On my way to problem 31!

Signed-off-by: Julien Lengrand-Lambert <julien@lengrand.fr>

e_31.py

@@ -12,27 +12,40 @@ It is possible to make L2 in the following way:
 1 * L1 + 1 * 50p + 2 * 20p + 1 * 5p + 1 * 2p + 3 * 1p
 How many different ways can L2 be made using any number of coins?
 ''' 
-def combinations_with_replacement(iterable, r):
-    # combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC
-    pool = tuple(iterable)
-    n = len(pool)
-    if not n and r:
-        return
-    indices = [0] * r
-    yield tuple(pool[i] for i in indices)
-    while True:
-        for i in reversed(range(r)):
-            if indices[i] != n - 1:
-                break
-        else:
-            return
-        indices[i:] = [indices[i] + 1] * (r - i)
-        yield tuple(pool[i] for i in indices)
 
+def listmul(list1, list2):
+    """Multiplies each elements of list1 and list 2 with each other"""
+    if len(list1) != len(list2):
+        raise ValueError("Lists are supposed to have the same length!")
+
+    else:
+        out = []
+        for ii in range(len(list1)):
+            out.append(list1[ii] * list2[ii])
+            
+        return out
 
 if __name__ == '__main__':
-    aa = combinations_with_replacement(range(8), 8)
-    val = 0
-    for a in aa:
-        print sum(a)
-    print val
+    
+    values = [1, 2, 5, 10, 20, 50, 100, 200]
+    goal = 200
+    
+    max_vals = [goal / val for val in values]
+    # we have to solve the equation a * 1 + b * 2 + c * 5 + d * 10 + e * 20 + f * 50 + g *100 + h * 200 = goal
+    cur_vals = [0] * len(values)
+    
+    sols = 0
+    for cur_vals[0] in range(max_vals[0] + 1):
+        print cur_vals[0]
+        for cur_vals[1] in range(max_vals[1] + 1):
+            print cur_vals[1]
+            for cur_vals[2] in range(max_vals[2] + 1):
+                for cur_vals[3] in range(max_vals[3] + 1):
+                    for cur_vals[4] in range(max_vals[4] + 1):
+                        for cur_vals[5] in range(max_vals[5] + 1):
+                            for cur_vals[6] in range(max_vals[6] + 1):
+                                for cur_vals[7] in range(max_vals[7] + 1):
+                                    if sum(listmul(cur_vals, values)) == goal:
+                                        sols += 1
+    print sols
+