] = { 2, 8, 5, 6 } R2[] = { 7, 4 } R3[] = { 1, 4 } What is a good method?

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  • How can I find the boundaries of a subset of a sorted list?

    - by Alex
    I have the following dilemma: I have a list of strings, and I want to find the set of string which start with a certain prefix. The list is sorted, so the naive solution is this: Perform binary search on the prefixes of the set, and when you find an element that starts with the prefix, traverse up linearly until you hit the top of the subset. This runs in linear time, however, and I was wondering if anyone can suggest a more efficient way to do it.

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  • question about Littles Law

    - by davit-datuashvili
    I know that Little's Law states (paraphrased): the average number of things in a system is the product of the average rate at which things leave the system and the average time each one spends in the system, or: n=x*(r+z); x-throughput r-response time z-think time r+z - average response time now i have question about a problem from programming pearls: Suppose that system makes 100 disk accesses to process a transaction (although some systems require fewer, some systems will require several hundred disk access per transaction). How many transactions per hour per disk can the system handle? please help

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  • binary number comparison

    - by EquinoX
    If I have a 32 bit two's complement number and I want to know what is the easiest way to know of two numbers are equal... what would be the fastest bitwise operator to know this? I know xor'ing both numbers and check if the results are zero works well... any other one's? how about if a number is greater than 0?? I can check the 31'st bit to see if it's greater or equal to 0..but how about bgtz?

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  • fill array with binary numbers

    - by davit-datuashvili
    hi, first of all this is not homework!! my question is from book: Algorithms in C++ third edition by robert sedgewick question is: there is given array of size n by 2^n(two dimensional) and we should fill it by binary numbers with bits size exactly n or for example n=5 so result will be 00001 00010 00011 00100 00101 00110 00111 and so on we should put this sequence of bits into arrays please help me

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  • Interview Q: given an array of numbers, return array of products of all other numbers (no division)

    - by polygenelubricants
    I was asked this question in a job interview, and I'd like to know how others would solve it. I'm most comfortable with Java, but solutions in other languages are welcome. Given an array of numbers, nums, return an array of numbers products, where products[i] is the product of all nums[j], j != i. Input : [1, 2, 3, 4, 5] Output: [(2*3*4*5), (1*3*4*5), (1*2*4*5), (1*2*3*5), (1*2*3*4)] = [120, 60, 40, 30, 24] You must do this in O(N) without using division.

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  • Common strategies to deal with rounding errors in currency-intensive soft?

    - by Max
    What is your advice on: compensation of accumulated error in bulk math operations on collections of Money objects. How is this implemented in your production code? (things like variable rounding, etc...) theory behind rounding in accountancy. any literature on topic. I currently read Fowler. He mentions Money type, but says nothing on strategies. Older posts on money-rounding (here, and here) do not provide a details and formality I need. Thanks for help.

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  • Need Multiple Sudoku Solutions

    - by user1567909
    I'm trying to output multiple sudoku solutions in my program. For example, when You enter this as input: 8..6..9.5.............2.31...7318.6.24.....73...........279.1..5...8..36..3...... .'s denote blank spaces. Numbers represent already-filled spaces. The output should be a sudoku solution like so: 814637925325149687796825314957318462241956873638274591462793158579481236183562749 However, I want to output multiple solutions. This would be all the solutions that should be printed: 814637925325149687796825314957318462241956873638274591462793158579481236183562749 814637925325941687796825314957318462241569873638472591462793158579184236183256749 834671925125839647796425318957318462241956873368247591682793154579184236413562789 834671925125839647796524318957318462241956873368247591682793154519482736473165289 834671925125839647796524318957318462241965873368247591682793154519482736473156289 But my program only prints out one solution. Below is my recursive solution to solving a sudoku solution bool sodoku::testTheNumber(sodoku *arr[9][9], int row, int column) { if(column == 9) { column = 0; row++; if(row == 9) return true; } if(arr[row][column]->number != 0) { return testTheNumber(arr, row, column+1); } for(int k = 1; k < 10; k++) { if(k == 10) { arr[row][column]->number = 0; return false; } if(rowIsValid(arr, k, row) && columnIsValid(arr, k, column) && boxIsValid(arr, k, row, column)) { arr[row][column]->number = k; if(testTheNumber(arr, row, column+1)==true) { return true; } arr[row][column]->number = 0; } } return false; } Could anyone help me come up with a way to print out multiple solutions? Thanks.

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  • longest increasing subsequent

    - by davit-datuashvili
    i have write this code is it correct? public class subsequent{ public static void main(String[] args){ int a[]=new int[]{0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15}; int a_b[]=new int[a.length]; a_b[0]=1; int int_max=0; int int_index=0; for (int i=0;i<a.length;i++){ for (int j=0;j<i;j++){ if (a[i]>a[j] && a_b[i]<(a_b[j]+1)){ a_b[i]=a_b[j]+1; } } if (a_b[i]>int_max){ int_max=a_b[i]; int_index=i; } } int k=int_max+1; int list[]=new int[k]; for (int i=int_index;i>0;i--){ if (a_b[i]==k-1){ list[k-1]=a[i]; k=a_b[i]; } } for (int g=0;g<list.length;g++){ System.out.println(list[g]); } } }

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  • question about permut-by-sorting

    - by davit-datuashvili
    hi i have following question from book introduction in algorithms second edition there is such problem suppose we have some array A int a[]={1,2,3,4} and we have some random priorities array P={36,3,97,19} we shoud permut array a randomly using this priorities array here is pseudo code P ERMUTE -B Y-S ORTING ( A) 1 n ? length[A] 2 for i ? 1 to n do P[i] = R ANDOM(1, n 3 ) 3 4 sort A, using P as sort keys 5 return A and result will be permuted array B={2, 4, 1, 3}; please help any ideas i have done this code and need aideas how continue import java.util.*; public class Permut { public static void main(String[]args){ Random r=new Random(); int a[]=new int[]{1,2,3,4}; int n=a.length; int b[]=new int[a.length]; int p[]=new int[a.length]; for (int i=0;i<p.length;i++){ p[i]=r.nextInt(n*n*n)+1; } // for (int i=0;i<p.length;i++){ // System.out.println(p[i]); //} } } please help

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  • Recurrent yearly date alert in Python

    - by coulix
    Hello Hackerz, Here is the idea A user can set a day alert for a birthday. (We do not care about the year of birth) He also picks if he wants to be alerted 0, 1, 2, ou 7 days (Delta) before the D day. Users have a timezone setting. I want the server to send the alerts at 8 am on the the D day - deleta +- user timezone Example: 12 jun, with "alert me 3 days before" will give 9 of Jun. My idea was to have a trigger_datetime extra field saved on the 'recurrent event' object. Like this a cron Job running every hour on my server will just check for all events matching irs current time hour, day and month and send to the alert. The problem from a year to the next the trigger_date could change ! If the alert is set on 1st of March, with a one day delay that could be either 28 or 29 of February .. Maybe i should not use the trigger date trick and use some other kind of scheme. All plans are welcome.

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  • i have question about job

    - by davit-datuashvili
    hi i will explain my situation i am study algorithms and data structures and i know many thing practical and others most thoereticaly and trying to implement in practise i want to get job where i will study more quickly i am interested if i have chance to start job when i have not expierence? thanks please advise what to do

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