diff --git a/d1/d9a/hopcroft__karp_8cpp.html b/d1/d9a/hopcroft__karp_8cpp.html index 8569b4935..d1fc9168f 100644 --- a/d1/d9a/hopcroft__karp_8cpp.html +++ b/d1/d9a/hopcroft__karp_8cpp.html @@ -138,22 +138,22 @@ Functions

Detailed Description

Implementation of Hopcroft–Karp algorithm.

The Hopcroft–Karp algorithm is an algorithm that takes as input a bipartite graph and produces as output a maximum cardinality matching, it runs in O(E√V) time in worst case.

-

+

Bipartite graph

A bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles.

-

+

Matching and Not-Matching edges

Given a matching M, edges that are part of matching are called Matching edges and edges that are not part of M (or connect free nodes) are called Not-Matching edges.

-

+

Maximum cardinality matching

Given a bipartite graphs G = ( V = ( X , Y ) , E ) whose partition has the parts X and Y, with E denoting the edges of the graph, the goal is to find a matching with as many edges as possible. Equivalently, a matching that covers as many vertices as possible.

-

+

Augmenting paths

Given a matching M, an augmenting path is an alternating path that starts from and ends on free vertices. All single edge paths that start and end with free vertices are augmenting paths.

-

+

Concept

A matching M is not maximum if there exists an augmenting path. It is also true other way, i.e, a matching is maximum if no augmenting path exists.

-

+

Algorithm

1) Initialize the Maximal Matching M as empty. 2) While there exists an Augmenting Path P Remove matching edges of P from M and add not-matching edges of P to M (This increases size of M by 1 as P starts and ends with a free vertex i.e. a node that is not part of matching.) 3) Return M.

Author
Krishna Pal Deora
diff --git a/d2/d26/count__inversions_8cpp.html b/d2/d26/count__inversions_8cpp.html index c4774323f..c8e62d71d 100644 --- a/d2/d26/count__inversions_8cpp.html +++ b/d2/d26/count__inversions_8cpp.html @@ -152,7 +152,7 @@ Functions

two elements a[i] and a[j] form an inversion if a[i] > a[j] and i < j

Time Complexity --> O(n.log n)

Space Complexity --> O(n) ; additional array temp[1..n]

-

+

Algorithm

  1. The idea is similar to merge sort, divide the array into two equal or almost equal halves in each step until the base case is reached.
  2. diff --git a/d3/df9/recursive__bubble__sort_8cpp.html b/d3/df9/recursive__bubble__sort_8cpp.html index 8e3b9c9ba..b62dad1de 100644 --- a/d3/df9/recursive__bubble__sort_8cpp.html +++ b/d3/df9/recursive__bubble__sort_8cpp.html @@ -136,7 +136,7 @@ Functions
    Author
    Aditya Prakash

    The working principle of the Bubble sort algorithm.

    Bubble sort is a simple sorting algorithm used to rearrange a set of ascending or descending order elements. Bubble sort gets its name from the fact that data "bubbles" to the top of the dataset.

    -

    +

    Algorithm

    What is Swap?

    Swapping two numbers means that we interchange their values. Often, an additional variable is required for this operation. This is further illustrated in the following:

    diff --git a/d4/d38/power__of__two_8cpp.html b/d4/d38/power__of__two_8cpp.html index 3540e16f3..c760567b1 100644 --- a/d4/d38/power__of__two_8cpp.html +++ b/d4/d38/power__of__two_8cpp.html @@ -126,7 +126,7 @@ Functions

    Detailed Description

    Implementation to check whether a number is a power of 2 or not.

    This algorithm uses bit manipulation to check if a number is a power of 2 or not.

    -

    +

    Algorithm

    Let the input number be n, then the bitwise and between n and n-1 will let us know whether the number is power of 2 or not

    For Example, If N= 32 then N-1 is 31, if we perform bitwise and of these two numbers then the result will be zero, which indicates that it is the power of 2 If N=23 then N-1 is 22, if we perform bitwise and of these two numbers then the result will not be zero , which indicates that it is not the power of 2

    Note
    This implementation is better than naive recursive or iterative approach.
    diff --git a/d4/d8d/jarvis__algorithm_8cpp.html b/d4/d8d/jarvis__algorithm_8cpp.html index 54c4762ce..b3e40c4ff 100644 --- a/d4/d8d/jarvis__algorithm_8cpp.html +++ b/d4/d8d/jarvis__algorithm_8cpp.html @@ -137,7 +137,7 @@ Functions

    Detailed Description

    Implementation of Jarvis’s algorithm.

    Given a set of points in the plane. the convex hull of the set is the smallest convex polygon that contains all the points of it.

    -

    +

    Algorithm

    The idea of Jarvis’s Algorithm is simple, we start from the leftmost point (or point with minimum x coordinate value) and we keep wrapping points in counterclockwise direction.

    The idea is to use orientation() here. Next point is selected as the point that beats all other points at counterclockwise orientation, i.e., next point is q if for any other point r, we have “orientation(p, q, r) = counterclockwise”.

    diff --git a/d5/d33/gram__schmidt_8cpp.html b/d5/d33/gram__schmidt_8cpp.html index ffe7f1f8b..abcc45385 100644 --- a/d5/d33/gram__schmidt_8cpp.html +++ b/d5/d33/gram__schmidt_8cpp.html @@ -140,7 +140,7 @@ Functions

    Detailed Description

    Gram Schmidt Orthogonalisation Process

    Takes the input of Linearly Independent Vectors, returns vectors orthogonal to each other.

    -

    +

    Algorithm

    Take the first vector of given LI vectors as first vector of Orthogonal vectors. Take projection of second input vector on the first vector of Orthogonal vector and subtract it from the 2nd LI vector. Take projection of third vector on the second vector of Othogonal vectors and subtract it from the 3rd LI vector. Keep repeating the above process until all the vectors in the given input array are exhausted.

    For Example: In R2, Input LI Vectors={(3,1),(2,2)} then Orthogonal Vectors= {(3, 1),(-0.4, 1.2)}

    diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html index 2c8e1dcb7..13fd21cc6 100644 --- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html +++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html @@ -104,12 +104,12 @@ $(document).ready(function(){initNavTree('d5/d88/md__d_i_r_e_c_t_o_r_y.html','..
  3. Rat Maze
  4. Sudoku Solve
  5. -

    +

    Bit Manipulation

    -

    +

    Ciphers

    -

    +

    Data Structures

    -

    +

    Dynamic Programming

    -

    +

    Geometry

    -

    +

    Graph

    -

    +

    Graphics

    -

    +

    Greedy Algorithms

    -

    +

    Hashing

    -

    +

    Linear Algebra

    -

    +

    Machine Learning

    -

    +

    Math

    -

    +

    Numerical Methods

    -

    +

    Operations On Datastructures

    -

    +

    Others

    -

    +

    Probability

    -

    +

    Range Queries

    -

    +

    Search

    -

    +

    Sorting

    -

    +

    Strings

    • Brute Force String Searching
    • diff --git a/d5/ddb/bogo__sort_8cpp.html b/d5/ddb/bogo__sort_8cpp.html index 03ef25a11..1e6108233 100644 --- a/d5/ddb/bogo__sort_8cpp.html +++ b/d5/ddb/bogo__sort_8cpp.html @@ -136,7 +136,7 @@ Functions

      Detailed Description

      Implementation of Bogosort algorithm

      In computer science, bogosort (also known as permutation sort, stupid sort, slowsort, shotgun sort, random sort, monkey sort, bobosort or shuffle sort) is a highly inefficient sorting algorithm based on the generate and test paradigm. Two versions of this algorithm exist: a deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.Randomized version is implemented here.

      -

      +

      Algorithm

      Shuffle the array untill array is sorted.

      Author
      Deep Raval
      diff --git a/d6/d10/cut__rod_8cpp.html b/d6/d10/cut__rod_8cpp.html index 914e8ae7d..405b1f024 100644 --- a/d6/d10/cut__rod_8cpp.html +++ b/d6/d10/cut__rod_8cpp.html @@ -136,7 +136,7 @@ Functions

      Detailed Description

      Implementation of cutting a rod problem.

      Given a rod of length n inches and an array of prices that contains prices of all pieces of size<=n. Determine the maximum profit obtainable by cutting up the rod and selling the pieces.

      -

      +

      Algorithm

      The idea is to break the given rod into every smaller piece as possible and then check profit for each piece, by calculating maximum profit for smaller pieces we will build the solution for larger pieces in bottom-up manner.

      Author
      Anmol
      diff --git a/d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html b/d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html index 0f676a5cb..f6d9ccb18 100644 --- a/d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html +++ b/d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html @@ -94,12 +94,15 @@ $(document).ready(function(){initNavTree('d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.htm
      CONTRIBUTION GUIDELINES
      -

      +

      Before contributing

      Welcome to TheAlgorithms/C-Plus-Plus! Before submitting pull requests, please make sure that you have read the whole guidelines. If you have any doubts about this contribution guide, please open an issue or ask in our Discord server, and clearly state your concerns.

      -

      +

      Contributing

      -

      +

      +Maintainer/reviewer

      +

      Please check the reviewer code file for maintainers and reviewers.

      +

      Contributor

      Being a contributor at The Algorithms, we request you to follow the points mentioned below:

        @@ -113,9 +116,9 @@ Contributor

      New implementation New implementations are welcome!

      You can add new algorithms or data structures which are not present in the repository or that can improve the old implementations (documentation, improving test cases, removing bugs or in any other resonable sense)

      Issues Please avoid opening issues asking to be "assigned” to a particular algorithm. This merely creates unnecessary noise for maintainers. Instead, please submit your implementation in a pull request, and it will be evaluated by project maintainers.

      -

      +

      Making Changes

      -

      +

      Code

      • Please use the directory structure of the repository.
      • @@ -130,7 +133,7 @@ Code
      • Please conform to Doxygen standard and document the code as much as possible. This not only facilitates the readers but also generates the correct info on the website.
      • Be consistent in the use of these guidelines.
      -

      +

      Documentation

      • Make sure you put useful comments in your code. Do not comment on obvious things.
      • @@ -139,28 +142,28 @@ Documentation
      • Do not update README.md along with other changes. First, create an issue and then link to that issue in your pull request to suggest specific changes required to README.md.
      • The repository follows Doxygen standards and auto-generates the repository website. Please ensure the code is documented in this structure. A sample implementation is given below.
      -

      +

      Test

      • Make sure to add examples and test cases in your main() function.
      • If you find an algorithm or document without tests, please feel free to create a pull request or issue describing suggested changes.
      • -
      • Please try to add one or more test() functions that will invoke the algorithm implementation on random test data with the expected output. Use the assert() function to confirm that the tests will pass. Requires including the cassert header.
      • +
      • Please try to add one or more test() functions that will invoke the algorithm implementation on random test data with the expected output. Use the assert() function to confirm that the tests will pass. Requires including the cassert library.
      -

      +

      Typical structure of a program

      /**
      * @file
      * @brief Add one line description here
      * @details
      -
      * This is a multi line
      +
      * This is a multi-line
      * description containing links, references,
      -
      * math equations, etc
      +
      * math equations, etc.
      * @author [Name](https://github.com/handle)
      * @see related_file.cpp, another_file.cpp
      */
      -
      #include <cassert>
      -
      #include
      +
      #include <cassert> /// for assert
      +
      #include /// for `some function here`
      /**
      * @namespace <check from other files in this repo>
      @@ -168,7 +171,7 @@ Typical structure of a program
      namespace name {
      /**
      -
      * Class documentation
      +
      * @brief Class documentation
      */
      class class_name {
      private:
      @@ -180,7 +183,7 @@ Typical structure of a program
      }
      /**
      -
      * Function documentation
      +
      * @brief Function documentation
      * @tparam T this is a one-line info about T
      * @param param1 on-line info about param1
      * @param param2 on-line info about param2
      @@ -199,7 +202,7 @@ Typical structure of a program
      } // namespace name
      /**
      -
      * @brief Test implementations
      +
      * @brief Self-test implementations
      * @returns void
      */
      static void test() {
      @@ -216,13 +219,13 @@ Typical structure of a program
      * @returns 0 on exit
      */
      int main(int argc, char *argv[]) {
      -
      test(); // execute the tests
      +
      test(); // run self-test implementations
      // code here
      return 0;
      }
      int main()
      Definition: graph_coloring.cpp:96
      static void test()
      Test implementations.
      Definition: rat_maze.cpp:84
      -

      +

      New File Name guidelines

      • Use lowercase words with "_" as a separator
      • @@ -232,10 +235,10 @@ New File Name guidelines
        my_new_cpp_class.cpp is correct format
      • It will be used to dynamically create a directory of files and implementation.
      • -
      • File name validation will run on docker to ensure validity.
      • +
      • File name validation will run on Docker to ensure validity.
      • If an implementation of the algorithm already exists and your version is different from that implemented, please use incremental numeric digit as a suffix. For example: if median_search.cpp already exists in the search folder, and you are contributing a new implementation, the filename should be median_search2.cpp and for a third implementation, median_search3.cpp.
      -

      +

      New Directory guidelines

      • We recommend adding files to existing directories as much as possible.
      • @@ -248,7 +251,7 @@ New Directory guidelines
      • Filepaths will be used to dynamically create a directory of our algorithms.
      • Filepath validation will run on GitHub Actions to ensure compliance.
      -

      +

      Commit Guidelines

      • It is recommended to keep your changes grouped logically within individual commits. Maintainers find it easier to understand changes that are logically spilled across multiple commits. Try to modify just one or two files in the same directory. Pull requests that span multiple directories are often rejected.
      • @@ -267,22 +270,22 @@ Commit Guidelines
      • docs: Documentation changes
      • test: Correct existing tests or add new ones
      -

      +

      Pull Requests

      -

      +

      Building Locally

      Before submitting a pull request, build the code locally or using the convenient Gitpod Ready-to-Code service.

      cmake -B build -S .
      -

      +

    Static Code Analyzer

    -

    We use clang-tidy as a static code analyzer with a configuration in .clang-tidy.

    +

    We use clang-tidy as a static code analyzer with a configuration in .clang-tidy.

    clang-tidy --fix --quiet -p build subfolder/file_to_check.cpp --
    -

    +

    Code Formatter

    -

    clang-format is used for code forrmating.

    +

    __clang-format__ is used for code forrmating.

    • Installation (only needs to be installed once.)
      • Mac (using home-brew): brew install clang-format
      • @@ -293,7 +296,7 @@ Code Formatter
      • Running (all platforms): clang-format -i -style="file" my_file.cpp
      -

      +

      GitHub Actions

      • Enable GitHub Actions on your fork of the repository. After enabling, it will execute clang-tidy and clang-format after every push (not a commit).
          diff --git a/d7/d00/list__array_8cpp.html b/d7/d00/list__array_8cpp.html index 3813c52f9..21cbd2efc 100644 --- a/d7/d00/list__array_8cpp.html +++ b/d7/d00/list__array_8cpp.html @@ -138,7 +138,7 @@ Functions

          Detailed Description

          Dynamic Array

          The list_array is the implementation of list represented using array. We can perform basic CRUD operations as well as other operations like sorting etc.

          -

          +

          Algorithm

          It implements various method like insert, sort, search etc. efficiently. You can select the operation and methods will do the rest work for you. You can insert element, sort them in order, search efficiently, delete values and print the list.

          Function Documentation

          diff --git a/d7/d73/abbreviation_8cpp.html b/d7/d73/abbreviation_8cpp.html index df71ff846..ecf90bfa9 100644 --- a/d7/d73/abbreviation_8cpp.html +++ b/d7/d73/abbreviation_8cpp.html @@ -141,7 +141,7 @@ Functions
        • Capitalize zero or more of a's lowercase letters.
        • Delete all of the remaining lowercase letters in a.
-

+

Algorithm

The idea is in the problem statement itself: iterate through characters of string a and b (for character indexes i and j respectively):

  1. If a[i] and b[j] are equal, then move to next position
  2. diff --git a/d8/d90/iterative__tree__traversals_8cpp.html b/d8/d90/iterative__tree__traversals_8cpp.html index 1b8b77723..b30bdedae 100644 --- a/d8/d90/iterative__tree__traversals_8cpp.html +++ b/d8/d90/iterative__tree__traversals_8cpp.html @@ -158,13 +158,13 @@ Functions

    Detailed Description

    Iterative version of Preorder, Postorder, and preorder Traversal of the Tree

    Author
    Motasim
    -

    +

    Iterative Preorder Traversal of a tree

    Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first right child then left child. Repeat the same set of steps untill the Stack becomes empty. And return the result array as the preorder traversal of a tree.

    -

    +

    Iterative Postorder Traversal of a tree

    Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first left child then right child. Repeat the same set of steps untill the Stack becomes empty. Now reverse the result array and then return it to the calling function as a postorder traversal of a tree.

    -

    +

    Iterative Inorder Traversal of a tree

    Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current. Now iterate and take the current to the extreme left of the tree by traversing only to its left. Pop the elemnt from the stack and assign it to the current. Store the data of current into the result array. Repeat the same set of steps until the Stack becomes empty or the current becomes NULL. And return the result array as the inorder traversal of a tree.

    Function Documentation

    diff --git a/d8/d99/connected__components__with__dsu_8cpp.html b/d8/d99/connected__components__with__dsu_8cpp.html index 9bb25592b..c469b5cfd 100644 --- a/d8/d99/connected__components__with__dsu_8cpp.html +++ b/d8/d99/connected__components__with__dsu_8cpp.html @@ -156,7 +156,7 @@ uint32_t graph::disjoint_u

    Detailed Description

    Disjoint union

    The Disjoint union is the technique to find connected component in graph efficiently.

    -

    +

    Algorithm

    In Graph, if you have to find out the number of connected components, there are 2 options

    1. Depth first search
    2. diff --git a/d8/df0/queue__using__array_8cpp.html b/d8/df0/queue__using__array_8cpp.html index 26c6d6504..2c9ffa454 100644 --- a/d8/df0/queue__using__array_8cpp.html +++ b/d8/df0/queue__using__array_8cpp.html @@ -141,7 +141,7 @@ Variables

      Detailed Description

      Implementation of Linear Queue using array.

      The Linear Queue is a data structure used for holding a sequence of values, which can be added to the end line (enqueue), removed from head of line (dequeue) and displayed.

      -

      +

      Algorithm

      Values can be added by increasing the rear variable by 1 (which points to the end of the array), then assigning new value to rear's element of the array.

      Values can be removed by increasing the front variable by 1 (which points to the first of the array), so it cannot reached any more.

      diff --git a/da/d52/minimum__edit__distance_8cpp.html b/da/d52/minimum__edit__distance_8cpp.html index c88ced249..977c6c4fa 100644 --- a/da/d52/minimum__edit__distance_8cpp.html +++ b/da/d52/minimum__edit__distance_8cpp.html @@ -137,7 +137,7 @@ Functions

      Detailed Description

      Implementation of Minimum Edit Distance using Dynamic Programing.

      Given two strings str1 & str2 and we have to calculate the minimum number of operations (Insert, Remove, Replace) required to convert str1 to str2.

      -

      +

      Algorithm

      We will solve this problem using Naive recursion. But as we are approaching with a DP solution. So, we will take a DP array to store the solution of all sub-problems so that we don't have to perform recursion again and again. Now to solve the problem, We can traverse all characters from either right side of the strings or left side. Suppose we will do it from the right side. So, there are two possibilities for every pair of characters being traversed.

      1. If the last characters of two strings are the same, Ignore the characters and get the count for the remaining string. So, we get the solution for lengths m-1 and n-1 in a DP array.
      2. diff --git a/da/dc3/linked__list_8cpp.html b/da/dc3/linked__list_8cpp.html index 9478f439c..bea9bfa18 100644 --- a/da/dc3/linked__list_8cpp.html +++ b/da/dc3/linked__list_8cpp.html @@ -137,7 +137,7 @@ Functions

        Detailed Description

        Implementation of singly linked list algorithm.

        The linked list is a data structure used for holding a sequence of values, which can be added, removed and displayed.

        -

        +

        Algorithm

        Values can be added by iterating to the end of a list(by following the pointers) starting from the first link. Whichever link points to null is considered the last link and is pointed to the new value.

        Values can be removed by also iterating through the list. When the node containing the value is found, the node pointing to the current node is made to point to the node that the current node is pointing to, and then returning the current node to heap store.

        diff --git a/db/d16/0__1__knapsack_8cpp.html b/db/d16/0__1__knapsack_8cpp.html index 6ca0c6191..ce5f21b48 100644 --- a/db/d16/0__1__knapsack_8cpp.html +++ b/db/d16/0__1__knapsack_8cpp.html @@ -136,7 +136,7 @@ Functions

        Detailed Description

        Implementation of 0-1 Knapsack Problem

        Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays val[0..n-1] and wt[0..n-1] which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)

        -

        +

        Algorithm

        The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than W. From all such subsets, pick the maximum value subset.

        Author
        Anmol
        diff --git a/db/dca/kadane2_8cpp.html b/db/dca/kadane2_8cpp.html index 3cc9ebdf0..4900b22f3 100644 --- a/db/dca/kadane2_8cpp.html +++ b/db/dca/kadane2_8cpp.html @@ -132,7 +132,7 @@ Functions

        Detailed Description

        Implementation of Kadane Algorithm

        Kadane algorithm is used to find the maximum sum subarray in an array and maximum sum subarray problem is the task of finding a contiguous subarray with the largest sum

        -

        +

        Algorithm

        The simple idea of the algorithm is to search for all positive contiguous segments of the array and keep track of maximum sum contiguous segment among all positive segments(curr_sum is used for this) Each time we get a positive sum we compare it with max_sum and update max_sum if it is greater than curr_sum

        Author
        Ayush Singh
        diff --git a/dc/d64/md__coding_guidelines.html b/dc/d64/md__coding_guidelines.html new file mode 100644 index 000000000..431635398 --- /dev/null +++ b/dc/d64/md__coding_guidelines.html @@ -0,0 +1,122 @@ + + + + + + + +Algorithms_in_C++: Code style convention + + + + + + + + + + + + + + + +
        +
        + + + + + + +
        +
        Algorithms_in_C++ +  1.0.0 +
        +
        Set of algorithms implemented in C++.
        +
        +
        + + + + + + + +
        +
        + +
        +
        +
        + +
        + +
        +
        + + +
        + +
        + +
        +
        +
        Code style convention
        +
        +
        +

        Please orient on this guide before you sent a pull request.
        +

        +
        +

        +User-interface

        +

        Please write a simple user interface for your programs. Not a blinking cursor!
        + What does the program do?
        + What want the program an user informations?
        +

        +
        +

        +Code style conventions

        +

        See here
        + Don't push all code in one line!
        +

        +
        +
        +
        + + + + diff --git a/dd/d47/namespacemath.html b/dd/d47/namespacemath.html index 44dd6916d..75cff0bc9 100644 --- a/dd/d47/namespacemath.html +++ b/dd/d47/namespacemath.html @@ -146,7 +146,7 @@ Functions

        for std::cin and std::cout

        Mathematical algorithms

        Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is f(n) = f(n-1) + f(n-2) where f(0) = 0 and f(1) = 1. Note that the method used only demonstrates recurrence relation with one variable (n), unlike nCr problem, since it has two (n, r)

        -

        +

        Algorithm

        This problem can be solved using matrix exponentiation method.

        See also
        here for simple number exponentiation algorithm or explaination here.
        Author
        Ashish Daulatabad for assert for IO operations for std::vector STL
        diff --git a/df/d66/vector__cross__product_8cpp.html b/df/d66/vector__cross__product_8cpp.html index 0d3aa1b92..949492280 100644 --- a/df/d66/vector__cross__product_8cpp.html +++ b/df/d66/vector__cross__product_8cpp.html @@ -145,7 +145,7 @@ Functions

        The direction ratios (DR) are calculated as follows: 1st DR, J: (b * z) - (c * y) 2nd DR, A: -((a * z) - (c * x)) 3rd DR, N: (a * y) - (b * x)

        Therefore, the direction ratios of the cross product are: J, A, N The following C++ Program calculates the direction ratios of the cross products of two vector. The program uses a function, cross() for doing so. The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.

        Magnitude of a vector is the square root of the sum of the squares of the direction ratios.

        -

        +

        Example:

        An example of a running instance of the executable program:

        Pass the first Vector: 1 2 3
         

        Pass the second Vector: 4 5 6 The cross product is: -3 6 -3 Magnitude: 7.34847

        diff --git a/index.html b/index.html index 472814649..c5eb3e973 100644 --- a/index.html +++ b/index.html @@ -96,10 +96,10 @@ $(document).ready(function(){initNavTree('index.html',''); initResizable(); });

        Gitpod Ready-to-Code Language grade: C/C++ CodeQL CI Gitter chat contributions welcome GitHub repo size Doxygen CI Awesome CI Income Discord chat Donate

        -

        +

        Overview

        The repository is a collection of open-source implementation of a variety of algorithms implemented in C++ and licensed under MIT License. The algorithms span a variety of topics from computer science, mathematics and statistics, data science, machine learning, engineering, etc.. The implementations and the associated documentation are meant to provide a learning resource for educators and students. Hence, one may find more than one implementation for the same objective but using a different algorithm strategies and optimizations.

        -

        +

        Features

        • The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - C++.
        • @@ -110,12 +110,12 @@ Features
        • Self-checks within programs ensure correct implementations with confidence.
        • Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.
        -

        +

        Documentation

        Online Documentation is generated from the repository source codes directly. The documentation contains all resources including source code snippets, details on execution of the programs, diagrammatic representation of program flow, and links to external resources where necessary. The documentation also introduces interactive source code with links to documentation for C++ STL library functions used. Click on Files menu to see the list of all the files documented with the code.

        Documentation of Algorithms in C++ by The Algorithms Contributors is licensed under CC BY-SA 4.0
        Creative Commons LicenseCredit must be given to the creatorAdaptations must be shared under the same terms

        -

        +

        Contributions

        As a community developed and maintained repository, we welcome new un-plagiarized quality contributions. Please read our Contribution Guidelines.

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