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  • Algorithm for finding all paths in a NxN grid

    - by Periastron
    Imagine a robot sitting on the upper left hand corner of an NxN grid. The robot can only move in two directions: right and down. How many possible paths are there for the robot? I could find solution to this problem on Google, but I am not very clear with the explanations. I am trying to clearly understand the logic on how to solve this and implement in Java. Any help is appreciated. Update: This is an interview question. For now, I am trying to reach the bottom-right end and print the possible paths.

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  • How can I improve the performance of this algorithm

    - by Justin
    // Checks whether the array contains two elements whose sum is s. // Input: A list of numbers and an integer s // Output: return True if the answer is yes, else return False public static boolean calvalue (int[] numbers, int s){ for (int i=0; i< numbers.length; i++){ for (int j=i+1; j<numbers.length;j++){ if (numbers[i] < s){ if (numbers[i]+numbers[j] == s){ return true; } } } } return false; }

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  • Need an efficient algorithm solve this kind of complex structure

    - by Rizvan
    Problem Statement is : Given 2 Dimensional array, print output for example If 4 rows and 6 columns, output would be: 1 2 3 4 5 6 16 17 18 19 20 7 15 24 23 22 21 8 14 13 12 11 10 9 I tried it is looking like square within square but when I attempted this problem, I put so many while and if loops but didn't got exact answer. If row and columns increases how to handle it? This is not homework. I was learning solving complex structure so I need to understand it by some guidance.

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  • algorithm to find the three majority elements in an array

    - by Qiang Li
    Let's say there are three elements in a non-sorted array all of which appear more than one-fourth times of the total number of elements. What is the most efficient way to find these elements? Both for non-online and online versions of this question. Thank you! Edit The non-online version I was referring to is: this array is specified in full. The online version means the array elements are coming one at a time. I require the space in addition to time complexity to be tight. disclaimer: THIS IS NOT HOMEWORK! I consider this as research-level question.

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  • Iterative Reduction to Null Matrix

    - by user1459032
    Here's the problem: I'm given a matrix like Input: 1 1 1 1 1 1 1 1 1 At each step, I need to find a "second" matrix of 1's and 0's with no two 1's on the same row or column. Then, I'll subtract the second matrix from the original matrix. I will repeat the process until I get a matrix with all 0's. Furthermore, I need to take the least possible number of steps. I need to print all the "second" matrices in O(n) time. In the above example I can get to the null matrix in 3 steps by subtracting these three matrices in order: Expected output: 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 I have coded an attempt, in which I am finding the first maximum value and creating the second matrices based on the index of that value. But for the above input I am getting 4 output matrices, which is wrong: My output: 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 My solution works for most of the test cases but fails for the one given above. Can someone give me some pointers on how to proceed, or find an algorithm that guarantees optimality? Test case that works: Input: 0 2 1 0 0 0 3 0 0 Output 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0

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  • Giving a Bomberman AI intelligent bomb placement

    - by Paul Manta
    I'm trying to implement an AI algorithm for Bomberman. Currently I have a working but not very smart rudimentary implementation (the current AI is overzealous in placing bombs). This is the first AI I've ever tried implementing and I'm a bit stuck. The more sophisticated algorithms I have in mind (the ones that I expect to make better decisions) are too convoluted to be good solutions. What general tips do you have for implementing a Bomberman AI? Are there radically different approaches for making the bot either more defensive or offensive? Edit: Current algorithm My current algorithm goes something like this (pseudo-code): 1) Try to place a bomb and then find a cell that is safe from all the bombs, including the one that you just placed. To find that cell, iterate over the four directions; if you can find any safe divergent cell and reach it in time (eg. if the direction is up or down, look for a cell that is found to the left or right of this path), then it's safe to place a bomb and move in that direction. 2) If you can't find and safe divergent cells, try NOT placing a bomb and look again. This time you'll only need to look for a safe cell in only one direction (you don't have to diverge from it). 3) If you still can't find a safe cell, don't do anything. for $(direction) in (up, down, left, right): place bomb at current location if (can find and reach divergent safe cell in current $(direction)): bomb = true move = $(direction) return for $(direction) in (up, down, left, right): do not place bomb at current location if (any safe cell in the current $(direction)): bomb = false move = $(direction) return else: bomb = false move = stay_put This algorithm makes the bot very trigger-happy (it'll place bombs very frequently). It doesn't kill itself, but it does have a habit of making itself vulnerable by going into dead ends where it can be blocked and killed by the other players. Do you have any suggestions on how I might improve this algorithm? Or maybe I should try something completely different? One of the problems with this algorithm is that it tends to leave the bot with very few (frequently just one) safe cells on which it can stand. This is because the bot leaves a trail of bombs behind it, as long as it doesn't kill itself. However, leaving a trail of bombs behind leaves few places where you can hide. If one of the other players or bots decide to place a bomb somewhere near you, it often happens that you have no place to hide and you die. I need a better way to decide when to place bombs.

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  • Dynamic Dijkstra

    - by Dani
    I need dynamic dijkstra algorithm that can update itself when edge's cost is changed without a full recalculation. Full recalculation is not an option. I've tryed to "brew" my own implemantion with no success. I've also tryed to find on the Internet but found nothing. A link to an article explaining the algorithm or even it's name will be good. Edit: Thanks everyone for answering. I managed to make algorithm of my own that runs in O(V+E) time, if anyone wishes to know the algorithm just say so and I will post it.

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  • How can I use the Boost Graph Library to lay out verticies?

    - by Mike
    I'm trying to lay out vertices using the Boost Graph Library. However, I'm running into some compilation issues which I'm unsure about. Am I using the BGL in an improper manner? My code is: PositionVec position_vec(2); PositionMap position(position_vec.begin(), get(vertex_index, g)); int iterations = 100; double width = 100.0; double height = 100.0; minstd_rand gen; rectangle_topology<> topology(gen, 0, 0, 100, 100); fruchterman_reingold_force_directed_layout(g, position, topology); //Compile fails on this line The diagnostics produced by clang++(I've also tried GCC) are: In file included from test.cpp:2: /Volumes/Data/mike/Downloads/boost_1_43_0/boost/graph/fruchterman_reingold.hpp:95:3: error: no member named 'dimensions' in 'boost::simple_point<double>' BOOST_STATIC_ASSERT (Point::dimensions == 2); ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In file included from test.cpp:2: In file included from /Volumes/Data/mike/Downloads/boost_1_43_0/boost/graph/fruchterman_reingold.hpp:13: In file included from /Volumes/Data/mike/Downloads/boost_1_43_0/boost/graph/graph_traits.hpp:15: In file included from /Volumes/Data/mike/Downloads/boost_1_43_0/boost/tuple/tuple.hpp:24: /Volumes/Data/mike/Downloads/boost_1_43_0/boost/static_assert.hpp:118:49: note: instantiated from: sizeof(::boost::STATIC_ASSERTION_FAILURE< BOOST_STATIC_ASSERT_BOOL_CAST( B ) >)>\ ^ In file included from test.cpp:2: /Volumes/Data/mike/Downloads/boost_1_43_0/boost/graph/fruchterman_reingold.hpp:95:3: note: instantiated from: BOOST_STATIC_ASSERT (Point::dimensions == 2); ^ ~~~~~~~ /Volumes/Data/mike/Downloads/boost_1_43_0/boost/graph/fruchterman_reingold.hpp:95:31: note: instantiated from: BOOST_STATIC_ASSERT (Point::dimensions == 2); ~~~~~~~^ /Volumes/Data/mike/Downloads/boost_1_43_0/boost/graph/fruchterman_reingold.hpp:417:19: note: in instantiation of template class 'boost::grid_force_pairs<boost::rectangle_topology<boost::random::linear_congruential<int, 48271, 0, 2147483647, 399268537> >, boost::iterator_property_map<__gnu_cxx::__normal_iterator<boost::simple_point<double> *, std::vector<boost::simple_point<double>, std::allocator<boost::simple_point<double> > > >, boost::vec_adj_list_vertex_id_map<boost::property<boost::vertex_name_t, std::basic_string<char>, boost::no_property>, unsigned long>, boost::simple_point<double>, boost::simple_point<double> &> >' requested here make_grid_force_pairs(topology, position, g)), ^ /Volumes/Data/mike/Downloads/boost_1_43_0/boost/graph/fruchterman_reingold.hpp:431:3: note: in instantiation of function template specialization 'boost::fruchterman_reingold_force_directed_layout<boost::rectangle_topology<boost::random::linear_congruential<int, 48271, 0, 2147483647, 399268537> >, boost::adjacency_list<boost::listS, boost::vecS, boost::undirectedS, boost::property<boost::vertex_name_t, std::basic_string<char>, boost::no_property>, boost::no_property, boost::no_property, boost::listS>, boost::iterator_property_map<__gnu_cxx::__normal_iterator<boost::simple_point<double> *, std::vector<boost::simple_point<double>, std::allocator<boost::simple_point<double> > > >, boost::vec_adj_list_vertex_id_map<boost::property<boost::vertex_name_t, std::basic_string<char>, boost::no_property>, unsigned long>, boost::simple_point<double>, boost::simple_point<double> &>, boost::square_distance_attractive_force, boost::attractive_force_t, boost::no_property>' requested here fruchterman_reingold_force_directed_layout ^ test.cpp:48:3: note: in instantiation of function template specialization 'boost::fruchterman_reingold_force_directed_layout<boost::rectangle_topology<boost::random::linear_congruential<int, 48271, 0, 2147483647, 399268537> >, boost::adjacency_list<boost::listS, boost::vecS, boost::undirectedS, boost::property<boost::vertex_name_t, std::basic_string<char>, boost::no_property>, boost::no_property, boost::no_property, boost::listS>, boost::iterator_property_map<__gnu_cxx::__normal_iterator<boost::simple_point<double> *, std::vector<boost::simple_point<double>, std::allocator<boost::simple_point<double> > > >, boost::vec_adj_list_vertex_id_map<boost::property<boost::vertex_name_t, std::basic_string<char>, boost::no_property>, unsigned long>, boost::simple_point<double>, boost::simple_point<double> &> >' requested here fruchterman_reingold_force_directed_layout(g, position, topology); ^ 1 error generated.

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  • algorithm - How to sort a 0/1 array with 2n/3 comparisons?

    - by Jackson Tale
    In Algorithm Design Manual, there is such an excise 4-26 Consider the problem of sorting a sequence of n 0’s and 1’s using comparisons. For each comparison of two values x and y, the algorithm learns which of x < y, x = y, or x y holds. (a) Give an algorithm to sort in n - 1 comparisons in the worst case. Show that your algorithm is optimal. (b) Give an algorithm to sort in 2n/3 comparisons in the average case (assuming each of the n inputs is 0 or 1 with equal probability). Show that your algorithm is optimal. For (a), I think it is fairly easy. I can choose a[n-1] as pivot, then do something like in quicksort partition, scan 0 to n - 2, find the middle point where left side is all 0 and right side is all 1, this take n - 1 comparisons. But for (b), I can't get a clue. It says "each of the n inputs is 0 or 1 with equal probability", so I guess I can assume the numbers of 0 and 1 equal? But how can I get a result which is related to 1/3? divide the whole array into 3 groups? Thanks

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  • Is there an efficient algorithm to distribute resources in a way that both avoids conflict and allows bias?

    - by Steve V.
    Background (Skip this if you only care about the algorithm) At the university where I work, one of the biggest hassles in our department is classroom scheduling. For illustration purposes and to lay out the scope of the problem, here's how we do scheduling now: Professors give us a list of the classes they're teaching with the time slots they'd prefer to teach, ranked in order of priority (most desired to least desired). Administration gives us a list of the rooms we may assign along with the times those rooms are available for our department's use. We start assigning professors to rooms trying (at first) to take into account the preferences of the various professors. Inevitably, conflicts arise, professors start asking for changes, and the plan falls to pieces somewhere around professor number 30, at which point we start assigning rooms basically wherever we can fit them in, crumpled pieces of paper are everywhere, and nobody's happy. (If you've ever wondered why your class was at 9.30 in the morning on Thursday but 4 pm every other day, now you know) I have been asked to quietly investigate whether software could do this more optimally. The Actual Question Is there an algorithm to efficiently schedule a set of resources such that the following criteria are met: The algorithm must never assign two professors to the same room at the same time. The task is not complete until every professor has been assigned a room / time. The algorithm need not worry about having too many professors for the amount of time slots available. (We're not that well funded.) As much as is possible the algorithm should respect the scheduling preferences of the individual professors. I feel like I can't be the first one to ask this. Is there a efficient algorithm for this, or is this the sort of problem that can only be brute-forced?

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  • Am I right about the differences between Floyd-Warshall, Dijkstra's and Bellman-Ford algorithms?

    - by Programming Noob
    I've been studying the three and I'm stating my inferences from them below. Could someone tell me if I have understood them accurately enough or not? Thank you. Dijkstra's algorithm is used only when you have a single source and you want to know the smallest path from one node to another, but fails in cases like this Floyd-Warshall's algorithm is used when any of all the nodes can be a source, so you want the shortest distance to reach any destination node from any source node. This only fails when there are negative cycles (this is the most important one. I mean, this is the one I'm least sure about:) 3.Bellman-Ford is used like Dijkstra's, when there is only one source. This can handle negative weights and its working is the same as Floyd-Warshall's except for one source, right? If you need to have a look, the corresponding algorithms are (courtesy Wikipedia): Bellman-Ford: procedure BellmanFord(list vertices, list edges, vertex source) // This implementation takes in a graph, represented as lists of vertices // and edges, and modifies the vertices so that their distance and // predecessor attributes store the shortest paths. // Step 1: initialize graph for each vertex v in vertices: if v is source then v.distance := 0 else v.distance := infinity v.predecessor := null // Step 2: relax edges repeatedly for i from 1 to size(vertices)-1: for each edge uv in edges: // uv is the edge from u to v u := uv.source v := uv.destination if u.distance + uv.weight < v.distance: v.distance := u.distance + uv.weight v.predecessor := u // Step 3: check for negative-weight cycles for each edge uv in edges: u := uv.source v := uv.destination if u.distance + uv.weight < v.distance: error "Graph contains a negative-weight cycle" Dijkstra: 1 function Dijkstra(Graph, source): 2 for each vertex v in Graph: // Initializations 3 dist[v] := infinity ; // Unknown distance function from 4 // source to v 5 previous[v] := undefined ; // Previous node in optimal path 6 // from source 7 8 dist[source] := 0 ; // Distance from source to source 9 Q := the set of all nodes in Graph ; // All nodes in the graph are 10 // unoptimized - thus are in Q 11 while Q is not empty: // The main loop 12 u := vertex in Q with smallest distance in dist[] ; // Start node in first case 13 if dist[u] = infinity: 14 break ; // all remaining vertices are 15 // inaccessible from source 16 17 remove u from Q ; 18 for each neighbor v of u: // where v has not yet been 19 removed from Q. 20 alt := dist[u] + dist_between(u, v) ; 21 if alt < dist[v]: // Relax (u,v,a) 22 dist[v] := alt ; 23 previous[v] := u ; 24 decrease-key v in Q; // Reorder v in the Queue 25 return dist; Floyd-Warshall: 1 /* Assume a function edgeCost(i,j) which returns the cost of the edge from i to j 2 (infinity if there is none). 3 Also assume that n is the number of vertices and edgeCost(i,i) = 0 4 */ 5 6 int path[][]; 7 /* A 2-dimensional matrix. At each step in the algorithm, path[i][j] is the shortest path 8 from i to j using intermediate vertices (1..k-1). Each path[i][j] is initialized to 9 edgeCost(i,j). 10 */ 11 12 procedure FloydWarshall () 13 for k := 1 to n 14 for i := 1 to n 15 for j := 1 to n 16 path[i][j] = min ( path[i][j], path[i][k]+path[k][j] );

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  • Algorithm for nice graph labels for time/date axis?

    - by Aaron
    Hello, I'm looking for a "nice numbers" algorithm for determining the labels on a date/time value axis. I'm familar with Paul Heckbert's Nice Numbers algorithm (http://tinyurl.com/5gmk2c). I have a plot that displays time/date on the X axis and the user can zoom in and look at a smaller time frame. I'm looking for an algorithm that picks nice dates to display on the ticks. For example: Looking at a day or so: 1/1 12:00, 1/1 4:00, 1/1 8:00... Looking at a week: 1/1, 1/2, 1/3... Looking at a month: 1/09, 2/09, 3/09... The nice label ticks don't need to correspond to the first visible point, but close to it. Is anybody familar with such an algorithm? Thanks

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  • What are graphs in laymen's terms

    - by Justin984
    What are graphs, in computer science, and what are they used for? In laymen's terms preferably. I have read the definition on Wikipedia: In computer science, a graph is an abstract data type that is meant to implement the graph and hypergraph concepts from mathematics. A graph data structure consists of a finite (and possibly mutable) set of ordered pairs, called edges or arcs, of certain entities called nodes or vertices. As in mathematics, an edge (x,y) is said to point or go from x to y. The nodes may be part of the graph structure, or may be external entities represented by integer indices or references. but I'm looking for a less formal, easier to understand definition.

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  • Designing binary operations(AND, OR, NOT) in graphs DB's like neo4j

    - by Nicholas
    I'm trying to create a recipe website using a graph database, specifically neo4j using spring-data-neo4j, to try and see what can be done in Graph Databases. My model so far is: (Chef)-[HAS_INGREDIENT]->(Ingredient) (Chef)-[HAS_VALUE]->(Value) (Ingredient)-[HAS_INGREDIENT_VALUE]->(Value) (Recipe)-[REQUIRES_INGREDIENT]->(Ingredient) (Recipe)-[REQUIRES_VALUE]->(Value) I have this set up so I can do things like have the "chef" enter ingredients they have on hand, and suggest recipes, as well as suggest recipes that are close matches, but missing one ingredient. Some recipes can get complex, utilizing AND, OR, and NOT type logic, something like (Milk AND (Butter OR spread OR (vegetable oil OR olive oil))) and I'm wondering if it would be sane to model this in a graph using a tree type representation? An example of what I was thinking is to create three "node" types of AND, OR, and NOT and have each of them connect to the nodes value underneath. How else might this be represented in a Graph Database or is my example above a decent representation?

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  • Prim's MST algorithm implementation with Java

    - by user1290164
    I'm trying to write a program that'll find the MST of a given undirected weighted graph with Kruskal's and Prim's algorithms. I've successfully implemented Kruskal's algorithm in the program, but I'm having trouble with Prim's. To be more precise, I can't figure out how to actually build the Prim function so that it'll iterate through all the vertices in the graph. I'm getting some IndexOutOfBoundsException errors during program execution. I'm not sure how much information is needed for others to get the idea of what I have done so far, but hopefully there won't be too much useless information. This is what I have so far: I have a Graph, Edge and a Vertex class. Vertex class mostly just an information storage that contains the name (number) of the vertex. Edge class can create a new Edge that has gets parameters (Vertex start, Vertex end, int edgeWeight). The class has methods to return the usual info like start vertex, end vertex and the weight. Graph class reads data from a text file and adds new Edges to an ArrayList. The text file also tells us how many vertecis the graph has, and that gets stored too. In the Graph class, I have a Prim() -method that's supposed to calculate the MST: public ArrayList<Edge> Prim(Graph G) { ArrayList<Edge> edges = G.graph; // Copies the ArrayList with all edges in it. ArrayList<Edge> MST = new ArrayList<Edge>(); Random rnd = new Random(); Vertex startingVertex = edges.get(rnd.nextInt(G.returnVertexCount())).returnStartingVertex(); // This is just to randomize the starting vertex. // This is supposed to be the main loop to find the MST, but this is probably horribly wrong.. while (MST.size() < returnVertexCount()) { Edge e = findClosestNeighbour(startingVertex); MST.add(e); visited.add(e.returnStartingVertex()); visited.add(e.returnEndingVertex()); edges.remove(e); } return MST; } The method findClosesNeighbour() looks like this: public Edge findClosestNeighbour(Vertex v) { ArrayList<Edge> neighbours = new ArrayList<Edge>(); ArrayList<Edge> edges = graph; for (int i = 0; i < edges.size() -1; ++i) { if (edges.get(i).endPoint() == s.returnVertexID() && !visited(edges.get(i).returnEndingVertex())) { neighbours.add(edges.get(i)); } } return neighbours.get(0); // This is the minimum weight edge in the list. } ArrayList<Vertex> visited and ArrayList<Edges> graph get constructed when creating a new graph. Visited() -method is simply a boolean check to see if ArrayList visited contains the Vertex we're thinking about moving to. I tested the findClosestNeighbour() independantly and it seemed to be working but if someone finds something wrong with it then that feedback is welcome also. Mainly though as I mentioned my problem is with actually building the main loop in the Prim() -method, and if there's any additional info needed I'm happy to provide it. Thank you. Edit: To clarify what my train of thought with the Prim() method is. What I want to do is first randomize the starting point in the graph. After that, I will find the closest neighbor to that starting point. Then we'll add the edge connecting those two points to the MST, and also add the vertices to the visited list for checking later, so that we won't form any loops in the graph. Here's the error that gets thrown: Exception in thread "main" java.lang.IndexOutOfBoundsException: Index: 0, Size: 0 at java.util.ArrayList.rangeCheck(Unknown Source) at java.util.ArrayList.get(Unknown Source) at Graph.findClosestNeighbour(graph.java:203) at Graph.Prim(graph.java:179) at MST.main(MST.java:49) Line 203: return neighbour.get(0); in findClosestNeighbour() Line 179: Edge e = findClosestNeighbour(startingVertex); in Prim()

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  • Creating dynamic plots

    - by geoff92
    I'm completely new to web programming but I do have a programming background. I'd like to create a site that allows users to visit, enter some specifications into a form, submit the form, and then receive a graph. I have a few questions about this, only because I'm pretty ignorant: Is there a good framework I should start in? I know a lot of java, I'm okay with python, and I learned Ruby in the past. I figure I might use ruby on rails only because I hear of it so often and I think I've also heard it's easy. If anyone has some other recommendation, please suggest. The user will be entering data into a form. I'm guessing the request they'll be making should be one of a GET request, right? Because I don't intend for any of the data they're entering to modify my server (in fact, I don't intend on having a database). The data the user inputs will be used to perform calculations involving lots of matrices. I've written this functionality in python. If I use ruby on rails, should it be instead written in Ruby? Somewhere I've heard that you can either place the load of the work on your server or on the client's computer. Since the code performs heavy math, which option is preferable? How do I alter the setup to either make the client do the work or my server? Should I be using a "cgi-bin"? In the code that I have now, I use matplotlib, a python library, and then "show" the plot in order to see the graph. I specify the x and y limits, but I am able to "drag" the graph in order to see more data within the plot window. Ultimately, I want a graph to be shown on my site with the drag functionality. Is this possible? What if the client drags the graph so far, more computations must be made? Thanks!

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  • How to display a graph only for business hours with CACTI?

    - by Blast Raider
    I have noticed that I can only display an uninterrupted period with Cacti. I am wondering whether is possible or not to make a custom graph which displaying only the business hours during a period (a week, a month, etc.). If it is possible, how could I configure it on Cacti ? For example, I would like to be able to display a graph with an average inbound/outbound traffic between 8am and 7pm for 5 business days a week of the last month. I would apreciate any help. Thank you.

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  • How can I prepare a cake graph in excel with a result based on 100%?

    - by Pitto
    Hello my friends... I need to distribute correctly a little data in an excel graph. I have the total I've earned last year which should represent the 100% of the cake. Then I have my insurance expenses and I want to understand, graphically, how much of my total income went away to pay insurance... I know that a basic proportion like: total expenses : total insurance costs = 100 : x do the correct math but I can't find a way to display this in a cake graph... Any hints?

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  • Reverse Bredth First Search in C#

    - by Ngu Soon Hui
    Anyone has a ready implementation of the Reverse Bredth First Search algorithm in C#? By Reverse Bredth First Search, I mean instead of searching a tree starting from a common node, I want to search the tree from the bottom and gradually converged to a common node. Let's see the below figure, this is the output of a Bredth First Search: In my reverse bredth first search, 9,10,11 and 12 will be the first few nodes found ( the order of them are not important as they are all first order). 5, 6, 7 and 8 are the second few nodes found, and so on. 1 would be the last node found. Any ideas or pointers?

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  • Reverse Breath First Search in C#

    - by Ngu Soon Hui
    Anyone has a ready implementation of the Reverse Breath First Search algorithm in C#? By Reverse Breath First Search, I mean instead of searching a tree starting from a common node, I want to search the tree from the bottom and gradually converged to a common node. Let's see the below figure, this is the output of a Breath First Search: In my reverse breath first search, 9,10,11 and 12 will be the first few nodes found ( the order of them are not important as they are all first order). 5, 6, 7 and 8 are the second few nodes found, and so on. 1 would be the last node found. Any ideas or pointers?

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  • Calculate shortest path through a grocery store

    - by Bart
    Hi, I'm trying to find a way to find the shortest path through a grocery store, visiting a list of locations (shopping list). The path should start at a specified startposition and can end at multiple endpositions (there are multiple checkout counters). Also, I have some predefined constraints on the path, such as "item x on the shopping list needs to be the last, second last, or third last item on the path". There is a function that will return true or false for a given path. Finally, this needs to be calculated with limited cpu power (on a smartphone) and within a second or so. If this isn't possible, then an approximation to the optimal path is also ok. Is this possible? So far I think I need to start by calculating the distance between every item on the list using something like A* or Dijkstra's. After that, should I treat it like the travelling salesman problem? Because in my problem there is a specified startnode, specified endnodes, and some constraints, which are not in the travelling salesman problem. Any help would be appreciated :)

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