diff --git a/backtracking/n_queens_all_solution_optimised.cpp b/backtracking/n_queens_all_solution_optimised.cpp new file mode 100644 index 000000000..1db730f63 --- /dev/null +++ b/backtracking/n_queens_all_solution_optimised.cpp @@ -0,0 +1,75 @@ +#include +#define n 4 +#define inc_loop(var, start, stop) for (int var=start; var <= stop; var++) +#define dec_loop(var, start, stop) for (int var=start; var >= stop; var--) +void PrintSol(int Board[n][n]) { + inc_loop(i, 0, n-1) { + inc_loop(j, 0, n-1) + std::cout << Board[i][j] << " "; + std::cout << std::endl; + } + std::cout << std::endl; + if (n%2 == 0 || (n%2 == 1 && Board[n/2+1][0] != 1)) { + inc_loop(i, 0, n-1) { + dec_loop(j, n-1, 0) + std::cout << Board[i][j] << " "; + std::cout << std::endl; + } + std::cout << std::endl; + } +} + +bool CanIMove(int Board[n][n], int row, int col) { + /// check in the row + inc_loop(i, 0, col-1) { + if (Board[row][i] == 1) + return false; + } + /// check the first diagonal + for (int i = row, j = col; i >= 0 && j >= 0; i--, j--) { + if (Board[i][j] == 1) + return false; + } + /// check the second diagonal + for (int i = row, j = col; i <= n - 1 && j >= 0; i++, j--) { + if (Board[i][j] == 1) + return false; + } + return true; +} + +void NQueenSol(int Board[n][n], int col) { + if (col >= n) { + PrintSol(Board); + return; + } + inc_loop(i, 0, n-1) { + if (CanIMove(Board, i, col)) { + Board[i][col] = 1; + NQueenSol(Board, col + 1); + Board[i][col] = 0; + } + } +} + +int main() { + int Board[n][n] = {0}; + if (n%2 == 0) { + inc_loop(i, 0, n/2-1) { + if (CanIMove(Board, i, 0)) { + Board[i][0] = 1; + NQueenSol(Board, 1); + Board[i][0] = 0; + } + } + } else { + inc_loop(i, 0, n/2) { + if (CanIMove(Board, i, 0)) { + Board[i][0] = 1; + NQueenSol(Board, 1); + Board[i][0] = 0; + } + } + } + return 0; +}