Counting integer partitions

dynamic_programming/integer_partition.py

@@ -0,0 +1,45 @@
+from __future__ import print_function
+
+try:
+	xrange		#Python 2
+except NameError:
+	xrange = range	#Python 3
+
+try:
+	raw_input		#Python 2
+except NameError:
+	raw_input = input	#Python 3
+
+'''
+The number of partitions of a number n into at least k parts equals the number of partitions into exactly k parts
+plus the number of partitions into at least k-1 parts. Subtracting 1 from each part of a partition of n into k parts
+gives a partition of n-k into k parts. These two facts together are used for this algorithm.
+'''
+def partition(m):
+	memo = [[0 for _ in xrange(m)] for _ in xrange(m+1)]
+	for i in xrange(m+1):
+		memo[i][0] = 1
+
+	for n in xrange(m+1):
+		for k in xrange(1, m):
+			memo[n][k] += memo[n][k-1]
+			if n-k > 0:
+				memo[n][k] += memo[n-k-1][k]
+
+	return memo[m][m-1]
+
+if __name__ == '__main__':
+	import sys
+
+	if len(sys.argv) == 1:
+		try:
+			n = int(raw_input('Enter a number: '))
+			print(partition(n))
+		except ValueError:
+			print('Please enter a number.')
+	else:
+		try:
+			n = int(sys.argv[1])
+			print(partition(n))
+		except ValueError:
+			print('Please pass a number.')