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fix: Add namespace member: n_queens

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David Leal 2020-08-10 18:37:51 -05:00
parent 358f56f9be
commit b7621157cb
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1 changed files with 81 additions and 75 deletions
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156
backtracking/n_queens.cpp
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@ -23,87 +23,93 @@
* @brief Backtracking algorithms * @brief Backtracking algorithms
*/ */
namespace backtracking { namespace backtracking {
/** /**
* Utility function to print matrix * @namespace n_queens
* @tparam n number of matrix size * @brief Functions for [Eight Queens](https://en.wikipedia.org/wiki/Eight_queens_puzzle) puzzle.
* @param board matrix where numbers are saved */
*/ namespace n_queens {
template <size_t n> /**
void printSolution(const std::array<std::array<int, n>, n> &board) { * Utility function to print matrix
std::cout << "\n"; * @tparam n number of matrix size
for (int i = 0; i < n; i++) { * @param board matrix where numbers are saved
for (int j = 0; j < n; j++) { */
std::cout << "" << board[i][j] << " "; 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 * Check if a queen can be placed on matrix
* @tparam n number of matrix size * @tparam n number of matrix size
* @param board matrix where numbers are saved * @param board matrix where numbers are saved
* @param row current index in rows * @param row current index in rows
* @param col current index in columns * @param col current index in columns
* @returns `true` if queen can be placed on matrix * @returns `true` if queen can be placed on matrix
* @returns `false` if queen can't be placed on matrix * @returns `false` if queen can't be placed on matrix
*/ */
template <size_t n> template <size_t n>
bool isSafe(const std::array<std::array<int, n>, n> &board, const int &row, bool isSafe(const std::array<std::array<int, n>, n> &board, const int &row,
const int &col) { const int &col) {
int i = 0, j = 0; int i = 0, j = 0;
// Check this row on left side // Check this row on left side
for (i = 0; i < col; i++) { for (i = 0; i < col; i++) {
if (board[row][i]) { if (board[row][i]) {
return false; 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--) { * Solve n queens problem
if (board[i][j]) { * @tparam n number of matrix size
return false; * @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
// 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 backtracking } // namespace backtracking
/** /**