17: Add proof

2015/17.py

@@ -1,43 +1,42 @@
 # Fill Input
 
-input = ""
-
 try:
 	with open("17.txt", 'r', encoding='utf-8') as file:
-		input += file.read()
+		input = file.read()
 except Exception as e:
 	print(f"An error occurred: {e}")
 
-# Check if sum of permutation equal 150
-def sum_equal_150(input, i):
-	sum = 0
-	for j in range(l):
-		if i & 1<<j:
-			sum += input[j]
-			if sum > 150:
-				return False
-	return sum == 150
-
 # Reverse sort input
 input= [ int(x) for x in input.split()]
-input.sort(reverse=True)
-
 l = len(input)
+
 res1, res2, min_popcount = 0, 0, l
+for i in range(1<<l):
+	"""
+	Let: 
+		f: i -> [input[j] for j in range(len(X)) if i & 1<<j ]
 
-for i in range(2**l):
+	Then:
-	if not sum_equal_150(input, i):
+		f is bijection between range(2**len(X)) and the subsets of X.
+
+	Futhermore:
+		popcount(i) == len(f(i))
+	"""
+
+
+	if sum([input[j] for j in range(l) if i & 1<<j ]) != 150:
 		continue
 
-	popcount =  i.bit_count()
-
-	if popcount < min_popcount:
-		min_popcount = popcount
-		res2 = 0;
-
-	if popcount == min_popcount:
-		res2 += 1;
-
 	res1 += 1
 
+	popcount =  i.bit_count()
+	if popcount < min_popcount:
+		min_popcount = popcount
+		res2 = 0;
+	if popcount == min_popcount:
+		res2 += 1;
+
 print(res1, res2)
+
+# One Liner
+print( sum([ sum( [input[j] for j in range(l) if i & 1<<j ]) == 150 for i in range(1<<l)] ))