R Recursion

How it works

A recursive function calls itself on a smaller problem. The base case must be reachable and return the correct result. Recursion consumes call-stack space, so this teaching function deliberately accepts only integers from zero through twenty. A vectorised formula or loop would be simpler for large sums.

Run this R example

These examples run locally with R, not PHP, Python or JavaScript. The reviewed baseline is R 4.5.2 on Windows x64/UCRT, using only packages shipped with R. This is a tested version, not a newest-release claim. Install your own R from the official R project; an IDE is optional. Save the complete source as recursion.R in a separate learning folder and run Rscript --vanilla recursion.R. Keep code and fictional fixtures separate from a real project.

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The complete download uses a local scope, restores its temporary options and treats unexpected warnings as errors. Examples that handle an expected warning do so narrowly. Random examples change only their R process’s RNG state. File examples own their temporary output; figure examples leave their named PNG in the current learning folder and refuse to overwrite it. Use a new empty folder to rerun a figure.

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Example

local({
  previous_options <- options(warn = 2, digits = 8, stringsAsFactors = FALSE)
  on.exit(options(previous_options), add = TRUE)
  sum_to <- function(n) {
    if (!is.numeric(n) || length(n) != 1L || is.na(n) ||
        !is.finite(n) || n < 0 || n > 20 || n != floor(n)) {
      stop("Use one integer from 0 to 20")
    }
    if (n == 0) return(0)
    n + sum_to(n - 1)
  }
  cat("zero:", sum_to(0), "four:", sum_to(4), "\n")
  invisible(NULL)
})

sum_to <- function(n) {
  if (!is.numeric(n) || length(n) != 1L || is.na(n) ||
      !is.finite(n) || n < 0 || n > 20 || n != floor(n)) {
    stop("Use one integer from 0 to 20")
  }
  if (n == 0) return(0)
  n + sum_to(n - 1)
}
cat("zero:", sum_to(0), "four:", sum_to(4), "\n")

Expected result

zero: 0 four: 10

The recursive argument decreases by one until zero is reached. Validation also rejects missing, infinite, fractional and over-budget values. This is a demonstration of the recurrence, not a claim that every recursive function will scale safely in R.