两道硬币面试题 2011-11-24

Q1: 一个均匀硬币不断抛啊抛,假如抛个100次,那么连续抛出同一面的次数,这个次数最多是多少?

coin.len = function(v) {
    x = rbinom(1:v, 1, 0.5)
    len = 1
    for (i in 1:v)
      {
      for (j in 1:(v-i+1))
        {
        if ((sum(x[i:(i+j-1)]) == 0) | (sum(x[i:(i+j-1)]) == j))
          {
          len = max(len, j)
          }
        }
      }
    return(len)
}
set.seed(1024)
mean(len <- replicate(1000, coin.len(1000))
# [1] 10.288

Q2: 一个均匀硬币不断抛啊抛,一直抛到出现HTT(正反反)和HTH(正反正),哪个需要抛的次数多?

coin.seq = function(v) {
    x = NULL
    n = 0
    while (!identical(x, v)) {
        x = append(x[length(x) - 1:0], rbinom(1, 1, 0.5))
        n = n + 1
    }
    n
}
set.seed(1024)
mean(htt <- replicate(1e+05, coin.seq(c(1, 0, 0))))
# [1] 8.003
mean(hth <- replicate(1e+05, coin.seq(c(1, 0, 1))))
# [1] 10.006


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