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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