计算R程序 [英] Computation R program

问题描述

我想计算出可能的最小数字，该数字可以被1到20的所有自然数均分.我已经用R语言编写了以下程序，但并没有获得所需的输出(相反，看来我的循环几乎永无止境).

I want to compute the smallest possible number that is divisible evenly by all the natural numbers from 1-20; I have written the following program in R and am not getting the desired output (rather it seems my loop is almost never ending).

我的程序如下:

a = 21
c = 0
while ( c < 20){
    c = 0
    n = 1
    while ( n < 21 ){
        if (a%%n == 0) c = c + 1
        n = n+1
    }
    a = a + 1
}
print (a)

我哪里出错了?

推荐答案

这是一个更像R的解决方案，使用的事实是答案将是素数p <= 20的乘积，每个素数均会升至索引i，例如p^i <=20

Here's a more R-like solution using that fact that the answer will be the product of primes, p <= 20, each raised to an index i such that p^i <=20

sMult <- function(x)
# calculates smallest number that 1:x divides
{
    v <- 1:x
    require(gmp) # for isprime
    primes <- v[as.logical(isprime(v))]
    index <- floor(log(x)/log(primes))
    prod(rep(primes,index))
}

哪个产量:

> sMult(20)
[1] 232792560
> sMult(20)%%1:20
 [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

虽然此解决方案很一般，但应注意，对于大的x，isprime是概率性的.当然，当这很可能会导致错误的结果时，您也可能会拥有一个太大的数字，以致于无法准确存储该数字.幸运的是，gmp包实现了一个大的整数类bigz.若要将此更改用于函数的最后一行，请执行以下操作:

While this solution is general, it should be noted that for large x, isprime is probabalistic. Of course, when this is likely to give false results, you are also likely to have a number so large that it will not be able to be stored accurately. Fortunately the gmp package implements a large integer class, bigz. To use this change to final line of the function to:

prod(as.bigz(rep(primes,index)))

比较以下结果:

> sMult(1000)
[1] Inf
> sMult2(1000)
[1] "7128865274665093053166384155714272920668358861885893040452001991154324087581111499476444151913871586911717817019575256512980264067621009251465871004305131072686268143200196609974862745937188343705015434452523739745298963145674982128236956232823794011068809262317708861979540791247754558049326475737829923352751796735248042463638051137034331214781746850878453485678021888075373249921995672056932029099390891687487672697950931603520000"

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