dist.r

# Read the data
setwd('/')
words <- read.csv(
  '/usr/share/dict/words',
  colClasses="character",
  header=FALSE
)

# Insert a header to the words
names(words) <- c("word")

require(dplyr)

# Add the words length column
words <- mutate(words, len=nchar(word))
# Compute the cost per word: w * (2^w)
words <- mutate(words, cost=(len * (2**(len))))
# Compute the total cost
total_cost = sum(words$cost)
# Total number of characters
n_characters = sum(words$len)

# Approach 3: cost = min(2^w, nchars)
words <- mutate(words, cost2=(pmin(2**len, n_characters)))
# Compute the total cost for approach 3
total_cost2 = sum(words$cost2)

# Diplay histogram
colors = c("#b2e7f5")
hist(
  words$len, 
  col=colors,
  main="Words by length",
  xlab="Number of characters"
)