函数查找Pi的第n个位数 [英] Function to find the nth digit of Pi
问题描述
我一直想找到一种算法,这样做。我不在乎它有多慢,只是只要它可以返回Pi的第n个位:
I have always wanted to find an algorithm that did this. I do not care how slow it is, just as long as it can return the nth digit of Pi:
例如:
size_t piAt(long long int n)
{
}
preferably,不使用无限系列。
Preferably, not using an infinite series.
如果任何人有一个函数或类,这是否在C或C ++我真的有兴趣看到它。
If anyone has a function or class that does this, in C or C++ I'd really be interested in seeing it.
感谢
推荐答案
这种不寻常的解决方案说明如何计算这n 日π的O(N)的时间和O的数字(日志·N)的空间,这样做,而不必计算所有导致它的数字。
This remarkable solution shows how to compute the Nth digit of π in O(N) time and O(log·N) space, and to do so without having to compute all the digits leading up to it.
呵呵,这是十六进制。
Oh, and it’s in hex.
如果你不想这样做,你可以从外壳很轻松地做到这一点:
If you don’t want to do that, you can do this from the shell easily enough:
% perl -Mbignum=bpi -wle 'print bpi(20)'
3.1415926535897932385
% perl -Mbignum=bpi -wle 'print bpi(50)'
3.1415926535897932384626433832795028841971693993751
% perl -Mbignum=bpi -wle 'print bpi(200)'
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303820
% perl -Mbignum=bpi -wle 'print bpi(1000)'
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199
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