eulerlib, P90, P222, P315, P345: Refactored the Python popcount() function into the shared library.

Author: nayuki

python/eulerlib.py

@@ -11,6 +11,12 @@
 	range = xrange
 
 
+# Returns the number of 1's in the binary representation of
+# the non-negative integer x. Also known as Hamming weight.
+def popcount(x):
+	return bin(x).count("1")
+
+
 # Given integer x, this returns the integer floor(sqrt(x)).
 def sqrt(x):
 	assert x >= 0

python/p090.py

@@ -6,14 +6,16 @@
 # https://github.com/nayuki/Project-Euler-solutions
 # 
 
+import eulerlib
+
 
 def compute():
 	# Each die has (10 choose 6) arrangements, so we have at most 44100 arrangements to check
 	ans = sum(1
 		for i in range(1 << 10)
 		for j in range(i, 1 << 10)  # Ensure i <= j to force the dice to be orderless
 		# If both have Hamming weight of 6
-		if bin(i).count("1") == bin(j).count("1") == 6 and is_arrangement_valid(i, j))
+		if eulerlib.popcount(i) == eulerlib.popcount(j) == 6 and is_arrangement_valid(i, j))
 	return str(ans)
 
 

python/p222.py

@@ -6,7 +6,7 @@
 # https://github.com/nayuki/Project-Euler-solutions
 # 
 
-import math
+import eulerlib, math
 
 
 def compute():
@@ -32,7 +32,7 @@ def find_minimum_length(currentsphereindex, setofspheres):
 
 		# Memoization
 		if minlength[currentsphereindex][setofspheres] is None:
-			if bin(setofspheres).count("1") == 1:
+			if eulerlib.popcount(setofspheres) == 1:
 				result = sphereradii[currentsphereindex]  # This sphere is rightmost
 			else:
 				result = float("inf")

python/p315.py

@@ -25,11 +25,11 @@ def sam_transitions_minus_max_transitions(n):
 		newstate = number_to_segments(n)
 		if newstate == segmentstate:
 			break
-		maxtrans += bin(newstate ^ segmentstate).count("1")
+		maxtrans += eulerlib.popcount(newstate ^ segmentstate)
 		segmentstate = newstate
-		samtrans += 2 * bin(newstate).count("1")
+		samtrans += 2 * eulerlib.popcount(newstate)
 		n = digit_sum(n)
-	maxtrans += bin(segmentstate).count("1")
+	maxtrans += eulerlib.popcount(segmentstate)
 	return samtrans - maxtrans
 
 

python/p345.py

@@ -6,19 +6,18 @@
 # https://github.com/nayuki/Project-Euler-solutions
 # 
 
+import eulerlib
+
 
 def compute():
 	# Memoization
 	maxsum = [[None] * (2**COLUMNS) for _ in range(ROWS)]
 
-	def hamming_weight(x):
-		return bin(x).count("1")
-	
 	# Returns the maximum sum when considering the submatrix from row 'startrow' until the bottom,
 	# with the bit set 'setofcols' indicating which column indexes are still free to be used.
 	def find_maximum_sum(startrow, setofcols):
 		if startrow == ROWS:
-			assert hamming_weight(setofcols) == COLUMNS - ROWS
+			assert eulerlib.popcount(setofcols) == COLUMNS - ROWS
 			return 0
 		if maxsum[startrow][setofcols] is None:
 			result = 0