How much work do आप think it took to write Snapes backstory?

That's a good question, and one only JK knows the answer to.

Speaking as a writer, complex characters aren't always the hardest characters to write. Sometimes it's the basic, black-and-white characters that give the most trouble. And sometimes the backgrounds just flow easily, regardless of the complexity of the character, either because it fits with the story या because it's just "right" for the character. It also depends on the authors personal strengths and weakness. Sometimes developing characters --regardless of complexity -- is just naturally a struggle for some authors.

This is one of one of those सवालों where it's anyine's guess and, until JK says otherwise, there really isn't a right या wrong answer.

OK, difficult to answer, because I'm not J. K. Rowling.
But as a writer I must say, that sometimes, when I'm in a good mood, when I have a character I love, I'm able to make up his past (in my mind) within some little moments. It is the structure of what I see in him, या of what he means to me. To write the whole thing down is much और complicated. It can take years! But thats only what I think about this stuff.