coin-change -- count sets of coins (pennies, nickles, dimes, quarters) that add to a specific total

coin-change1 output

$ ./coin-change1.rb 
For total = 40
There are 31 sets of coins

Set  $.25  $.10  $.05  $.01
  1:    0     0     0    40
  2:    0     0     1    35
  3:    0     0     2    30
  4:    0     0     3    25
  5:    0     0     4    20
  6:    0     0     5    15
  7:    0     0     6    10
  8:    0     0     7     5
  9:    0     0     8     0
 10:    0     1     0    30
 11:    0     1     1    25
 12:    0     1     2    20
 13:    0     1     3    15
 14:    0     1     4    10
 15:    0     1     5     5
 16:    0     1     6     0
 17:    0     2     0    20
 18:    0     2     1    15
 19:    0     2     2    10
 20:    0     2     3     5
 21:    0     2     4     0
 22:    0     3     0    10
 23:    0     3     1     5
 24:    0     3     2     0
 25:    0     4     0     0
 26:    1     0     0    15
 27:    1     0     1    10
 28:    1     0     2     5
 29:    1     0     3     0
 30:    1     1     0     5
 31:    1     1     1     0

coin-change1.rb

#!/usr/bin/env ruby
# coin-change1.rb
#
# count sets of coins (pennies, nickles, dimes, quarters) that
# add to a specific total
#
# Count the different sets of the polynomial: 
#   total = P + N*5 + D*10 * Q*25
# 
# A "coin set" is a 4-tuple of [P,N,D,Q]
#

$coin_values = [ 1, 5, 10, 25 ]

# given a total, find the maximum number of coins for each
# denomination

def compute_max_coins(total)
  $max_coins = $coin_values.map {|value| Integer(total / value)}
  $max_pennies  = $max_coins[0]
  $max_nickles  = $max_coins[1]
  $max_dimes    = $max_coins[2]
  $max_quarters = $max_coins[3]
end

# get all the coin sets for a given total

def get_coin_sets(total)
  coin_sets = []
  (0..$max_quarters).each { |q|
    break if total < q*25
    qtotal = total - q*25
    (0..$max_dimes).each { |d|
      break if qtotal < d*10
      dtotal = qtotal - d*10
      (0..$max_nickles).each { |n|
        break if dtotal < n*5
        p = dtotal - n*5
        coin_sets += [[q,d,n,p]]
      }
    }
  }
  coin_sets
end

if ARGV.size > 0
  total = ARGV.shift.to_i
else
  total = 40
end

compute_max_coins(total)
coin_sets = get_coin_sets(total)

puts "For total = #{total}"
puts "There are #{coin_sets.size} sets of coins"
puts ''
set = 1
printf "Set  $.25  $.10  $.05  $.01\n"
coin_sets.each do |q,d,n,p| 
  printf "%3d: %4d  %4d  %4d  %4d\n", set, q, d, n, p
  set += 1
end

exit