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  • Optimizing / simplifying a path

    - by user146780
    Say I have a path with 150 nodes / verticies. How could I simplify if so that for example a straight line with 3 verticies, would remove the middle one since it does nothing to add to the path. Also how could I avoid destroying sharp corners? And how could I remove tiny variations and have smooth curves remaining. Thanks

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  • Simple Big O with lg(n) proof

    - by halohunter
    I'm attempting to guess and prove the Big O for: f(n) = n^3 - 7n^2 + nlg(n) + 10 I guess that big O is n^3 as it is the term with the largest order of growth However, I'm having trouble proving it. My unsuccesful attempt follows: f(n) <= cg(n) f(n) <= n^3 - 7n^2 + nlg(n) + 10 <= cn^3 f(n) <= n^3 + (n^3)*lg(n) + 10n^3 <= cn^3 f(n) <= N^3(11 + lg(n)) <= cn^3 so 11 + lg(n) = c But this can't be right because c must be constant. What am I doing wrong?

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  • How to find same-value rectangular areas of a given size in a matrix most efficiently?

    - by neo
    My problem is very simple but I haven't found an efficient implementation yet. Suppose there is a matrix A like this: 0 0 0 0 0 0 0 4 4 2 2 2 0 0 4 4 2 2 2 0 0 0 0 2 2 2 1 1 0 0 0 0 0 1 1 Now I want to find all starting positions of rectangular areas in this matrix which have a given size. An area is a subset of A where all numbers are the same. Let's say width=2 and height=3. There are 3 areas which have this size: 2 2 2 2 0 0 2 2 2 2 0 0 2 2 2 2 0 0 The result of the function call would be a list of starting positions (x,y starting with 0) of those areas. List((2,1),(3,1),(5,0)) The following is my current implementation. "Areas" are called "surfaces" here. case class Dimension2D(width: Int, height: Int) case class Position2D(x: Int, y: Int) def findFlatSurfaces(matrix: Array[Array[Int]], surfaceSize: Dimension2D): List[Position2D] = { val matrixWidth = matrix.length val matrixHeight = matrix(0).length var resultPositions: List[Position2D] = Nil for (y <- 0 to matrixHeight - surfaceSize.height) { var x = 0 while (x <= matrixWidth - surfaceSize.width) { val topLeft = matrix(x)(y) val topRight = matrix(x + surfaceSize.width - 1)(y) val bottomLeft = matrix(x)(y + surfaceSize.height - 1) val bottomRight = matrix(x + surfaceSize.width - 1)(y + surfaceSize.height - 1) // investigate further if corners are equal if (topLeft == bottomLeft && topLeft == topRight && topLeft == bottomRight) { breakable { for (sx <- x until x + surfaceSize.width; sy <- y until y + surfaceSize.height) { if (matrix(sx)(sy) != topLeft) { x = if (x == sx) sx + 1 else sx break } } // found one! resultPositions ::= Position2D(x, y) x += 1 } } else if (topRight != bottomRight) { // can skip x a bit as there won't be a valid match in current row in this area x += surfaceSize.width } else { x += 1 } } } return resultPositions } I already tried to include some optimizations in it but I am sure that there are far better solutions. Is there a matlab function existing for it which I could port? I'm also wondering whether this problem has its own name as I didn't exactly know what to google for. Thanks for thinking about it! I'm excited to see your proposals or solutions :)

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  • [C++] std::tring manipulation: whitespace, "newline escapes '\'" and comments #

    - by rubenvb
    Kind of looking for affirmation here. I have some hand-written code, which I'm not shy to say I'm proud of, which reads a file, removes leading whitespace, processes newline escapes '\' and removes comments starting with #. It also removes all empty lines (also whitespace-only ones). Any thoughts/recommendations? I could probably replace some std::cout's with std::runtime_errors... but that's not a priority here :) const int RecipeReader::readRecipe() { ifstream is_recipe(s_buffer.c_str()); if (!is_recipe) cout << "unable to open file" << endl; while (getline(is_recipe, s_buffer)) { // whitespace+comment removeLeadingWhitespace(s_buffer); processComment(s_buffer); // newline escapes + append all subsequent lines with '\' processNewlineEscapes(s_buffer, is_recipe); // store the real text line if (!s_buffer.empty()) v_s_recipe.push_back(s_buffer); s_buffer.clear(); } is_recipe.close(); return 0; } void RecipeReader::processNewlineEscapes(string &s_string, ifstream &is_stream) { string s_temp; size_t sz_index = s_string.find_first_of("\\"); while (sz_index <= s_string.length()) { if (getline(is_stream,s_temp)) { removeLeadingWhitespace(s_temp); processComment(s_temp); s_string = s_string.substr(0,sz_index-1) + " " + s_temp; } else cout << "Error: newline escape '\' found at EOF" << endl; sz_index = s_string.find_first_of("\\"); } } void RecipeReader::processComment(string &s_string) { size_t sz_index = s_string.find_first_of("#"); s_string = s_string.substr(0,sz_index); } void RecipeReader::removeLeadingWhitespace(string &s_string) { const size_t sz_length = s_string.size(); size_t sz_index = s_string.find_first_not_of(" \t"); if (sz_index <= sz_length) s_string = s_string.substr(sz_index); else if ((sz_index > sz_length) && (sz_length != 0)) // "empty" lines with only whitespace s_string.clear(); } Some extra info: std::string s_buffer is a class data member, so is std::vector v_s_recipe. Any comment is welcome :)

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  • Minimize the sequence by putting appropriate operations ' DP'

    - by Vikas
    Given a sequence,say, 222 We have to put a '+' or '* ' between each adjacent pair. '* ' has higher precedence over '+' We have to o/p the string whose evaluation leads to minimum value. O/p must be lexicographically smallest if there are more than one. inp:222 o/p: 2*2+2 Explaination: 2+2+2=6 2+2*2=6 2*2+2=6 of this 3rd is lexicographically smallest. I was wondering how to construct a DP solution for this.

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  • Find a common element within N arrays

    - by kunjaan
    If I have N arrays, what is the best(Time complexity. Space is not important) way to find the common elements. You could just find 1 element and stop. Edit: The elements are all Numbers. Edit: These are unsorted. Please do not sort and scan. This is not a homework problem. Somebody asked me this question a long time ago. He was using a hash to solve the problem. I was thinking if SO has solved similar problems.

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  • Java array of arry [matrix] of an integer partition with fixed term

    - by user335209
    Hello, for my study purpose I need to build an array of array filled with the partitions of an integer with fixed term. That is given an integer, suppose 10 and given the fixed number of terms, suppose 5 I need to populate an array like this 10 0 0 0 0 9 0 0 0 1 8 0 0 0 2 7 0 0 0 3 ............ 9 0 0 1 0 8 0 0 1 1 ............. 7 0 1 1 0 6 0 1 1 1 ............ ........... 0 6 1 1 1 ............. 0 0 0 0 10 am pretty new to Java and am getting confused with all the for loops. Right now my code can do the partition of the integer but unfortunately it is not with fixed term public class Partition { private static int[] riga; private static void printPartition(int[] p, int n) { for (int i= 0; i < n; i++) System.out.print(p[i]+" "); System.out.println(); } private static void partition(int[] p, int n, int m, int i) { if (n == 0) printPartition(p, i); else for (int k= m; k > 0; k--) { p[i]= k; partition(p, n-k, n-k, i+1); } } public static void main(String[] args) { riga = new int[6]; for(int i = 0; i<riga.length; i++){ riga[i] = 0; } partition(riga, 6, 1, 0); } } the output I get it from is like this: 1 5 1 4 1 1 3 2 1 3 1 1 1 2 3 1 2 2 1 1 2 1 2 1 2 1 1 1 what i'm actually trying to understand how to proceed is to have it with a fixed terms which would be the columns of my array. So, am stuck with trying to get a way to make it less dynamic. Any help?

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  • Find all numbers that appear in each of a set of lists

    - by Ankur
    I have several ArrayLists of Integer objects, stored in a HashMap. I want to get a list (ArrayList) of all the numbers (Integer objects) that appear in each list. My thinking so far is: Iterate through each ArrayList and put all the values into a HashSet This will give us a "listing" of all the values in the lists, but only once Iterate through the HashSet 2.1 With each iteration perform ArrayList.contains() 2.2 If none of the ArrayLists return false for the operation add the number to a "master list" which contains all the final values. If you can come up with something faster or more efficient, funny thing is as I wrote this I came up with a reasonably good solution. But I'll still post it just in case it is useful for someone else. But of course if you have a better way please do let me know.

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  • What is the most efficient method to find x contiguous values of y in an array?

    - by Alec
    Running my app through callgrind revealed that this line dwarfed everything else by a factor of about 10,000. I'm probably going to redesign around it, but it got me wondering; Is there a better way to do it? Here's what I'm doing at the moment: int i = 1; while ( ( (*(buffer++) == 0xffffffff && ++i) || (i = 1) ) && i < desiredLength + 1 && buffer < bufferEnd ); It's looking for the offset of the first chunk of desiredLength 0xffffffff values in a 32 bit unsigned int array. It's significantly faster than any implementations I could come up with involving an inner loop. But it's still too damn slow.

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  • Algorithms for finding the intersections of intervals

    - by tomwu
    I am wondering how I can find the number of intervals that intersect with the ones before it. for the intervals [2, 4], [1, 6], [5, 6], [0, 4], the output should be 2. from [2,4] [5,6] and [5,6] [0,4]. So now we have 1 set of intervals with size n all containing a point a, then we add another set of intervals size n as well, and all of the intervals are to the right of a. Can you do this in O(nlgn) and O(nlg^2n)?

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  • question about quicksort

    - by davit-datuashvili
    i have write code of quicksort from programming pearls here is code public class Quick{ public static void quicksort(int x[], int l,int u) { if (l>=u) return ; int t=x[l]; int i=l; int j=u; do { i++; } while (i<=u && x[i]<t); do { j--; if (i>=j) break; } while ( x[j]>t); swap(x,i,j); swap(x, l,j); quicksort(x, l,j-1); quicksort(x, j+1,u); } public static void main(String[]args){ int x[]=new int[]{55,41,59,26,53,58,97,93}; quicksort(x,0,x.length-1); for (int i=0;i<x.length;i++){ System.out.println(x[i]); } } public static void swap(int x[], int i,int j){ int s=x[i]; x[i]=x[j]; x[j]=s; } } but it does not work here is output 59 41 55 26 53 97 58 93 any idea?

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  • A question about matrix manipulation

    - by appi
    Given a 1*N matrix or an array, how do I find the first 4 elements which have the same value and then store the index for those elements? PS: I'm just curious. What if we want to find the first 4 elements whose value differences are within a certain range, say below 2? For example, M=[10,15,14.5,9,15.1,8.5,15.5,9.5], the elements I'm looking for will be 15,14.5,15.1,15.5 and the indices will be 2,3,5,7.

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  • Finding if a string is an iterative substring?

    - by EsotericMe
    I have a string S. How can I find if the string follows S = nT. Examples: Function should return true if 1) S = "abab" 2) S = "abcdabcd" 3) S = "abcabcabc" 4) S = "zzxzzxzzx" But if S="abcb" returns false. I though maybe we can repeatedly call KMP on substrings of S and then decide. eg: for "abab": call on KMP on "a". it returns 2(two instances). now 2*len("a")!=len(s) call on KMP on "ab". it returns 2. now 2*len("ab")==len(s) so return true Can you suggest any better algorithms?

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  • How does pattern matching work behind the scenes in F#?

    - by kryptic
    Hello Everyone, I am completely new to F# (and functional programming in general) but I see pattern matching used everywhere in sample code. I am wondering for example how pattern matching actually works? For example, I imagine it working the same as a for loop in other languages and checking for matches on each item in a collection. This is probably far from correct, how does it actually work behind the scenes?

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  • Solving a recurrence T(n) = 2T(n/2) + n^4

    - by user563454
    I am studying using the MIT Courseware and the CLRS book Introduction to Algorithms. Solving recurrence T(n) = 2T(n/2) + n4 (page 107) If I make a recurrence tree I get: level 0 n^4 level 1 2(n/2)^4 level 2 4(n/4)^4 level 3 8(n/8)^4 The tree has lg(n) levels. Therefore the recurrence is T(n) = Theta(lg(n)n^4)) But, If I use the Master method I get. Apply case 3: T(n) = Theta(n^4) If I apply the substitution method both seem to hold. Which one is ri?

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  • Graph search problem with route restrictions

    - by Darcara
    I want to calculate the most profitable route and I think this is a type of traveling salesman problem. I have a set of nodes that I can visit and a function to calculate cost for traveling between nodes and points for reaching the nodes. The goal is to reach a fixed known score while minimizing the cost. This cost and rewards are not fixed and depend on the nodes visited before. The starting node is fixed. There are some restrictions on how nodes can be visited. Some simplified examples include: Node B can only be visited after A After node C has been visited, D or E can be visited. Visiting at least one is required, visiting both is permissible. Z can only be visited after at least 5 other nodes have been visited Once 50 nodes have been visited, the nodes A-M will no longer reward points Certain nodes can (and probably must) be visited multiple times Currently I can think of only two ways to solve this: a) Genetic Algorithms, with the fitness function calculating the cost/benefit of the generated route b) Dijkstra search through the graph, since the starting node is fixed, although the large number of nodes will probably make that not feasible memory wise. Are there any other ways to determine the best route through the graph? It doesn't need to be perfect, an approximated path is perfectly fine, as long as it's error acceptable. Would TSP-solvers be an option here?

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  • F# insert/remove item from list

    - by Timothy
    How should I go about removing a given element from a list? As an example, say I have list ['A'; 'B'; 'C'; 'D'; 'E'] and want to remove the element at index 2 to produce the list ['A'; 'B'; 'D'; 'E']? I've already written the following code which accomplishes the task, but it seems rather inefficient to traverse the start of the list when I already know the index. let remove lst i = let rec remove lst lst' = match lst with | [] -> lst' | h::t -> if List.length lst = i then lst' @ t else remove t (lst' @ [h]) remove lst [] let myList = ['A'; 'B'; 'C'; 'D'; 'E'] let newList = remove myList 2 Alternatively, how should I insert an element at a given position? My code is similar to the above approach and most likely inefficient as well. let insert lst i x = let rec insert lst lst' = match lst with | [] -> lst' | h::t -> if List.length lst = i then lst' @ [x] @ lst else insert t (lst' @ [h]) insert lst [] let myList = ['A'; 'B'; 'D'; 'E'] let newList = insert myList 2 'C'

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  • Finding the longest road in a Settlers of Catan game algorithmically

    - by Jay
    I'm writing a Settlers of Catan clone for a class. One of the extra credit features is automatically determining which player has the longest road. I've thought about it, and it seems like some slight variation on depth-first search could work, but I'm having trouble figuring out what to do with cycle detection, how to handle the joining of a player's two initial road networks, and a few other minutiae. How could I do this algorithmically? For those unfamiliar with the game, I'll try to describe the problem concisely and abstractly: I need to find the longest possible path in an undirected cyclic graph.

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  • public (static) swap() method vs. redundant (non-static) private ones...

    - by Helper Method
    I'm revisiting data structures and algorithms to refresh my knowledge and from time to time I stumble across this problem: Often, several data structures do need to swap some elements on the underlying array. So I implement the swap() method in ADT1, ADT2 as a private non-static method. The good thing is, being a private method I don't need to check on the parameters, the bad thing is redundancy. But if I put the swap() method in a helper class as a public static method, I need to check the indices every time for validity, making the swap call very unefficient when many swaps are done. So what should I do? Neglect the performance degragation, or write small but redundant code?

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  • Length of Encrypted String

    - by Agnel Kurian
    I need to create a database column which will store a string encrypted using Triple DES. How do I determine the length of the encrypted string column? (Answers for algorithms other than Triple DES are also welcome.)

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  • more efficient version of this?

    - by john connor
    i have this thingy here : function numOfPackets(bufferSize, packetSize) { if (bufferSize <= 0 || packetSize > bufferSize) return 0; if (packetSize < 0) throw Error(); var out = 0; for(;;){ out++; bufferSize = bufferSize - packetSize; if( packetSize > bufferSize ) break; } return out; } which i run at often , can u give me more efficent variant of it?

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