Solution to Problem 76

Author: daniel-s-ingram

Project Euler/Problem 76/sol1.py

@@ -0,0 +1,35 @@
+from __future__ import print_function
+'''
+Counting Summations
+Problem 76
+
+It is possible to write five as a sum in exactly six different ways:
+
+4 + 1
+3 + 2
+3 + 1 + 1
+2 + 2 + 1
+2 + 1 + 1 + 1
+1 + 1 + 1 + 1 + 1
+
+How many different ways can one hundred be written as a sum of at least two positive integers?
+'''
+try:
+	xrange		#Python 2
+except NameError:
+	xrange = range	#Python 3
+
+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:
+				memo[n][k] += memo[n-k-1][k]
+
+	return (memo[m][m-1] - 1)
+
+print(partition(100))