Update p031.py

python/p031.py

@@ -6,20 +6,30 @@
 # https://github.com/nayuki/Project-Euler-solutions
 # 
 
-
-# We use the standard dynamic programming algorithm to solve the subset sum problem over integers.
-# The order of the coin values does not matter, but the values need to be unique.
 def compute():
-	TOTAL = 200
-
-	# At the start of each loop iteration, ways[i] is the number of ways to use {any copies
-	# of the all the coin values seen before this iteration} to form an unordered sum of i
-	ways = [1] + [0] * TOTAL
-	for coin in [1, 2, 5, 10, 20, 50, 100, 200]:
-		for i in range(len(ways) - coin):
-			ways[i + coin] += ways[i]
-	return str(ways[-1])
+      from itertools import combinations_with_replacement
+
+      cvs = [1, 2, 5, 10, 20, 50, 100, 200]  # Coins and their values
+      TOTAL = 10 # Use 10 coins (for example)
+      count = 0 # Solutions (combinations) counter
+      tracing = True  # Not necessary but used just for tracing the combinations
+      if tracing:
+        sol = []  # List with solutions
+      lst = sorted(list(combinations_with_replacement(cvs, TOTAL)))
+      for i in range(len(lst)):
+        if sum(lst[i]) == 200: 
+          count += 1
+          if tracing:
+            sol.append(lst[i])
 
+      print("Total combinations:", count)
+      if tracing:
+        print("Solutions:", sol)
+      '''
+      Total solutions: 22
+      Solutions: [(1, 1, 1, 1, 1, 5, 20, 20, 50, 100), (1, 1, 1, 2, 5, 10, 10, 20, 50, 100), (1, 1, 1, 2, 5, 20, 20, 50, 50, 50), (1, 1, 2, 2, 2, 2, 20, 20, 50, 100),  ...
+                        (10, 10, 10, 20, 20, 20, 20, 20, 20, 50), (20, 20, 20, 20, 20, 20, 20, 20, 20, 20)]      
+      '''
 
 if __name__ == "__main__":
-	print(compute())
+    compute()