From 7808390bbef847ca5f2957ac1dd8088cab7776ce Mon Sep 17 00:00:00 2001
From: David Leal <halfpacho@gmail.com>
Date: Tue, 18 Aug 2020 17:13:16 -0500
Subject: [PATCH] [fix/docs]: Improve backtracking/n_queens_...

...all_solution_optimised.cpp
---
 .../n_queens_all_solution_optimised.cpp       | 164 ++++++++++++------
 1 file changed, 110 insertions(+), 54 deletions(-)

diff --git a/backtracking/n_queens_all_solution_optimised.cpp b/backtracking/n_queens_all_solution_optimised.cpp
index 4f42fba6f..d506f0d7a 100644
--- a/backtracking/n_queens_all_solution_optimised.cpp
+++ b/backtracking/n_queens_all_solution_optimised.cpp
@@ -1,73 +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]) {
+
+/**
+ * @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) {
+  inc_loop(i, 0, n - 1) {
+    inc_loop(j, 0, n - 1) { 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) {
-        inc_loop(j, 0, n - 1) std::cout << Board[i][j] << " ";
-        std::cout << std::endl;
+      dec_loop(j, n - 1, 0) { 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] << " ";
-            std::cout << std::endl;
-        }
-        std::cout << std::endl;
-    }
+  }
 }
 
-bool CanIMove(int Board[n][n], int row, int col) {
-    /// check in the row
-    inc_loop(i, 0, col - 1) {
-        if (Board[row][i] == 1)
-            return false;
+/**
+ * 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) {
+      return false;
     }
-    /// check the first diagonal
-    for (int i = row, j = col; i >= 0 && j >= 0; i--, j--) {
-        if (Board[i][j] == 1)
-            return false;
+  }
+  /// check the first diagonal
+  for (int i = row, j = col; i >= 0 && j >= 0; i--, j--) {
+    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)
-            return false;
+  }
+  /// check the second diagonal
+  for (int i = row, j = col; i <= n - 1 && j >= 0; i++, j--) {
+    if (board[i][j] == 1) {
+      return false;
     }
-    return true;
+  }
+  return true;
 }
 
-void NQueenSol(int Board[n][n], int col) {
-    if (col >= n) {
-        PrintSol(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;
-        }
+/**
+ * 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<n>(board);
+    return;
+  }
+  inc_loop(i, 0, n - 1) {
+    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
 
+/**
+ * Main function
+ */
 int main() {
-    int Board[n][n] = {0};
-    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;
-            }
-        }
-    } else {
-        inc_loop(i, 0, n / 2) {
-            if (CanIMove(Board, i, 0)) {
-                Board[i][0] = 1;
-                NQueenSol(Board, 1);
-                Board[i][0] = 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 (backtracking::n_queens_optimized::CanIMove(board, i, 0)) {
+        board[i][0] = 1;
+        backtracking::n_queens_optimized::NQueenSol(board, 1);
+        board[i][0] = 0;
+      }
     }
-    return 0;
+  } else {
+    inc_loop(i, 0, n / 2) {
+      if (backtracking::n_queens_optimized::CanIMove(board, i, 0)) {
+        board[i][0] = 1;
+        backtracking::n_queens_optimized::NQueenSol(board, 1);
+        board[i][0] = 0;
+      }
+    }
+  }
+  return 0;
 }