[fix/docs]: Improve backtracking/n_queens_all_solution_optimised.cpp (#1041)

* updating DIRECTORY.md

* [fix/docs]: Improve backtracking/n_queens_...

...all_solution_optimised.cpp

* fix: Remove function-like macros

* clang-format and clang-tidy fixes for 689b788c

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

backtracking/n_queens_all_solution_optimised.cpp

@@ -1,71 +1,129 @@
+/**
+ * @file
+ * @brief [N queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) all
+ * optimized
+ *
+ * @author [Sombit Bose](https://github.com/deadshotsb)
+ * @author [David Leal](https://github.com/Panquesito7)
+ */
+
+#include <array>
 #include <iostream>
-#define n 4
-#define inc_loop(var, start, stop) for (int var = start; var <= stop; var++)
-#define dec_loop(var, start, stop) for (int var = start; var >= stop; var--)
-void PrintSol(int Board[n][n]) {
-    inc_loop(i, 0, n - 1) {
-        inc_loop(j, 0, n - 1) std::cout << Board[i][j] << " ";
+
+/**
+ * @namespace backtracking
+ * @brief Backtracking algorithms
+ */
+namespace backtracking {
+/**
+ * @namespace n_queens_optimized
+ * @brief Functions for [Eight
+ * Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) puzzle optimized.
+ */
+namespace n_queens_optimized {
+/**
+ * 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 << std::endl;
     }
     std::cout << std::endl;
-    if (n % 2 == 0 || (n % 2 == 1 && Board[n / 2 + 1][0] != 1)) {
-        inc_loop(i, 0, n - 1) {
-            dec_loop(j, n - 1, 0) std::cout << Board[i][j] << " ";
+    if (n % 2 == 0 || (n % 2 == 1 && board[n / 2 + 1][0] != 1)) {
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                std::cout << board[j][i] << " ";
+            }
             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
-    inc_loop(i, 0, col - 1) {
-        if (Board[row][i] == 1)
+    for (int i = 0; i <= col; i++) {
+        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<n>(board);
         return;
     }
-    inc_loop(i, 0, n - 1) {
-        if (CanIMove(Board, i, col)) {
-            Board[i][col] = 1;
-            NQueenSol(Board, col + 1);
-            Board[i][col] = 0;
+    for (int i = 0; i < n; i++) {
+        if (CanIMove<n>(board, i, col)) {
+            board[i][col] = 1;
+            NQueenSol<n>(board, col + 1);
+            board[i][col] = 0;
         }
     }
 }
+}  // namespace n_queens_optimized
+}  // namespace backtracking
 
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
 int main() {
-    int Board[n][n] = {0};
+    const int n = 4;
+    std::array<std::array<int, n>, n> board{};
+
     if (n % 2 == 0) {
-        inc_loop(i, 0, n / 2 - 1) {
-            if (CanIMove(Board, i, 0)) {
-                Board[i][0] = 1;
-                NQueenSol(Board, 1);
-                Board[i][0] = 0;
+        for (int i = 0; i <= n / 2 - 1; i++) {  // 😎
+            if (backtracking::n_queens_optimized::CanIMove(board, i, 0)) {
+                board[i][0] = 1;
+                backtracking::n_queens_optimized::NQueenSol(board, 1);
+                board[i][0] = 0;
             }
         }
     } else {
-        inc_loop(i, 0, n / 2) {
-            if (CanIMove(Board, i, 0)) {
-                Board[i][0] = 1;
-                NQueenSol(Board, 1);
-                Board[i][0] = 0;
+        for (int i = 0; i <= n / 2; i++) {  // 😏
+            if (backtracking::n_queens_optimized::CanIMove(board, i, 0)) {
+                board[i][0] = 1;
+                backtracking::n_queens_optimized::NQueenSol(board, 1);
+                board[i][0] = 0;
             }
         }
     }