Add solution for problem 76 in C and python

Python/p075.py

@@ -68,7 +68,6 @@ def main():
         if l[i] == 1:
             count = count + 1
 
-
     end = default_timer()
 
     print('Project Euler, Problem 75')

Python/p076.py

@@ -0,0 +1,24 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+from projecteuler import partition_fn
+
+def main():
+    start = default_timer()
+
+    partitions = [0] * 101
+
+#   The number of ways a number can be written as a sum is given by the partition function
+#   (-1 because the partition function includes also the number itself).
+#   The function is implemented in projecteuler.py.
+    n = partition_fn(100, partitions) - 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 76')
+    print('Answer: {}'.format(n))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/projecteuler.py

@@ -1,6 +1,6 @@
 #!/usr/bin/python3
 
-from math import sqrt, floor, gcd
+from math import sqrt, floor, ceil, gcd
 
 from numpy import ndarray, zeros
 
@@ -397,3 +397,33 @@ def phi(n, primes):
         ph = ph * (1 - 1 / n)
 
     return ph
+
+# Function implementing the partition function.
+def partition_fn(n, partitions):
+#   The partition function for negative numbers is 0 by definition.
+    if n < 0:
+        return 0
+
+#   The partition function for zero is 1 by definition.
+    if n == 0:
+        partitions[n] = 1
+        return 1
+
+#   If the partition for the current n has already been calculated, return the value.
+    if partitions[n] != 0:
+        return partitions[n]
+
+    res = 0
+    k = -ceil((sqrt(24*n+1)-1)//6)
+    limit = floor((sqrt(24*n+1)+1)//6)
+
+    while k <= limit:
+        if k != 0:
+            res = res + pow(-1, k+1) * partition_fn(n-k*(3*k-1)//2, partitions)
+        k = k + 1
+
+    partitions[n] = res
+
+    return int(res)
+
+