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[fix/docs]: Update backtracking folder (#916)
* [fix/docs]: Update backtracking/graph_coloring.cpp * Add CMakeLists.txt in backtracking folder * Add backtracking to CMakeLists.txt * fix: Fix build issues * docs: Various documentation fixes * fix: minimax.cpp issues * fix: sudoku_solve.cpp fixes * formatting source-code for8ffbbb35ce* make he code neat and clean without global variables * fix 2 stars in comment * fix MSVC errors by forcing template parameter in function calls Note: This is identical to passing it as a function parameter, and may not be helpful * Update minimax.cpp * docs: minimax.cpp improvements * docs: Add Wikipedia link in minimax.cpp * fix: minimax.cpp vector fix * docs: fix Wikipedia link in minimax.cpp * docs: fix return statement in minimax.cpp * fix: sudoku_solve.cpp fixes * fix: more sudoku_solve.cpp fixes * fix: sudoku_solve.cpp fixes * fix: sudoku_solve.cpp * formatting source-code for13b5b9b829* docs: update graph_coloring.cpp description * fix: use array instead of vector (minimax.cpp) * feat: add namespace (minimax.cpp) * docs: update namespace description (graph_coloring.cpp) * fix: graph_coloring.cpp * fix: sudoku_solve.cpp fixes * fix: graph_coloring.cpp * fix: minimax.cpp * fix: more sudoku_solve.cpp fixes * fix: more graph_coloring.cpp fixes * fix: graph_coloring.cpp fixes * fix: sudoku_solve.cpp fixes * fix: minimax.cpp * fix: sudoku_solve.cpp fixes * fix: too few template arguments (std::array) * fix: too few template arguments (std::array, minimax.cpp) * fix: narrowing conversion from double to int (minimax.cpp) * fix: excess elements in struct initializer (graph_coloring.cpp) * fix: no matching function (graph_coloring.cpp) * fix: graph_coloring.cpp issues/errors * fix: knight_tour.cpp issues/errors * fix: sudoku_solve.cpp issues/errors * [fix/docs]: Various fixes in graph_coloring.cpp * fix: More graph_coloring.cpp fixes * docs: Add initial comment block (sudoku_solve.cpp) * fix: Add return statement (knight_tour.cpp) * fix: array fixes (graph_coloring.cpp) * docs: documentation improvements (sudoku_solve.cpp) * docs: documentation improvements (knight_tour.cpp) * docs: documentation improvements (sudoku_solve.cpp) * docs: documentation improvements (graph_coloring.cpp) * docs: Documentation improvements (graph_coloring.cpp) Thanks, @kvedala! * docs: Documentation improvements (sudoku_solve.cpp) * docs: Document function parameter (sudoku_solve.cpp) * docs: Documentation improvements (knight_tour.cpp) * docs: Add long description (graph_coloring.cpp) * docs: Add long description (minimax.cpp) * docs: Add long description (sudoku_solve.cpp) * docs: Documentation improvements (knight_tour.cpp) * docs: Documentation improvements (sudoku_solve.cpp) * docs: Documentation improvements (minimax.cpp) * docs: More documentation improvements (minimax.cpp) * docs: Documentation improvements (sudoku_solve.cpp) * fix: sudoku_solve.cpp improvements Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Krishna Vedala <7001608+kvedala@users.noreply.github.com>
This commit is contained in:
David Leal
@@ -1,72 +1,117 @@
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#include <stdio.h>
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/**
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* @file
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* @brief prints the assigned colors
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* using [Graph Coloring](https://en.wikipedia.org/wiki/Graph_coloring) algorithm
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*
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* @details
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* In graph theory, graph coloring is a special case of graph labeling;
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* it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
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* 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;
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* this is called a vertex coloring. Similarly, an edge coloring assigns
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* a color to each edge so that no two adjacent edges are of the same color,
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* and a face coloring of a planar graph assigns a color to each face or
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* region so that no two faces that share a boundary have the same color.
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*
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* @author [Anup Kumar Panwar](https://github.com/AnupKumarPanwar)
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* @author [David Leal](https://github.com/Panquesito7)
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*/
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#include <iostream>
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#include <array>
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#include <vector>
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// Number of vertices in the graph
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#define V 4
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void printSolution(int color[]);
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/* A utility function to check if the current color assignment
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is safe for vertex v */
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bool isSafe(int v, bool graph[V][V], int color[], int c) {
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for (int i = 0; i < V; i++)
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if (graph[v][i] && c == color[i])
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return false;
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return true;
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}
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/* A recursive utility function to solve m coloring problem */
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void graphColoring(bool graph[V][V], int m, int color[], int v) {
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/* base case: If all vertices are assigned a color then
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return true */
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if (v == V) {
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printSolution(color);
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return;
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/**
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* @namespace
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* @brief Backtracking algorithms
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*/
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namespace backtracking {
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/** A utility function to print solution
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* @tparam V number of vertices in the graph
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* @param color array of colors assigned to the nodes
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*/
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template <size_t V>
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void printSolution(const std::array <int, V>& color) {
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std::cout << "Following are the assigned colors\n";
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for (auto &col : color) {
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std::cout << col;
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}
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std::cout << "\n";
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}
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/* Consider this vertex v and try different colors */
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for (int c = 1; c <= m; c++) {
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/* Check if assignment of color c to v is fine*/
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if (isSafe(v, graph, color, c)) {
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color[v] = c;
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/** A utility function to check if the current color assignment is safe for
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* vertex v
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* @tparam V number of vertices in the graph
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* @param v index of graph vertex to check
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* @param graph matrix of graph nonnectivity
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* @param color vector of colors assigned to the graph nodes/vertices
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* @param c color value to check for the node `v`
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* @returns `true` if the color is safe to be assigned to the node
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* @returns `false` if the color is not safe to be assigned to the node
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*/
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template <size_t V>
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bool isSafe(int v, const std::array<std::array <int, V>, V>& graph, const std::array <int, V>& color, int c) {
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for (int i = 0; i < V; i++) {
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if (graph[v][i] && c == color[i]) {
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return false;
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}
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}
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return true;
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}
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/* recur to assign colors to rest of the vertices */
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graphColoring(graph, m, color, v + 1);
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/** A recursive utility function to solve m coloring problem
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* @tparam V number of vertices in the graph
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* @param graph matrix of graph nonnectivity
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* @param m number of colors
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* @param [in,out] color description // used in,out to notify in documentation
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* that this parameter gets modified by the function
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* @param v index of graph vertex to check
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*/
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template <size_t V>
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void graphColoring(const std::array<std::array <int, V>, V>& graph, int m, std::array <int, V> color, int v) {
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// base case:
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// If all vertices are assigned a color then return true
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if (v == V) {
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backtracking::printSolution<V>(color);
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return;
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}
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/* If assigning color c doesn't lead to a solution
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then remove it */
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color[v] = 0;
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// Consider this vertex v and try different colors
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for (int c = 1; c <= m; c++) {
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// Check if assignment of color c to v is fine
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if (backtracking::isSafe<V>(v, graph, color, c)) {
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color[v] = c;
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// recur to assign colors to rest of the vertices
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backtracking::graphColoring<V>(graph, m, color, v + 1);
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// If assigning color c doesn't lead to a solution then remove it
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color[v] = 0;
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}
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}
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}
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}
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} // namespace backtracking
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/* A utility function to print solution */
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void printSolution(int color[]) {
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printf(" Following are the assigned colors \n");
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for (int i = 0; i < V; i++) printf(" %d ", color[i]);
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printf("\n");
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}
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// driver program to test above function
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/**
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* Main function
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*/
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int main() {
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/* Create following graph and test whether it is 3 colorable
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(3)---(2)
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| / |
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| / |
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| / |
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(0)---(1)
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*/
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bool graph[V][V] = {
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{0, 1, 1, 1},
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{1, 0, 1, 0},
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{1, 1, 0, 1},
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{1, 0, 1, 0},
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// Create following graph and test whether it is 3 colorable
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// (3)---(2)
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// | / |
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// | / |
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// | / |
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// (0)---(1)
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const int V = 4; // number of vertices in the graph
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std::array <std::array <int, V>, V> graph = {
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std::array <int, V>({0, 1, 1, 1}),
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std::array <int, V>({1, 0, 1, 0}),
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std::array <int, V>({1, 1, 0, 1}),
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std::array <int, V>({1, 0, 1, 0})
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};
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int m = 3; // Number of colors
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std::array <int, V> color{};
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int color[V];
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for (int i = 0; i < V; i++) color[i] = 0;
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graphColoring(graph, m, color, 0);
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backtracking::graphColoring<V>(graph, m, color, 0);
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return 0;
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}
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