## C++, , graph_coloringg.cpp

``````/**
* @file
* @brief prints the assigned colors
* using [Graph Coloring](https://en.wikipedia.org/wiki/Graph_coloring)
* algorithm
*
* @details
* In graph theory, graph coloring is a special case of graph labeling;
* it is an assignment of labels traditionally called "colors" to elements of a
* graph subject to certain constraints. In its simplest form, it is a way of
* coloring the vertices of a graph such that no two adjacent vertices are of
* the same color; this is called a vertex coloring. Similarly, an edge coloring
* assigns a color to each edge so that no two adjacent edges are of the same
* color, and a face coloring of a planar graph assigns a color to each face or
* region so that no two faces that share a boundary have the same color.
*
* @author [Anup Kumar Panwar](https://github.com/AnupKumarPanwar)
* @author [David Leal](https://github.com/Panquesito7)
*/

#include <array>     /// for std::array
#include <iostream>  /// for IO operations
#include <vector>    /// for std::vector

/**
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/**
* @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\n";
for (auto& col : color) {
std::cout << col;
}
std::cout << "\n";
}

/**
* @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
* @param graph matrix of graph nonnectivity
* @param color vector of colors assigned to the graph nodes/vertices
* @param c color value to check for the node `v`
* @returns `true` if the color is safe to be assigned to the node
* @returns `false` if the color is not safe to be assigned to the node
*/
template <size_t V>
bool isSafe(int v, const std::array<std::array<int, V>, V>& graph,
const std::array<int, V>& color, int c) {
for (int i = 0; i < V; i++) {
if (graph[v][i] && c == color[i]) {
return false;
}
}
return true;
}

/**
* @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
* @param [in,out] color description // used in,out to notify in documentation
* that this parameter gets modified by the function
* @param v index of graph vertex to check
*/
template <size_t V>
void graphColoring(const std::array<std::array<int, V>, V>& graph, int m,
std::array<int, V> color, int v) {
// base case:
// If all vertices are assigned a color then return true
if (v == V) {
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 (isSafe<V>(v, graph, color, c)) {
color[v] = c;

// recur to assign colors to rest of the vertices
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

/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
// Create following graph and test whether it is 3 colorable
// (3)---(2)
// |   / |
// |  /  |
// | /   |
// (0)---(1)

const int V = 4;  // number of vertices in the graph
std::array<std::array<int, V>, V> graph = {
std::array<int, V>({0, 1, 1, 1}), std::array<int, V>({1, 0, 1, 0}),
std::array<int, V>({1, 1, 0, 1}), std::array<int, V>({1, 0, 1, 0})};

int m = 3;  // Number of colors
std::array<int, V> color{};

backtracking::graph_coloring::graphColoring<V>(graph, m, color, 0);
return 0;
}
``````