N- Queens Algorithm
The eight queens puzzle is an example of the more general N queens problem of put N non-attacking queens on an n×n chessboard, for which solutions exist for all natural numbers N with the exception of N = 2 and N = 3.The eight queens puzzle is the problem of put eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution necessitates that no two queens share the same row, column, or diagonal. Chess composer Max Bezzel published the eight queens puzzle in 1848.Nauck also extended the puzzle to the N queens problem, with N queens on a chessboard of n×n squares. In 1874, S. Gunther proposed a method use determinants to find solutions.
class Solution {
public:
vector<vector<string> > solveNQueens(int n) {
vector<vector<string>> result;
if (n == 0) {
return result;
}
vector<string> sol(n, string(n, '.'));
vector<vector<bool>> visited(3, vector<bool>(2*n, false));
dfs(result, sol, visited, 0);
return result;
}
void dfs(vector<vector<string>>& result, vector<string>& sol, vector<vector<bool>>& visited, int row) {
int n = sol.size();
if (row == n) {
result.push_back(sol);
return;
}
for (int col = 0; col < n; col++) {
if (visited[0][col] || visited[1][row+col] || visited[2][n-1-row+col]) {
continue;
}
visited[0][col] = true;
visited[1][row+col] = true;
visited[2][n-1-row+col] = true;
sol[row][col] = 'Q';
dfs(result, sol, visited, row + 1);
sol[row][col] = '.';
visited[0][col] = false;
visited[1][row+col] = false;
visited[2][n-1-row+col] = false;
}
}
};
