[feat/fix/docs]: Improvements in the backtracking folder (TheAlgori…

…thms#1553) * [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 9cc3951 Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Abhinn Mishra <[email protected]>
Vanshjain2701 · Oct 29, 2021 · 4e3abd4 · 4e3abd4
1 parent a9312b3
commit 4e3abd4
Show file tree

Hide file tree

Showing 8 changed files with 346 additions and 301 deletions.
diff --git a/backtracking/graph_coloring.cpp b/backtracking/graph_coloring.cpp
@@ -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;
 }
diff --git a/backtracking/knight_tour.cpp b/backtracking/knight_tour.cpp
@@ -1,6 +1,7 @@
 /**
  * @file
- * @brief [Knight's tour](https://en.wikipedia.org/wiki/Knight%27s_tour) algorithm
+ * @brief [Knight's tour](https://en.wikipedia.org/wiki/Knight%27s_tour)
+ * algorithm
  *
  * @details
  * A knight's tour is a sequence of moves of a knight on a chessboard
@@ -12,92 +13,102 @@
  * @author [Nikhil Arora](https://github.com/nikhilarora068)
  * @author [David Leal](https://github.com/Panquesito7)
  */
-#include <iostream>
-#include <array>
+#include <array>     /// for std::array
+#include <iostream>  /// for IO operations
 
 /**
  * @namespace backtracking
  * @brief Backtracking algorithms
  */
 namespace backtracking {
-    /**
-     * A utility function to check if i,j are valid indexes for N*N chessboard
-     * @tparam V number of vertices in array
-     * @param x current index in rows
-     * @param y current index in columns
-     * @param sol matrix where numbers are saved
-     * @returns `true` if ....
-     * @returns `false` if ....
-     */
-    template <size_t V>
-    bool issafe(int x, int y, const std::array <std::array <int, V>, V>& sol) {
-        return (x < V && x >= 0 && y < V && y >= 0 && sol[x][y] == -1);
-    }
+/**
+ * @namespace knight_tour
+ * @brief Functions for the [Knight's
+ * tour](https://en.wikipedia.org/wiki/Knight%27s_tour) algorithm
+ */
+namespace knight_tour {
+/**
+ * A utility function to check if i,j are valid indexes for N*N chessboard
+ * @tparam V number of vertices in array
+ * @param x current index in rows
+ * @param y current index in columns
+ * @param sol matrix where numbers are saved
+ * @returns `true` if ....
+ * @returns `false` if ....
+ */
+template <size_t V>
+bool issafe(int x, int y, const std::array<std::array<int, V>, V> &sol) {
+    return (x < V && x >= 0 && y < V && y >= 0 && sol[x][y] == -1);
+}
 
-    /**
-     * Knight's tour algorithm
-     * @tparam V number of vertices in array
-     * @param x current index in rows
-     * @param y current index in columns
-     * @param mov movement to be done
-     * @param sol matrix where numbers are saved
-     * @param xmov next move of knight (x coordinate)
-     * @param ymov next move of knight (y coordinate)
-     * @returns `true` if solution exists
-     * @returns `false` if solution does not exist
-     */
-    template <size_t V>
-    bool solve(int x, int y, int mov, std::array <std::array <int, V>, V> &sol,
-        const std::array <int, V> &xmov, std::array <int, V> &ymov) {
-        int k, xnext, ynext;
+/**
+ * Knight's tour algorithm
+ * @tparam V number of vertices in array
+ * @param x current index in rows
+ * @param y current index in columns
+ * @param mov movement to be done
+ * @param sol matrix where numbers are saved
+ * @param xmov next move of knight (x coordinate)
+ * @param ymov next move of knight (y coordinate)
+ * @returns `true` if solution exists
+ * @returns `false` if solution does not exist
+ */
+template <size_t V>
+bool solve(int x, int y, int mov, std::array<std::array<int, V>, V> &sol,
+           const std::array<int, V> &xmov, std::array<int, V> &ymov) {
+    int k = 0, xnext = 0, ynext = 0;
 
-        if (mov == V * V) {
-            return true;
-        }
+    if (mov == V * V) {
+        return true;
+    }
 
-        for (k = 0; k < V; k++) {
-            xnext = x + xmov[k];
-            ynext = y + ymov[k];
+    for (k = 0; k < V; k++) {
+        xnext = x + xmov[k];
+        ynext = y + ymov[k];
 
-            if (backtracking::issafe<V>(xnext, ynext, sol)) {
-                sol[xnext][ynext] = mov;
+        if (issafe<V>(xnext, ynext, sol)) {
+            sol[xnext][ynext] = mov;
 
-                if (backtracking::solve<V>(xnext, ynext, mov + 1, sol, xmov, ymov) == true) {
-                    return true;
-                }
-                else {
-                    sol[xnext][ynext] = -1;
-                }
+            if (solve<V>(xnext, ynext, mov + 1, sol, xmov, ymov) == true) {
+                return true;
+            } else {
+                sol[xnext][ynext] = -1;
             }
         }
-        return false;
     }
-} // namespace backtracking
+    return false;
+}
+}  // namespace knight_tour
+}  // namespace backtracking
 
 /**
- * Main function
+ * @brief Main function
+ * @returns 0 on exit
  */
 int main() {
     const int n = 8;
-    std::array <std::array <int, n>, n> sol = { 0 };
+    std::array<std::array<int, n>, n> sol = {0};
 
-    int i, j;
+    int i = 0, j = 0;
     for (i = 0; i < n; i++) {
-        for (j = 0; j < n; j++) { sol[i][j] = -1; }
+        for (j = 0; j < n; j++) {
+            sol[i][j] = -1;
+        }
     }
 
-    std::array <int, n> xmov = { 2, 1, -1, -2, -2, -1, 1, 2 };
-    std::array <int, n> ymov = { 1, 2, 2, 1, -1, -2, -2, -1 };
+    std::array<int, n> xmov = {2, 1, -1, -2, -2, -1, 1, 2};
+    std::array<int, n> ymov = {1, 2, 2, 1, -1, -2, -2, -1};
 
     sol[0][0] = 0;
 
-    bool flag = backtracking::solve<n>(0, 0, 1, sol, xmov, ymov);
+    bool flag = backtracking::knight_tour::solve<n>(0, 0, 1, sol, xmov, ymov);
     if (flag == false) {
         std::cout << "Error: Solution does not exist\n";
-    }
-    else {
+    } else {
         for (i = 0; i < n; i++) {
-            for (j = 0; j < n; j++) { std::cout << sol[i][j] << "  "; }
+            for (j = 0; j < n; j++) {
+                std::cout << sol[i][j] << "  ";
+            }
             std::cout << "\n";
         }
     }

diff --git a/backtracking/minimax.cpp b/backtracking/minimax.cpp
@@ -6,33 +6,34 @@
  * @details
  * Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in
  * artificial intelligence, decision theory, game theory, statistics,
- * and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario.
- * When dealing with gains, it is referred to as "maximin"—to maximize the minimum gain.
- * Originally formulated for two-player zero-sum game theory, covering both the cases where players take
- * alternate moves and those where they make simultaneous moves, it has also been extended to more
- * complex games and to general decision-making in the presence of uncertainty.
- * 
+ * and philosophy for minimizing the possible loss for a worst case (maximum
+ * loss) scenario. When dealing with gains, it is referred to as "maximin"—to
+ * maximize the minimum gain. Originally formulated for two-player zero-sum game
+ * theory, covering both the cases where players take alternate moves and those
+ * where they make simultaneous moves, it has also been extended to more complex
+ * games and to general decision-making in the presence of uncertainty.
+ *
  * @author [Gleison Batista](https://github.com/gleisonbs)
  * @author [David Leal](https://github.com/Panquesito7)
  */
-#include <algorithm>
-#include <cmath>
-#include <iostream>
-#include <array>
+#include <algorithm>  /// for std::max, std::min
+#include <array>      /// for std::array
+#include <cmath>      /// for log2
+#include <iostream>   /// for IO operations
 
-/** 
+/**
  * @namespace backtracking
  * @brief Backtracking algorithms
  */
 namespace backtracking {
 /**
- * Check which number is the maximum/minimum in the array
+ * @brief Check which is the maximum/minimum number in the array
  * @param depth current depth in game tree
  * @param node_index current index in array
  * @param is_max if current index is the longest number
  * @param scores saved numbers in array
  * @param height maximum height for game tree
- * @return maximum or minimum number
+ * @returns the maximum or minimum number
  */
 template <size_t T>
 int minimax(int depth, int node_index, bool is_max,
@@ -46,16 +47,17 @@ int minimax(int depth, int node_index, bool is_max,
 
     return is_max ? std::max(v1, v2) : std::min(v1, v2);
 }
-} // namespace backtracking
+}  // namespace backtracking
 
 /**
- * Main function
+ * @brief Main function
+ * @returns 0 on exit
  */
 int main() {
     std::array<int, 8> scores = {90, 23, 6, 33, 21, 65, 123, 34423};
     double height = log2(scores.size());
 
-    std::cout << "Optimal value: " << backtracking::minimax(0, 0, true, scores, height)
-              << std::endl;
+    std::cout << "Optimal value: "
+              << backtracking::minimax(0, 0, true, scores, height) << std::endl;
     return 0;
 }