Padovan sequence: Difference between revisions

=={{header|R}}==

<syntaxhighlight lang="R" line># Function to calculate Padovan sequence iteratively

padovan_sequence <- function(n) {

recurrences <- numeric(n)

recurrences[1:3] <- c(1, 1, 1)

if (n > 3) {

for (i in 4:n) {

recurrences[i] <- recurrences[i-2] + recurrences[i-3]

}

}

recurrences

}

# Function to calculate Padovan floor

padovan_floor <- function(aN) {

PP <- 1.324717957244746025960908854

SS <- 1.0453567932525329623

floor((PP^(aN - 1)) / SS + 0.5)

}

# Function to create L-system

create_l_system<- function() {

words <- c("A")

text <- "A"

while (length(words) < 32) {

text <- strsplit(text, "")[[1]] # Split the string into a list of characters

text <- sapply(text, function(char) {

if (char == "A") {

return("B")

} else if (char == "B") {

return("C")

} else if (char == "C") {

return("AB")

}

})

text <- paste(text, collapse = "") # Collapse the list back into a single string

words <- c(words, text) # Append the new word to the list

}

words

}

# Main script

num_terms <- 64

padovan_seq <- padovan_sequence(num_terms)

floors <- sapply(0:(num_terms-1), padovan_floor)

cat("The first 20 terms of the Padovan sequence:\n")

cat(padovan_seq[1:20], sep=" ", end="\n")

cat("\n")

cat("Recurrence and floor functions agree for first 64 terms?", all(padovan_seq == floors), "\n\n")

words <- create_l_system()

cat("The first 10 terms of the L-system:\n")

cat(words[1:10], sep=" ", end="\n")

cat("\n")

cat("Length of first 32 terms produced from the L-system match Padovan sequence? ")

word_lengths <- sapply(words, nchar)

cat(all(word_lengths[1:32] == padovan_seq[1:32]))</syntaxhighlight>

{{out}}

<pre>

The first 20 terms of the Padovan sequence:

1 1 1 2 2 3 4 5 7 9 12 16 21 28 37 49 65 86 114 151

Recurrence and floor functions agree for first 64 terms? TRUE

The first 10 terms of the L-system:

A B C AB BC CAB ABBC BCCAB CABABBC ABBCBCCAB

Length of first 32 terms produced from the L-system match Padovan sequence? TRUE

</pre>