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  1. // Much shorter than the version below;
  2. // uses C++11 threads to parallelize the computation; also uses backtracking
  3. // Outputs all solutions for any table size
  4. #include <vector>
  5. #include <iostream>
  6. #include <iomanip>
  7. #include <thread>
  8. #include <future>
  9.  
  10. // Print table. 'pos' is a vector of positions – the index in pos is the row,
  11. // and the number at that index is the column where the queen is placed.
  12. static void print(const std::vector<int> &pos)
  13. {
  14. 	// print table header
  15. 	for (int i = 0; i < pos.size(); i++) {
  16. 		std::cout << std::setw(3) << char('a' + i);
  17. 	}
  18.  
  19. 	std::cout << '\n';
  20.  
  21. 	for (int row = 0; row < pos.size(); row++) {
  22. 		int col = pos[row];
  23. 		std::cout << row + 1 << std::setw(3 * col + 3) << " # ";
  24. 		std::cout << '\n';
  25. 	}
  26.  
  27. 	std::cout << "\n\n";
  28. }
  29.  
  30. static bool threatens(int row_a, int col_a, int row_b, int col_b)
  31. {
  32. 	return row_a == row_b // same row
  33. 		or col_a == col_b // same column
  34. 		or std::abs(row_a - row_b) == std::abs(col_a - col_b); // diagonal
  35. }
  36.  
  37. // the i-th queen is in the i-th row
  38. // we only check rows up to end_idx
  39. // so that the same function can be used for backtracking and checking the final solution
  40. static bool good(const std::vector<int> &pos, int end_idx)
  41. {
  42. 	for (int row_a = 0; row_a < end_idx; row_a++) {
  43. 		for (int row_b = row_a + 1; row_b < end_idx; row_b++) {
  44. 			int col_a = pos[row_a];
  45. 			int col_b = pos[row_b];
  46. 			if (threatens(row_a, col_a, row_b, col_b)) {
  47. 				return false;
  48. 			}
  49. 		}
  50. 	}
  51.  
  52. 	return true;
  53. }
  54.  
  55. static std::mutex print_count_mutex; // mutex protecting 'n_sols'
  56. static int n_sols = 0; // number of solutions
  57.  
  58. // recursive DFS backtracking solver
  59. static void n_queens(std::vector<int> &pos, int index)
  60. {
  61. 	// if we have placed a queen in each row (i. e. we are at a leaf of the search tree), check solution and return
  62. 	if (index >= pos.size()) {
  63. 		if (good(pos, index)) {
  64. 			std::lock_guard<std::mutex> lock(print_count_mutex);
  65. 			print(pos);
  66. 			n_sols++;
  67. 		}
  68.  
  69. 		return;
  70. 	}
  71.  
  72. 	// backtracking step
  73. 	if (not good(pos, index)) {
  74. 		return;
  75. 	}
  76.  
  77. 	// optimization: the first level of the search tree is parallelized
  78. 	if (index == 0) {
  79. 		std::vector<std::future<void>> fts;
  80. 		for (int col = 0; col < pos.size(); col++) {
  81. 			pos[index] = col;
  82. 			auto ft = std::async(std::launch::async, [=]{ auto cpos(pos); n_queens(cpos, index + 1); });
  83. 			fts.push_back(std::move(ft));
  84. 		}
  85.  
  86. 		for (const auto &ft : fts) {
  87. 			ft.wait();
  88. 		}
  89. 	} else { // deeper levels are not
  90. 		for (int col = 0; col < pos.size(); col++) {
  91. 			pos[index] = col;
  92. 			n_queens(pos, index + 1);
  93. 		}
  94. 	}
  95. }
  96.  
  97. int main()
  98. {
  99. 	std::vector<int> start(12); // 12: table size
  100. 	n_queens(start, 0);
  101. 	std::cout << n_sols << " solutions found.\n";
  102. 	return 0;
  103. }
Runtime error #stdin #stdout 0.04s 35232KB
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https://ideone.com/Db8e6k
language:
C++14 (gcc 8.3)
created:
7 years ago
visibility:
public

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