How to determine if double would be precise enough?

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I was trying to solve the problem FTRIP Field Trip. I came to the conclusion that I have to calculate some binomial coefficients C(n,k). But the ranges were high. At the worst case I have to calculate C(1000,500). This obviously will not fit 64 bit int. I could use doubles, but even that will not be precise enough ( or so I thought ). I tried thinking of other solutions that didn’t involve binomial coefficient, but didn’t find any. If only I could calculate C(n,k) with enough precision then problem would be solved.

Then I went to the editorial to see how they handled the situation. They used double. Now I am confused. How will I determine if the double would be precise enough to get me AC? Is it because this problem has special judge that using double leads to AC?

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double range is upto 10^307 and C(1000,500) is around 10^299

For calculating C(1000,500)-http://www.wolframalpha.com/input/?i=1000+choose+500&lk=4

For c++ ranges refer-http://www.cplusplus.com/doc/tutorial/variables/

Also note in double there is huge precision loss due to limited number of bits.

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I would suggest you to read http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

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That’s one big article! I read it a bit and discovered few new things, such as why 0/0 gives RE but 0/0.0 gives NAN. Thanks.