a021: 大數運算-1

a021: 大數運算-1

我們都知道電腦擅長於各種數字的計算，可是，我們又知道各種程式語言的變數又都有上限，比如整數只有2¹⁶ 或 2³² 個。如果要計算更大的數字時又該如何計算呢? 就交給聰明的您來解決囉。
以 + 代表加法
以 - 代表減法
以 * 代表乘法
以 / 代表除法 (取商數)


# check the numeric range of Python with huge factorials
# factorial(69) still checks out accurately! Has 98 digits in it!
# 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000
# tested with Python24      vegaseat    01aug2005

def getFactorial(n):
    """returns the factorial of n"""
    if n == 0:
        return 1
    else:
        k = n * getFactorial(n-1)
        return k
for k in range(1, 70):
    print ("factorial of", k,"=", getFactorial(k))

factorial of 1 = 1
factorial of 2 = 2
factorial of 3 = 6
factorial of 4 = 24
factorial of 5 = 120
factorial of 6 = 720
factorial of 7 = 5040
factorial of 8 = 40320
factorial of 9 = 362880
factorial of 10 = 3628800
factorial of 11 = 39916800
factorial of 12 = 479001600
factorial of 13 = 6227020800
factorial of 14 = 87178291200
factorial of 15 = 1307674368000
factorial of 16 = 20922789888000
factorial of 17 = 355687428096000
factorial of 18 = 6402373705728000
factorial of 19 = 121645100408832000
factorial of 20 = 2432902008176640000
factorial of 21 = 51090942171709440000
factorial of 22 = 1124000727777607680000
factorial of 23 = 25852016738884976640000
factorial of 24 = 620448401733239439360000
factorial of 25 = 15511210043330985984000000
factorial of 26 = 403291461126605635584000000
factorial of 27 = 10888869450418352160768000000
factorial of 28 = 304888344611713860501504000000
factorial of 29 = 8841761993739701954543616000000
factorial of 30 = 265252859812191058636308480000000
factorial of 31 = 8222838654177922817725562880000000
factorial of 32 = 263130836933693530167218012160000000
factorial of 33 = 8683317618811886495518194401280000000
factorial of 34 = 295232799039604140847618609643520000000
factorial of 35 = 10333147966386144929666651337523200000000
factorial of 36 = 371993326789901217467999448150835200000000
factorial of 37 = 13763753091226345046315979581580902400000000
factorial of 38 = 523022617466601111760007224100074291200000000
factorial of 39 = 20397882081197443358640281739902897356800000000
factorial of 40 = 815915283247897734345611269596115894272000000000
factorial of 41 = 33452526613163807108170062053440751665152000000000
factorial of 42 = 1405006117752879898543142606244511569936384000000000
factorial of 43 = 60415263063373835637355132068513997507264512000000000
factorial of 44 = 2658271574788448768043625811014615890319638528000000000
factorial of 45 = 119622220865480194561963161495657715064383733760000000000
factorial of 46 = 5502622159812088949850305428800254892961651752960000000000
factorial of 47 = 258623241511168180642964355153611979969197632389120000000000
factorial of 48 = 12413915592536072670862289047373375038521486354677760000000000
factorial of 49 = 608281864034267560872252163321295376887552831379210240000000000
factorial of 50 = 30414093201713378043612608166064768844377641568960512000000000000
factorial of 51 = 1551118753287382280224243016469303211063259720016986112000000000000
factorial of 52 = 80658175170943878571660636856403766975289505440883277824000000000000
factorial of 53 = 4274883284060025564298013753389399649690343788366813724672000000000000
factorial of 54 = 230843697339241380472092742683027581083278564571807941132288000000000000
factorial of 55 = 12696403353658275925965100847566516959580321051449436762275840000000000000
factorial of 56 = 710998587804863451854045647463724949736497978881168458687447040000000000000
factorial of 57 = 40526919504877216755680601905432322134980384796226602145184481280000000000000
factorial of 58 = 2350561331282878571829474910515074683828862318181142924420699914240000000000000
factorial of 59 = 138683118545689835737939019720389406345902876772687432540821294940160000000000000
factorial of 60 = 8320987112741390144276341183223364380754172606361245952449277696409600000000000000
factorial of 61 = 507580213877224798800856812176625227226004528988036003099405939480985600000000000000
factorial of 62 = 31469973260387937525653122354950764088012280797258232192163168247821107200000000000000
factorial of 63 = 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000
factorial of 64 = 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000
factorial of 65 = 8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000
factorial of 66 = 544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000
factorial of 67 = 36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000
factorial of 68 = 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000
factorial of 69 = 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000
>>>