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  • make tree in scheme

    - by ???
    (define (entry tree) (car tree)) (define (left-branch tree) (cadr tree)) (define (right-branch tree) (caddr tree)) (define (make-tree entry left right) (list entry left right)) (define (mktree order items_list) (cond ((= (length items_list) 1) (make-tree (car items_list) '() '())) (else (insert2 order (car items_list) (mktree order (cdr items_list)))))) (define (insert2 order x t) (cond ((null? t) (make-tree x '() '())) ((order x (entry t)) (make-tree (entry t) (insert2 order x (left-branch t)) (right-branch t))) ((order (entry t) x ) (make-tree (entry t) (left-branch t) (insert2 order x (right-branch t)))) (else t))) The result is: (mktree (lambda (x y) (< x y)) (list 7 3 5 1 9 11)) (11 (9 (1 () (5 (3 () ()) (7 () ()))) ()) ()) But I'm trying to get: (7 (3 (1 () ()) (5 () ())) (9 () (11 () ()))) Where is the problem?

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  • BFS algorithm problem

    - by Gorkamorka
    The problem is as follows: A wanderer begins on the grid coordinates (x,y) and wants to reach the coordinates (0,0). From every gridpoint, the wanderer can go 8 steps north OR 3 steps south OR 5 steps east OR 6 steps west (8N/3S/5E/6W). How can I find the shortest route from (X,Y) to (0,0) using breadth-first search? Clarifications: Unlimited grid Negative coordinates are allowed A queue (linked list or array) must be used No obstacles present

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  • What is it about Fibonacci numbers?

    - by Ian Bishop
    Fibonacci numbers have become a popular introduction to recursion for Computer Science students and there's a strong argument that they persist within nature. For these reasons, many of us are familiar with them. They also exist within Computer Science elsewhere too; in surprisingly efficient data structures and algorithms based upon the sequence. There are two main examples that come to mind: Fibonacci heaps which have better amortized running time than binomial heaps. Fibonacci search which shares O(log N) running time with binary search on an ordered array. Is there some special property of these numbers that gives them an advantage over other numerical sequences? Is it a density quality? What other possible applications could they have? It seems strange to me as there are many natural number sequences that occur in other recursive problems, but I've never seen a Catalan heap.

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  • question about qsort in c++

    - by davit-datuashvili
    i have following code in c++ #include <iostream> using namespace std; void qsort5(int a[],int n){ int i; int j; if (n<=1) return; for (i=1;i<n;i++) j=0; if (a[i]<a[0]) swap(++j,i,a); swap(0,j,a); qsort5(a,j); qsort(a+j+1,n-j-1); } int main() { return 0; } void swap(int i,int j,int a[]) { int t=a[i]; a[i]=a[j]; a[j]=t; } i have problem 1>c:\users\dato\documents\visual studio 2008\projects\qsort5\qsort5\qsort5.cpp(13) : error C2780: 'void std::swap(std::basic_string<_Elem,_Traits,_Alloc> &,std::basic_string<_Elem,_Traits,_Alloc> &)' : expects 2 arguments - 3 provided 1> c:\program files\microsoft visual studio 9.0\vc\include\xstring(2203) : see declaration of 'std::swap' 1>c:\users\dato\documents\visual studio 2008\projects\qsort5\qsort5\qsort5.cpp(13) : error C2780: 'void std::swap(std::pair<_Ty1,_Ty2> &,std::pair<_Ty1,_Ty2> &)' : expects 2 arguments - 3 provided 1> c:\program files\microsoft visual studio 9.0\vc\include\utility(76) : see declaration of 'std::swap' 1>c:\users\dato\documents\visual studio 2008\projects\qsort5\qsort5\qsort5.cpp(13) : error C2780: 'void std::swap(_Ty &,_Ty &)' : expects 2 arguments - 3 provided 1> c:\program files\microsoft visual studio 9.0\vc\include\utility(16) : see declaration of 'std::swap' 1>c:\users\dato\documents\visual studio 2008\projects\qsort5\qsort5\qsort5.cpp(14) : error C2780: 'void std::swap(std::basic_string<_Elem,_Traits,_Alloc> &,std::basic_string<_Elem,_Traits,_Alloc> &)' : expects 2 arguments - 3 provided 1> c:\program files\microsoft visual studio 9.0\vc\include\xstring(2203) : see declaration of 'std::swap' 1>c:\users\dato\documents\visual studio 2008\projects\qsort5\qsort5\qsort5.cpp(14) : error C2780: 'void std::swap(std::pair<_Ty1,_Ty2> &,std::pair<_Ty1,_Ty2> &)' : expects 2 arguments - 3 provided 1> c:\program files\microsoft visual studio 9.0\vc\include\utility(76) : see declaration of 'std::swap' 1>c:\users\dato\documents\visual studio 2008\projects\qsort5\qsort5\qsort5.cpp(14) : error C2780: 'void std::swap(_Ty &,_Ty &)' : expects 2 arguments - 3 provided 1> c:\program files\microsoft visual studio 9.0\vc\include\utility(16) : see declaration of 'std::swap' 1>c:\users\dato\documents\visual studio 2008\projects\qsort5\qsort5\qsort5.cpp(16) : error C2661: 'qsort' : no overloaded function takes 2 arguments 1>Build log was saved at "file://c:\Users\dato\Documents\Visual Studio 2008\Projects\qsort5\qsort5\Debug\BuildLog.htm" please help

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  • Inverse relationship of two variables

    - by Jam
    this one is maybe pretty stupid.. Or I am just exhausted or something, but I just cant seem to solve it.. Problem : two variables X and Y, value of Y is dependent on value of X. X can have values ranging from some value to some value (lets say from 0 to 250) and y can have different values (lets say from 0.1 to 1.0 or something..) - but it is inverse relatonship (what I mean is: if value of X is e.g. 250, then value of Y would be 0.1 and when X decreases up to 0, value of Y raises up to 1.0.. So how should I do it? lets say I have function: -- double computeValue (double X) { /computation/ return Y; } Also, is there some easy way to somehow make the scaling of the function not so linear? - For example when X raises, Y decreases slower at first but then more rapidly in the end.. (rly dont know how to say it but I hope you guys got it) Thanks in advance for this stupid question :/

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  • incremental way of counting quantiles for large set of data

    - by Gacek
    I need to count the quantiles for a large set of data. Let's assume we can get the data only through some portions (i.e. one row of a large matrix). To count the Q3 quantile one need to get all the portions of the data and store it somewhere, then sort it and count the quantile: List<double> allData = new List<double>(); foreach(var row in matrix) // this is only example. In fact the portions of data are not rows of some matrix { allData.AddRange(row); } allData.Sort(); double p = 0.75*allData.Count; int idQ3 = (int)Math.Ceiling(p) - 1; double Q3 = allData[idQ3]; Now, I would like to find a way of counting this without storing the data in some separate variable. The best solution would be to count some parameters od mid-results for first row and then adjust it step by step for next rows. Note: These datasets are really big (ca 5000 elements in each row) The Q3 can be estimated, it doesn't have to be an exact value. I call the portions of data "rows", but they can have different leghts! Usually it varies not so much (+/- few hundred samples) but it varies! This question is similar to this one: http://stackoverflow.com/questions/1058813/on-line-iterator-algorithms-for-estimating-statistical-median-mode-skewness But I need to count quantiles. ALso there are few articles in this topic, i.e.: http://web.cs.wpi.edu/~hofri/medsel.pdf http://portal.acm.org/citation.cfm?id=347195&dl But before I would try to implement these, I wanted to ask you if there are maybe any other, qucker ways of counting the 0.25/0.75 quantiles?

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  • k-combinations of a set of integers in ascending size order

    - by Adamski
    Programming challenge: Given a set of integers [1, 2, 3, 4, 5] I would like to generate all possible k-combinations in ascending size order in Java; e.g. [1], [2], [3], [4], [5], [1, 2], [1, 3] ... [1, 2, 3, 4, 5] It is fairly easy to produce a recursive solution that generates all combinations and then sort them afterwards but I imagine there's a more efficient way that removes the need for the additional sort.

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  • Clamping a vector to a minimum and maximum?

    - by user146780
    I came accross this: t = Clamp(t/d, 0, 1) but I'm not sure how to perform this operation on a vector. What are the steps to clamp a vector if one was writing their own vector implementation? Thanks clamp clamping a vector to a minimum and a maximum ex: pc = # the point you are coloring now p0 = # start point p1 = # end point v = p1 - p0 d = Length(v) v = Normalize(v) # or Scale(v, 1/d) v0 = pc - p0 t = Dot(v0, v) t = Clamp(t/d, 0, 1) color = (start_color * t) + (end_color * (1 - t))

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  • question bitonic sequence

    - by davit-datuashvili
    A sequence is bitonic if it monotonically increases and then monotonically de- creases, or if it can be circularly shifted to monotonically increase and then monotonically decrease. For example the sequences 1, 4, 6, 8, 3, -2 , 9, 2, -4, -10, -5 , and 1, 2, 3, 4 are bitonic, but 1, 3, 12, 4, 2, 10 is not bitonic. please help me to determine if given sequence is bitonic?

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  • R: Forecast package: Automatic algorithm for composite model involving ETS and AR

    - by phanikishan
    Hey, I would like to write a code involving automatic selection of a best composite model using ETS as well as autoregressive models. What is the criteria I should base my selection on? Also if I'm using the auto.arima function for deducing number of AR terms and corresponding coefficients from the forecast package in R, does my input series necessarily have to be stationary? or the value for d would be automatically selected thus returning a non-stationary model? Thanks, Phani

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  • How can I group an array of rectangles into "Islands" of connected regions?

    - by Eric
    The problem I have an array of java.awt.Rectangles. For those who are not familiar with this class, the important piece of information is that they provide an .intersects(Rectangle b) function. I would like to write a function that takes this array of Rectangles, and breaks it up into groups of connected rectangles. Lets say for example, that these are my rectangles (constructor takes the arguments x, y, width,height): Rectangle[] rects = new Rectangle[] { new Rectangle(0, 0, 4, 2), //A new Rectangle(1, 1, 2, 4), //B new Rectangle(0, 4, 8, 2), //C new Rectangle(6, 0, 2, 2) //D } A quick drawing shows that A intersects B and B intersects C. D intersects nothing. A tediously drawn piece of ascii art does the job too: +-------+ +---+ ¦A+---+ ¦ ¦ D ¦ +-+---+-+ +---+ ¦ B ¦ +-+---+---------+ ¦ +---+ C ¦ +---------------+ Therefore, the output of my function should be: new Rectangle[][]{ new Rectangle[] {A,B,C}, new Rectangle[] {D} } The failed code This was my attempt at solving the problem: public List<Rectangle> getIntersections(ArrayList<Rectangle> list, Rectangle r) { List<Rectangle> intersections = new ArrayList<Rectangle>(); for(Rectangle rect : list) { if(r.intersects(rect)) { list.remove(rect); intersections.add(rect); intersections.addAll(getIntersections(list, rect)); } } return intersections; } public List<List<Rectangle>> mergeIntersectingRects(Rectangle... rectArray) { List<Rectangle> allRects = new ArrayList<Rectangle>(rectArray); List<List<Rectangle>> groups = new ArrayList<ArrayList<Rectangle>>(); for(Rectangle rect : allRects) { allRects.remove(rect); ArrayList<Rectangle> group = getIntersections(allRects, rect); group.add(rect); groups.add(group); } return groups; } Unfortunately, there seems to be an infinite recursion loop going on here. My uneducated guess would be that java does not like me doing this: for(Rectangle rect : allRects) { allRects.remove(rect); //... } Can anyone shed some light on the issue?

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  • Dot Game and Dynamic Programming

    - by Albert Diego
    I'm trying to solve a variant of the dot game with dynamic programming. The regular dot game is played with a line of dots. Each player takes either one or two dots at their respective end of the line and the person who is left with no dots to take wins. In this version of the game, each dot has a different value. Each player takes alternate turns and takes either dot at either end of the line. I want to come up with a way to use dynamic programming to find the max amount that the first player is guaranteed to win. I'm having problems grasping my head around this and trying to write a recurrence for the solution. Any help is appreciated, thanks!

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  • Finding the largest subtree in a BST

    - by rakeshr
    Given a binary tree, I want to find out the largest subtree which is a BST in it. Naive approach: I have a naive approach in mind where I visit every node of the tree and pass this node to a isBST function. I will also keep track of the number of nodes in a sub-tree if it is a BST. Is there a better approach than this ?

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  • Travelling Salesman Problem Constraint Representation

    - by alex25
    Hey! I read a couple of articles and sample code about how to solve TSP with Genetic Algorithms and Ant Colony Optimization etc. But everything I found didn't include time (window) constraints, eg. "I have to be at customer x before 12am)" and assumed symmetry. Can somebody point me into the direction of some sample code or articles that explain how I can add constraints to TSP and how I can represent those in code. Thanks!

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  • Data Structure for a particular problem??

    - by AGeek
    Hi, Which data structure can perform insertion, deletion and searching operation in O(1) time in the worst case. We may assume the set of elements are integers drawn from a finite set 1,2,...,n, and initialization can take O(n) time. I can only think of implementing a hash table. Implementing it with Trees will not give O(1) time complexity for any of the operation. Or is it possible?? Kindly share your views on this, or any other data structure apart from these.. Thanks..

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  • how to elegantly duplicate a graph (neural network)

    - by macias
    I have a graph (network) which consists of layers, which contains nodes (neurons). I would like to write a procedure to duplicate entire graph in most elegant way possible -- i.e. with minimal or no overhead added to the structure of the node or layer. Or yet in other words -- the procedure could be complex, but the complexity should not "leak" to structures. They should be no complex just because they are copyable. I wrote the code in C#, so far it looks like this: neuron has additional field -- copy_of which is pointer the the neuron which base copied from, this is my additional overhead neuron has parameterless method Clone() neuron has method Reconnect() -- which exchanges connection from "source" neuron (parameter) to "target" neuron (parameter) layer has parameterless method Clone() -- it simply call Clone() for all neurons network has parameterless method Clone() -- it calls Clone() for every layer and then it iterates over all neurons and creates mappings neuron=copy_of and then calls Reconnect to exchange all the "wiring" I hope my approach is clear. The question is -- is there more elegant method, I particularly don't like keeping extra pointer in neuron class just in case of being copied! I would like to gather the data in one point (network's Clone) and then dispose it completely (Clone method cannot have an argument though).

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  • Non-Linear color interpolation?

    - by user146780
    If I have a straight line that mesures from 0 to 1, then I have colorA(255,0,0) at 0 on the line, then at 0.3 I have colorB(20,160,0) then at 1 on the line I have colorC(0,0,0). How could I find the color at 0.7? Thanks

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  • Way to store a large dictionary with low memory footprint + fast lookups (on Android)

    - by BobbyJim
    I'm developing an android word game app that needs a large (~250,000 word dictionary) available. I need: reasonably fast look ups e.g. constant time preferable, need to do maybe 200 lookups a second on occasion to solve a word puzzle and maybe 20 lookups within 0.2 second more often to check words the user just spelled. EDIT: Lookups are typically asking "Is in the dictionary?". I'd like to support up to two wildcards in the word as well, but this is easy enough by just generating all possible letters the wildcards could have been and checking the generated words (i.e. 26 * 26 lookups for a word with two wildcards). as it's a mobile app, using as little memory as possible and requiring only a small initial download for the dictionary data is top priority. My first naive attempts used Java's HashMap class, which caused an out of memory exception. I've looked into using the SQL lite databases available on android, but this seems like overkill. What's a good way to do what I need?

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  • simple plot algorithm with autoscale

    - by adrin
    I need to implement a simple plotting component in C#(WPF to be more precise). What i have is a collection of data samples containing time (X axis) and a value (both double types). I have a drawing canvas of a fixed size (Width x Height) and a DrawLine method/function that can draw on it. The problem I am facing now is how do I draw the plot so that it is autoscaled? In other words how do I map the samples I have to actual pixels on my Width x Height canvas?

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  • Avoiding dog-piling or thundering herd in a memcached expiration scenario

    - by Quintin Par
    I have the result of a query that is very expensive. It is the join of several tables and a map reduce job. This is cached in memcached for 15 minutes. Once the cache expires the queries are obviously run and the cache warmed again. But at the point of expiration the thundering herd problem issue can happen. One way to fix this problem, that I do right now is to run a scheduled task that kicks in the 14th minute. But somehow this looks very sub optimal to me. Another approach I like is nginx’s proxy_cache_use_stale updating; mechanism. The webserver/machine continues to deliver stale cache while a thread kicks in the moment expiration happens and updates the cache. Has someone applied this to memcached scenario though I understand this is a client side strategy? If it benefits, I use Django.

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  • How to find largest common sub-tree in the given two binary search trees?

    - by Bhushan
    Two BSTs (Binary Search Trees) are given. How to find largest common sub-tree in the given two binary trees? EDIT 1: Here is what I have thought: Let, r1 = current node of 1st tree r2 = current node of 2nd tree There are some of the cases I think we need to consider: Case 1 : r1.data < r2.data 2 subproblems to solve: first, check r1 and r2.left second, check r1.right and r2 Case 2 : r1.data > r2.data 2 subproblems to solve: - first, check r1.left and r2 - second, check r1 and r2.right Case 3 : r1.data == r2.data Again, 2 cases to consider here: (a) current node is part of largest common BST compute common subtree size rooted at r1 and r2 (b)current node is NOT part of largest common BST 2 subproblems to solve: first, solve r1.left and r2.left second, solve r1.right and r2.right I can think of the cases we need to check, but I am not able to code it, as of now. And it is NOT a homework problem. Does it look like?

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