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feat: Created midpoint integration numerical method (#1785)

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* Created composite Simpson's numerical integration method

* Created midpoint numerical integration method

* Corrections

* Midpoint method

* Improved Documentation

* added namespace numerical_methods

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for ec5e0cce

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for 7f16cc14

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update midpoint_integral_method.cpp

* All changes have been applied

* clang-format and clang-tidy fixes for 6617e060

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for a5a50f89

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for 4c60e180

* Create midpoint_integral_method.cpp

* Update numerical_methods/midpoint_integral_method.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for 27f76052

* Update midpoint_integral_method.cpp

Co-authored-by: ggkogkou <ggkogkou@ggkogkou.gr>
Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
This commit is contained in:
ggkogkou
2021-11-01 15:56:40 +02:00
committed by GitHub
parent 1e8376eedb
commit 8a6f2052e2
3 changed files with 262 additions and 71 deletions
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133
graph/is_graph_bipartite2.cpp
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@@ -1,22 +1,23 @@
/**
* @brief Check whether a given graph is bipartite or not
* @details
* A bipartite graph is the one whose nodes can be divided into two
* disjoint sets in such a way that the nodes in a set are not
* connected to each other at all, i.e. no intra-set connections.
* The only connections that exist are that of inter-set,
* i.e. the nodes from one set are connected to a subset of nodes
* A bipartite graph is the one whose nodes can be divided into two
* disjoint sets in such a way that the nodes in a set are not
* connected to each other at all, i.e. no intra-set connections.
* The only connections that exist are that of inter-set,
* i.e. the nodes from one set are connected to a subset of nodes
* in the other set.
* In this implementation, using a graph in the form of adjacency
* In this implementation, using a graph in the form of adjacency
* list, check whether the given graph is a bipartite or not.
*
* References used: [GeeksForGeeks](https://www.geeksforgeeks.org/bipartite-graph/)
*
* References used:
* [GeeksForGeeks](https://www.geeksforgeeks.org/bipartite-graph/)
* @author [tushar2407](https://github.com/tushar2407)
*/
#include <iostream> /// for IO operations
#include <queue> /// for queue data structure
#include <vector> /// for vector data structure
#include <cassert> /// for assert
#include <cassert> /// for assert
#include <iostream> /// for IO operations
#include <queue> /// for queue data structure
#include <vector> /// for vector data structure
/**
* @namespace graph
@@ -28,62 +29,61 @@ namespace graph {
* @param graph is a 2D matrix whose rows or the first index signify the node
* and values in that row signify the nodes it is connected to
* @param index is the valus of the node currently under observation
* @param visited is the vector which stores whether a given node has been
* @param visited is the vector which stores whether a given node has been
* traversed or not yet
* @returns boolean
*/
bool checkBipartite(
const std::vector<std::vector<int64_t>> &graph,
int64_t index,
std::vector<int64_t> *visited
)
{
std::queue<int64_t> q; ///< stores the neighbouring node indexes in squence
/// of being reached
q.push(index); /// insert the current node into the queue
(*visited)[index] = 1; /// mark the current node as travelled
while(q.size())
{
bool checkBipartite(const std::vector<std::vector<int64_t>> &graph,
int64_t index, std::vector<int64_t> *visited) {
std::queue<int64_t> q; ///< stores the neighbouring node indexes in squence
/// of being reached
q.push(index); /// insert the current node into the queue
(*visited)[index] = 1; /// mark the current node as travelled
while (q.size()) {
int64_t u = q.front();
q.pop();
for(uint64_t i=0;i<graph[u].size();i++)
{
int64_t v = graph[u][i]; ///< stores the neighbour of the current node
if(!(*visited)[v]) /// check whether the neighbour node is
/// travelled already or not
for (uint64_t i = 0; i < graph[u].size(); i++) {
int64_t v =
graph[u][i]; ///< stores the neighbour of the current node
if (!(*visited)[v]) /// check whether the neighbour node is
/// travelled already or not
{
(*visited)[v] = ((*visited)[u]==1)?-1:1; /// colour the neighbouring node with
/// different colour than the current node
q.push(v); /// insert the neighbouring node into the queue
}
else if((*visited)[v] == (*visited)[u]) /// if both the current node and its neighbour
/// has the same state then it is not a bipartite graph
(*visited)[v] =
((*visited)[u] == 1)
? -1
: 1; /// colour the neighbouring node with
/// different colour than the current node
q.push(v); /// insert the neighbouring node into the queue
} else if ((*visited)[v] ==
(*visited)[u]) /// if both the current node and its
/// neighbour has the same state then it
/// is not a bipartite graph
{
return false;
}
}
}
return true; /// return true when all the connected nodes of the current
/// nodes are travelled and satisify all the above conditions
return true; /// return true when all the connected nodes of the current
/// nodes are travelled and satisify all the above conditions
}
/**
* @brief returns true if the given graph is bipartite else returns false
* @param graph is a 2D matrix whose rows or the first index signify the node
* @param graph is a 2D matrix whose rows or the first index signify the node
* and values in that row signify the nodes it is connected to
* @returns booleans
*/
bool isBipartite(const std::vector<std::vector<int64_t>> &graph)
{
std::vector<int64_t> visited(graph.size()); ///< stores boolean values
/// which signify whether that node had been visited or not
for(uint64_t i=0;i<graph.size();i++)
{
if(!visited[i]) /// if the current node is not visited then check
/// whether the sub-graph of that node is a bipartite or not
bool isBipartite(const std::vector<std::vector<int64_t>> &graph) {
std::vector<int64_t> visited(
graph.size()); ///< stores boolean values
/// which signify whether that node had been visited or
/// not
for (uint64_t i = 0; i < graph.size(); i++) {
if (!visited[i]) /// if the current node is not visited then check
/// whether the sub-graph of that node is a bipartite
/// or not
{
if(!checkBipartite(graph, i, &visited))
{
if (!checkBipartite(graph, i, &visited)) {
return false;
}
}
@@ -96,39 +96,30 @@ bool isBipartite(const std::vector<std::vector<int64_t>> &graph)
* @brief Self-test implementations
* @returns void
*/
static void test()
{
std::vector<std::vector<int64_t>> graph = {
{1,3},
{0,2},
{1,3},
{0,2}
};
static void test() {
std::vector<std::vector<int64_t>> graph = {{1, 3}, {0, 2}, {1, 3}, {0, 2}};
assert(graph::isBipartite(graph) == true); /// check whether the above
/// defined graph is indeed bipartite
assert(graph::isBipartite(graph) ==
true); /// check whether the above
/// defined graph is indeed bipartite
std::vector<std::vector<int64_t>> graph_not_bipartite = {
{1,2,3},
{0,2},
{0,1,3},
{0,2}
};
{1, 2, 3}, {0, 2}, {0, 1, 3}, {0, 2}};
assert(graph::isBipartite(graph_not_bipartite) == false); /// check whether
/// the above defined graph is indeed bipartite
assert(graph::isBipartite(graph_not_bipartite) ==
false); /// check whether
/// the above defined graph is indeed bipartite
std::cout << "All tests have successfully passed!\n";
}
/**
* @brief Main function
* Instantitates a dummy graph of a small size with
* Instantitates a dummy graph of a small size with
* a few edges between random nodes.
* On applying the algorithm, it checks if the instantiated
* On applying the algorithm, it checks if the instantiated
* graph is bipartite or not.
* @returns 0 on exit
*/
int main()
{
int main() {
test(); // run self-test implementations
return 0;
}