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/**
* @file
* @brief [Knight's tour](https://en.wikipedia.org/wiki/Knight%27s_tour)
* algorithm
*
* @details
* A knight's tour is a sequence of moves of a knight on a chessboard
* such that the knight visits every square only once. If the knight
* ends on a square that is one knight's move from the beginning
* square (so that it could tour the board again immediately, following
* the same path, the tour is closed; otherwise, it is open.
*
* @author [Nikhil Arora](https://github.com/nikhilarora068)
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <array> /// for std::array
#include <iostream> /// for IO operations
/**
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/**
* @namespace knight_tour
* @brief Functions for the [Knight's
* tour](https://en.wikipedia.org/wiki/Knight%27s_tour) algorithm
*/
namespace knight_tour {
/**
* A utility function to check if i,j are valid indexes for N*N chessboard
* @tparam V number of vertices in array
* @param x current index in rows
* @param y current index in columns
* @param sol matrix where numbers are saved
* @returns `true` if ....
* @returns `false` if ....
*/
template <size_t V>
bool issafe(int x, int y, const std::array<std::array<int, V>, V> &sol) {
return (x < V && x >= 0 && y < V && y >= 0 && sol[x][y] == -1);
}
/**
* Knight's tour algorithm
* @tparam V number of vertices in array
* @param x current index in rows
* @param y current index in columns
* @param mov movement to be done
* @param sol matrix where numbers are saved
* @param xmov next move of knight (x coordinate)
* @param ymov next move of knight (y coordinate)
* @returns `true` if solution exists
* @returns `false` if solution does not exist
*/
template <size_t V>
bool solve(int x, int y, int mov, std::array<std::array<int, V>, V> &sol,
const std::array<int, V> &xmov, std::array<int, V> &ymov) {
int k = 0, xnext = 0, ynext = 0;
if (mov == V * V) {
return true;
}
for (k = 0; k < V; k++) {
xnext = x + xmov[k];
ynext = y + ymov[k];
if (issafe<V>(xnext, ynext, sol)) {
sol[xnext][ynext] = mov;
if (solve<V>(xnext, ynext, mov + 1, sol, xmov, ymov) == true) {
return true;
} else {
sol[xnext][ynext] = -1;
}
}
}
return false;
}
} // namespace knight_tour
} // namespace backtracking
/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
const int n = 8;
std::array<std::array<int, n>, n> sol = {0};
int i = 0, j = 0;
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
sol[i][j] = -1;
}
}
std::array<int, n> xmov = {2, 1, -1, -2, -2, -1, 1, 2};
std::array<int, n> ymov = {1, 2, 2, 1, -1, -2, -2, -1};
sol[0][0] = 0;
bool flag = backtracking::knight_tour::solve<n>(0, 0, 1, sol, xmov, ymov);
if (flag == false) {
std::cout << "Error: Solution does not exist\n";
} else {
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
std::cout << sol[i][j] << " ";
}
std::cout << "\n";
}
}
return 0;
}