I'm trying to go from Beijing to Shenzhen on the morning of April 12th... I land into Beijing at 10pm on April 11th... do you think I'll be able to just show up at the airport and buy my flight? Any idea how much I should expect to pay? On C-trip it looks like there are discounted flights as low as 800rmb, but when I try to book it says the flights are full.

I don't have a hotel in Beijing - i want to stay near the airport that first night, and am looking for the cheapest possible option... any ideas?
Thanks