N Days of Christmas

xmas_gifts.R

xmas_gifts <- function(days=12, pear_tree=FALSE){
  
  days <- abs(as.integer(days))
  gifts <- 0
  
  # for(i in 1:days){gifts <- gifts + i*(days + 1 - i)}  # general case: does N=days total summations
  
  # can ~half the number of summations because...
  # if days = even, summation is symmetric and reduces to e.g. 2*[12x1 + 11x2 + 10x3 + 9x4 + 8x5 + 7x6] for 12 total days
  for(i in 1:(days/2 - .5* days %% 2)){
    gifts <- gifts + i*(days + 1 - i)}
  gifts <- 2*gifts + ( ((days+1)/2)^2 * (days %% 2))   # and if days = odd, add the additional squared term in the middle
  
  # total hack to deal with days = 1
  gifts <- ifelse(days == 1, 1, gifts)
  
  # does a partridge in a pear tree count as two gifts? Who honestly cares at this point?
  if(pear_tree == TRUE){gifts <- gifts + days} 
  
  return(gifts) # gimme those gifts back
}

xmas_gifts() # 12 days by default
xmas_gifts(98172)

library(tidyverse)
tibble(days = 1:100) %>%
  mutate(gifts = sapply(days, xmas_gifts)) %>%
  ggplot(aes(x=days, y=gifts)) +
  geom_point(color="darkgreen", size=3) + geom_line(color="red") + theme_bw() + ggtitle("ALL THE GIFTS")