[2017-12-11] Challenge #344 [Easy] Baum-Sweet Sequence https://www.reddit.com/r/dailyprogrammer/comments/7j33iv/20171211_challenge_344_easy_baumsweet_sequence/

baumSweet.R

#
# [2017-12-11] Challenge #344 [Easy] Baum-Sweet Sequence
# https://www.reddit.com/r/dailyprogrammer/comments/7j33iv/20171211_challenge_344_easy_baumsweet_sequence/
#
# In mathematics, the Baum–Sweet sequence is an infinite automatic sequence of 0s and 1s defined by the rule:
#   
# b_n = 1 if the binary representation of n contains no block of consecutive 0s of odd length;
# b_n = 0 otherwise; for n >= 0.
#
# For example, b_4 = 1 because the binary representation of 4 is 100, which only contains one block of consecutive 0s of length 2;
# whereas b_5 = 0 because the binary representation of 5 is 101, which contains a block of consecutive 0s of length 1.
# When n is 19611206, b_n is 0.
#
# by Kory Becker
# http://primaryobjects.com
#

intToBin <- function(x) {
  # Convert a number to a list of bits.
  if (x == 1)
    1
  else if (x == 0)
    NULL
  else {
    mod <- x %% 2
    c(intToBin((x-mod) %/% 2), mod)
  }
}

baumSweet <- function(number) {
  z <- F
  count <- 0
  odds <- 0
  
  for (bit in intToBin(number)) {
    if (bit == 0) {
      # Count consecutive zeroes.
      z <- T
      count <- count + 1
    }
    else if (bit == 1) {
      # Record the count of odd consecutive zeroes.
      if (count %% 2 != 0) {
        odds <- odds + 1
      }
      
      count <- 0
      z <- F
    }
  }
  
  if (z == T) {
    if (count %% 2 != 0) {
      odds <- odds + 1
    }
  }
  
  as.numeric(odds == 0)
}

baumSweetRange <- function(number) {
  # Baum-Sweet from 0 to number.
  sapply(0:number, function(n) {
    c(baumSweet(n))
  })
}

# Run the program.
print(baumSweet(4))
print(baumSweet(5))
print(baumSweet(19611206))

result <- paste(baumSweetRange(20), collapse=', ')
answer <- '1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0'
print(result)
print(paste('Checking answer: ', result == answer))

output.txt

1
0
0
"1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0"
"Checking answer:  TRUE"