From b7621157cb978c5b5e3761bddf6f8ffbc6269216 Mon Sep 17 00:00:00 2001
From: David Leal <halfpacho@gmail.com>
Date: Mon, 10 Aug 2020 18:37:51 -0500
Subject: [PATCH] fix: Add namespace member: n_queens

---
 backtracking/n_queens.cpp | 156 ++++++++++++++++++++------------------
 1 file changed, 81 insertions(+), 75 deletions(-)

diff --git a/backtracking/n_queens.cpp b/backtracking/n_queens.cpp
index c864fff6a..7ba7cf52e 100644
--- a/backtracking/n_queens.cpp
+++ b/backtracking/n_queens.cpp
@@ -23,87 +23,93 @@
  * @brief Backtracking algorithms
  */
 namespace backtracking {
-/**
- * Utility function to print matrix
- * @tparam n number of matrix size
- * @param board matrix where numbers are saved
- */
-template <size_t n>
-void printSolution(const std::array<std::array<int, n>, n> &board) {
-  std::cout << "\n";
-  for (int i = 0; i < n; i++) {
-    for (int j = 0; j < n; j++) {
-      std::cout << "" << board[i][j] << " ";
+  /**
+   * @namespace n_queens
+   * @brief Functions for [Eight Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) puzzle.
+   */
+  namespace n_queens {
+    /**
+    * Utility function to print matrix
+    * @tparam n number of matrix size
+    * @param board matrix where numbers are saved
+    */
+    template <size_t n>
+    void printSolution(const std::array<std::array<int, n>, n> &board) {
+      std::cout << "\n";
+      for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++) {
+          std::cout << "" << board[i][j] << " ";
+        }
+        std::cout << "\n";
+      }
     }
-    std::cout << "\n";
-  }
-}
 
-/**
- * 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 isSafe(const std::array<std::array<int, n>, n> &board, const int &row,
-            const int &col) {
-  int i = 0, j = 0;
+    /**
+    * 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 isSafe(const std::array<std::array<int, n>, n> &board, const int &row,
+                const int &col) {
+      int i = 0, j = 0;
 
-  // Check this row on left side
-  for (i = 0; i < col; i++) {
-    if (board[row][i]) {
-      return false;
+      // Check this row on left side
+      for (i = 0; i < col; i++) {
+        if (board[row][i]) {
+          return false;
+        }
+      }
+
+      // Check upper diagonal on left side
+      for (i = row, j = col; i >= 0 && j >= 0; i--, j--) {
+        if (board[i][j]) {
+          return false;
+        }
+      }
+      // Check lower diagonal on left side
+      for (i = row, j = col; j >= 0 && i < n; i++, j--) {
+        if (board[i][j]) {
+          return false;
+        }
+      }
+      return true;
     }
-  }
 
-  // Check upper diagonal on left side
-  for (i = row, j = col; i >= 0 && j >= 0; i--, j--) {
-    if (board[i][j]) {
-      return false;
+    /**
+    * 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 solveNQ(std::array<std::array<int, n>, n> board, const int &col) {
+      if (col >= n) {
+        printSolution<n>(board);
+        return;
+      }
+
+      // Consider this column and try placing
+      // this queen in all rows one by one
+      for (int i = 0; i < n; i++) {
+        // Check if queen can be placed
+        // on board[i][col]
+        if (isSafe<n>(board, i, col)) {
+          // Place this queen in matrix
+          board[i][col] = 1;
+
+          // Recursive to place rest of the queens
+          solveNQ<n>(board, col + 1);
+
+          board[i][col] = 0; // backtrack
+        }
+      }
     }
-  }
-  // Check lower diagonal on left side
-  for (i = row, j = col; j >= 0 && i < n; i++, j--) {
-    if (board[i][j]) {
-      return false;
-    }
-  }
-  return true;
-}
-
-/**
- * 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 solveNQ(std::array<std::array<int, n>, n> board, const int &col) {
-  if (col >= n) {
-    printSolution<n>(board);
-    return;
-  }
-
-  // Consider this column and try placing
-  // this queen in all rows one by one
-  for (int i = 0; i < n; i++) {
-    // Check if queen can be placed
-    // on board[i][col]
-    if (isSafe<n>(board, i, col)) {
-      // Place this queen in matrix
-      board[i][col] = 1;
-
-      // Recursive to place rest of the queens
-      solveNQ<n>(board, col + 1);
-
-      board[i][col] = 0; // backtrack
-    }
-  }
-}
+  } // namespace n_queens
 } // namespace backtracking
 
 /**