[fix/docs]: Improve backtracking/nqueen_print_all_solutions.cpp (#1049)

* updating DIRECTORY.md

* updating DIRECTORY.md

* [fix/docs]: Improve backtracking/nqueen_print_all_solutions.cpp
Co-authored-by: Ngithub-actions <${GITHUB_ACTOR}@users.noreply.github.com>

backtracking/nqueen_print_all_solutions.cpp

+/**
+ * @file
+ * @brief [Eight Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) 
+ * puzzle, printing all solutions
+ *
+ * @author [Himani Negi](https://github.com/Himani2000)
+ * @author [David Leal](https://github.com/Panquesito7)
+ *
+ */
 #include <iostream>
-#define n 4
+#include <array>
 
-void PrintSol(int Board[n][n]) {
+/**
+ * @namespace backtracking
+ * @brief Backtracking algorithms
+ */
+namespace backtracking {
+/**
+ * @namespace n_queens_all_solutions
+ * @brief Functions for [Eight
+ * Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) puzzle with all solutions.
+ */
+namespace n_queens_all_solutions {
+/**
+ * Utility function to print matrix
+ * @tparam n number of matrix size
+ * @param board matrix where numbers are saved
+ */
+template <size_t n>
+void PrintSol(const std::array<std::array<int, n>, n>& board) {
     for (int i = 0; i < n; i++) {
         for (int j = 0; j < n; j++) {
-            std::cout << Board[i][j] << " ";
+            std::cout << board[i][j] << " ";
         }
         std::cout << std::endl;
     }
     std::cout << std::endl;
 }
 
-bool CanIMove(int Board[n][n], int row, int col) {
+/**
+ * Check if a queen can be placed on matrix
+ * @tparam n number of matrix size
+ * @param board matrix where numbers are saved
+ * @param row current index in rows
+ * @param col current index in columns
+ * @returns `true` if queen can be placed on matrix
+ * @returns `false` if queen can't be placed on matrix
+ */
+template <size_t n>
+bool CanIMove(const std::array<std::array<int, n>, n>& board, int row, int col) {
     /// check in the row
     for (int i = 0; i < col; i++) {
-        if (Board[row][i] == 1)
+        if (board[row][i] == 1) {
             return false;
+        }
     }
     /// check the first diagonal
     for (int i = row, j = col; i >= 0 && j >= 0; i--, j--) {
-        if (Board[i][j] == 1)
+        if (board[i][j] == 1) {
             return false;
+        }
     }
     /// check the second diagonal
     for (int i = row, j = col; i <= n - 1 && j >= 0; i++, j--) {
-        if (Board[i][j] == 1)
+        if (board[i][j] == 1) {
             return false;
+        }
     }
     return true;
 }
 
-void NQueenSol(int Board[n][n], int col) {
+/**
+ * Solve n queens problem
+ * @tparam n number of matrix size
+ * @param board matrix where numbers are saved
+ * @param col current index in columns
+ */
+template <size_t n>
+void NQueenSol(std::array<std::array<int, n>, n> board, int col) {
     if (col >= n) {
-        PrintSol(Board);
+        PrintSol(board);
         return;
     }
     for (int i = 0; i < n; i++) {
-        if (CanIMove(Board, i, col)) {
-            Board[i][col] = 1;
-            NQueenSol(Board, col + 1);
-            Board[i][col] = 0;
+        if (CanIMove(board, i, col)) {
+            board[i][col] = 1;
+            NQueenSol(board, col + 1);
+            board[i][col] = 0;
         }
     }
 }
+}   // namespace n_queens_all_solutions
+}  // namespace backtracking
 
+/**
+ * Main function
+ */
 int main() {
-    int Board[n][n] = {0};
-    NQueenSol(Board, 0);
+    const int n = 4;
+    std::array<std::array<int, n>, n> board{0};
+
+    backtracking::n_queens_all_solutions::NQueenSol(board, 0);
 }