//problem: en.m.wikipedia.org/wiki/Eight_queens_puzzle //Run on offline compiler to see the all result for more than 6 Queens. #include #include #include constexpr bool place_queen {true} ; constexpr bool remove_queen {false} ; void printBoard(); bool placeQueen(int); bool is_safe(int,int); constexpr int n = 6;//no of queens on the board. bool board[n][n]={};//initializing board with no queens in it. int count = 0;//to count the number of possible solution. //creating new structure to store coordinates of queens which has been placed on the board. struct coords{ int row,col; coords(int r , int c) : row{r} ,col{c} {} }; //to store the list of coordinates on which queen is present. std::vector Queens; int main() { Queens.reserve(n); //start placing the queen from first coloumn. placeQueen(0); if(n<7) std::cout << "Total no of solution found is : " << count; } //to print the board after all queen is placed. void printBoard(){ for(int i=0;i<=(n*5);i++,std::cout<<'-'); std::cout << '\n'; for(const auto& sub : board) { for(const auto& elem : sub) std::cout << (elem? " Q ": " ") << " |"; std::cout << '\n'; for(int i=0;i<=(n*5);i++,std::cout<<'-'); std::cout << '\n'; } std::cout << '\n'; count++; } //for checking the queens position before placing onto the board. bool is_safe(const int row,const int col){ for(auto& queen : Queens){ //if two queen is there on the same row. if(queen.row == row) return false; //if two queens are on the same diagonal then slope will be 1 so can not place there. if(std::abs(queen.row - row ) == std::abs(queen.col - col)) return false; } return true; } //for placing the queen on the board. bool placeQueen(const int col){ //if all queens are placed successfully on the board print the board and return true. if(col == n ){ printBoard(); return true; } //trying to place the queens on the different rows. for(int row = 0 ; row < n ; row++){ //checking to see if position is safe to place the queen or not. if(is_safe(row,col)){ //if it is safe to place queen then place it on the board. board[row][col] = place_queen; //add the coordinates on which queen is placed. Queens.emplace_back(row,col); //If there are more than 6 queens then app(sololearn) can't fetch all the result from server because time limit and I/O are to slow.... so better to retun after printing one solution. if(n>6) if(placeQueen(col+1)) return true; //now try to place the queens on the next columns. placeQueen(col+1); //now remove the queen from the last position to try different combinations. board[row][col] = remove_queen; //remove the coordinates from the list after removing the queen. Queens.pop_back(); } } return false; }

Queen's Problem