Anthony Hart / Algorithms

eating_cookies/eating_cookies.py

@@ -1,12 +1,42 @@
 #!/usr/bin/python
 
 import sys
+# from numpy import roots, flip
 
 # The cache parameter is here for if you want to implement
 # a solution that is more efficient than the naive 
 # recursive solution
-def eating_cookies(n, cache=None):
-  pass
+def eating_cookies(n, cache = None):
+  # Note: this program should work fine, in theory, but Numpy's implementation of root
+  # finding builds up floating-point errors too fast. It gives the wrong answer for 0,
+  # and it reliably gives almost, but not quite, correct answers on large values.
+  # int(round(sum(roots([1, -1, -1, -1]) ** (n + 2) * flip(roots([44, 0, 4, -1])))))
+
+  # this function passes all tests when implemented in Mathematica, however
+  # eatingCookies[n_] := 
+  #    Round[Inner[Times, 
+  #      Array[Root[-1 - # - #^2 + #^3 &, #] &, 3]^(n + 2), 
+  #      Array[Root[-1 + 4*# + 44*#^3 &, #] &, 3], Plus]]
+  # So, clearly, the concept is fine, but Python's libraries aren't.
+
+  if n < 2:
+    return 1
+  elif n == 2:
+    return 2
+
+  if cache == None:
+    cache = [None] * (n + 1)
+  else:
+    cache = cache
+
+  if cache[n] == None or cache[n] == 0:
+    cache[n - 3] = eating_cookies(n - 3, cache)
+    cache[n - 2] = eating_cookies(n - 2, cache)
+    cache[n - 1] = eating_cookies(n - 1, cache)
+
+    return cache[n - 1] + cache[n - 2] + cache[n - 3]
+  else:
+    return cache[n]
 
 if __name__ == "__main__":
   if len(sys.argv) > 1:

making_change/making_change.py

@@ -1,10 +1,33 @@
 #!/usr/bin/python
 
 import sys
+from math import ceil
 
-def making_change(amount, denominations):
-  pass 
+def remains(amount, denom):
+  return [ amount - i * denom for i in range(amount // denom + 1) ]
 
+def making_change(amount, denominations, caches = None):
+  """ Note: this assumes the denominations are pre-sorted.
+
+      This is also not very efficient.
+      If an expression for an explicit formula can be worked out,
+      it could be made very, very fast; but I don't think
+      numpy can maintain the accuracy for accurate answers.
+  """
+
+  if len(denominations) == 2:
+      return amount // denominations[1] + 1
+
+  if caches == None:
+      caches = { i: [None] * (amount + 1) for i in denominations }
+
+  if caches[denominations[-1]][amount] == None:
+      caches[denominations[-1]][amount] =\
+        sum([ making_change(a, denominations[:-1])
+              for a in remains(amount, denominations[-1]) ])
+      return caches[denominations[-1]][amount]
+  else:
+      return caches[denominations[-1]][amount]
 
 if __name__ == "__main__":
   # Test our your implementation from the command line

recipe_batches/recipe_batches.py

@@ -3,7 +3,8 @@
 import math
 
 def recipe_batches(recipe, ingredients):
-  pass 
+  return min([ ingredients.get(k, 0) // recipe[k] for k in recipe.keys() ])
+
 
 
 if __name__ == '__main__':

rock_paper_scissors/rps.py

@@ -2,9 +2,29 @@
 
 import sys
 
+def number_to_base(num, base, padding = 1):
+    """Change ''num'' to a given numerical base
+
+       The return value will be left-padded until it's length is ''padding''.
+    """
+
+    digit_list = []
+    currentnum = num
+    while currentnum:
+        mod = currentnum % base
+        currentnum = currentnum // base
+        digit_list = [mod] + digit_list
+    while len(digit_list) < padding:
+        digit_list = [0] + digit_list
+    return digit_list
+
 def rock_paper_scissors(n):
-  pass 
+  """ Enumerate all numbers from 0 to 3 ** n in base three, and map
+      0 to 'rock', 1 to 'paper', and 2 to 'scissors'.
+  """
 
+  rps = ["rock", "paper", "scissors"]
+  return [ [ rps[d] for d in number_to_base(i, 3, n) ] for i in range(3 ** n) ]
 
 if __name__ == "__main__":
   if len(sys.argv) > 1:

stock_prices/stock_prices.py

@@ -3,7 +3,7 @@
 import argparse
 
 def find_max_profit(prices):
-  pass
+  return max([ max(prices[i+1:]) - p for i, p in enumerate(prices[:-1]) ])
 
 
 if __name__ == '__main__':