merge_sequential_paths <- function(a,b) {
names(a) <- paste0("a_", names(a))
names(b) <- paste0("b_", names(b))
ab <- merge(a,b)
ab$n <- ab$a_n * ab$b_n
ab$length <- ab$a_length + ab$b_length
ab$p <- ab$a_p * ab$b_p
return(ab %>% select(n, length, p))
}
par_seq <- function(n,k){
return(choose((n+k),k))
}
merge_parrallel_paths <- function(a,b) {
names(a) <- paste0("a_", names(a))
names(b) <- paste0("b_", names(b))
ab <- merge(a,b)
ab$n <- ab$a_n * ab$b_n * mapply(par_seq, ab$a_length, ab$b_length)
ab$length <- ab$a_length + ab$b_length
ab$p <- (ab$a_p * ab$b_p)/mapply(par_seq, ab$a_length, ab$b_length)
return(ab %>% select(n, length, p))
}
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