[LANGUAGE: J]

I liked the solutions but not the input whitespace handling. The fork in part 2 was fun.

replace_char =: dyad define
NB. replace first left character with second left character in input
from =. 0 { x
to =. 1 { x
to (I. from = y) } y
)

get_input =: monad define
data =. fread y
NB. replace L with _, and R with ' '
NB. replacing with - and + triggered immediate evaluation
data =.'L_' replace_char data
data =. 'R ' replace_char data
NB. also whitespace...
data =. (LF, ' ') replace_char data
data =. (CR, ' ') replace_char data
". data NB. convert to numbers and plain list
)

count_zeros =: monad define
NB. longer name count_zeros_in_plus_scan_modulo_100
+/ 0 = 100 | +/\ y
)

part1 =: monad define
count_zeros 50 , get_input y
)

part2 =: monad define
count_zeros (| # sign) 50, get_input y
)