package q52

func findNSolutions(nQueen, row int, rows, cols, diag1, diag2 []bool) int {
	solutions := 0
	if row == nQueen {
		return 1
	}
	for col := range nQueen {
		// if grid[row][col] is placeable
		if !rows[row] && !cols[col] && !diag1[row+col] && !diag2[row-col+nQueen] {
			rows[row], cols[col], diag1[row+col], diag2[row-col+nQueen] = true, true, true, true
			solutions += findNSolutions(nQueen, row+1, rows, cols, diag1, diag2)
			rows[row], cols[col], diag1[row+col], diag2[row-col+nQueen] = false, false, false, false
		}
	}
	return solutions
}

func totalNQueens(n int) int {
	buf := make([]bool, 6*n)
	return findNSolutions(n, 0, buf[0:n], buf[n:2*n], buf[2*n:4*n], buf[4*n:])
}

var _ = totalNQueens