Given a number n, find the sum of all n-digit palindromes.

rendezvous_cassidoo_126.R

# Interview Question of the Week: Jan 13, 2020
# 126 of rendezvous with cassidoo
# https://cassidoo.co/newsletter/

# Given a number n, find the sum of all n-digit palindromes.
# >> nPalindromes(2)
# >> 495 // 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99

# Removing exponential notation
options(scipen=999)

nPalindrome <- function(n) {
  
  # returning 0 by default
  if (n == 0 | !is.numeric(n)) {
    return(0)
  }
  
  if (n == 1) {
    return(sum(1:9))
  }

  # this is how many inner loops we need to do
  # to get the sum of inner numbers
  times <- ceiling((n-2) / 2)
  
  # this will be the base number that will the the numbers in the extremes
  # i.e. for n = 3, 101, for n = 4, 1001, for n = 5, 10001
  base <- 10 ^ (n-1) + 1 
  # outer sum will be...
  outer_sum <- base * sum(1:9) * 10 ^ times

  # no need to do any inner loop if we're giving n = 2
  if (!times) { 
    return(outer_sum)
  }
  
  inner_sum <- 0
  is_n_odd <- (n / 2) %% 1 != 0
  
  for (i in 1:times) {

    # how many combinations do we have...
    # 9 (since when the first number is 0 it doesn't count)
    n_comb <- 9 * 10 ^ (times-1) 
    
    # we're adding 10 exponentiated to the i
    multiplier <- 10 ^ i
    # but don't do that if if it's last number to add AND
    # length of n is odd
    if (i == times & is_n_odd) {
      multiplier <- 0
    }
    
    inner_sum <- inner_sum + sum(1:9) * n_comb * (10 ^ (n - 1 - i) + multiplier)
  }

  return(outer_sum + inner_sum)
}

sapply(1:10, function(i) {
  print(paste(i, "=>", nPalindrome(i)))
})

# [1] "1 => 45"
# [1] "2 => 495"
# [1] "3 => 49500"
# [1] "4 => 495000"
# [1] "5 => 49500000"
# [1] "6 => 495000000"
# [1] "7 => 49500000000"
# [1] "8 => 495000000000"
# [1] "9 => 49500000000000"
# [1] "10 => 495000000000000"