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[feat/fix/docs]: Improvements in the backtracking folder (#1553)

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* [feat/fix/docs]: Improvements in the...

...`backtracking` folder, and minor fixes in the `others/iterative_tree_traversals.cpp` and the `math/check_prime.cpp` files.

* clang-format and clang-tidy fixes for 9cc3951d

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com>
This commit is contained in:
David Leal
2021-10-29 13:05:46 -05:00
committed by GitHub
parent a9312b3901
commit 4e3abd4601
8 changed files with 367 additions and 322 deletions
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40
backtracking/graph_coloring.cpp
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@@ -17,29 +17,38 @@
* @author [Anup Kumar Panwar](https://github.com/AnupKumarPanwar)
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <array>
#include <iostream>
#include <vector>
#include <array> /// for std::array
#include <iostream> /// for IO operations
#include <vector> /// for std::vector
/**
* @namespace
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/** A utility function to print solution
/**
* @namespace graph_coloring
* @brief Functions for the [Graph
* Coloring](https://en.wikipedia.org/wiki/Graph_coloring) algorithm,
*/
namespace graph_coloring {
/**
* @brief A utility function to print the solution
* @tparam V number of vertices in the graph
* @param color array of colors assigned to the nodes
*/
template <size_t V>
void printSolution(const std::array<int, V>& color) {
std::cout << "Following are the assigned colors" << std::endl;
std::cout << "Following are the assigned colors\n";
for (auto& col : color) {
std::cout << col;
}
std::cout << std::endl;
std::cout << "\n";
}
/** A utility function to check if the current color assignment is safe for
/**
* @brief Utility function to check if the current color assignment is safe for
* vertex v
* @tparam V number of vertices in the graph
* @param v index of graph vertex to check
@@ -60,7 +69,8 @@ bool isSafe(int v, const std::array<std::array<int, V>, V>& graph,
return true;
}
/** A recursive utility function to solve m coloring problem
/**
* @brief Recursive utility function to solve m coloring problem
* @tparam V number of vertices in the graph
* @param graph matrix of graph nonnectivity
* @param m number of colors
@@ -74,28 +84,30 @@ void graphColoring(const std::array<std::array<int, V>, V>& graph, int m,
// base case:
// If all vertices are assigned a color then return true
if (v == V) {
backtracking::printSolution<V>(color);
printSolution<V>(color);
return;
}
// Consider this vertex v and try different colors
for (int c = 1; c <= m; c++) {
// Check if assignment of color c to v is fine
if (backtracking::isSafe<V>(v, graph, color, c)) {
if (isSafe<V>(v, graph, color, c)) {
color[v] = c;
// recur to assign colors to rest of the vertices
backtracking::graphColoring<V>(graph, m, color, v + 1);
graphColoring<V>(graph, m, color, v + 1);
// If assigning color c doesn't lead to a solution then remove it
color[v] = 0;
}
}
}
} // namespace graph_coloring
} // namespace backtracking
/**
* Main function
* @brief Main function
* @returns 0 on exit
*/
int main() {
// Create following graph and test whether it is 3 colorable
@@ -113,6 +125,6 @@ int main() {
int m = 3; // Number of colors
std::array<int, V> color{};
backtracking::graphColoring<V>(graph, m, color, 0);
backtracking::graph_coloring::graphColoring<V>(graph, m, color, 0);
return 0;
}