tasks a-s

Task/Catalan-numbers/Python/catalan-numbers.py

@@ -0,0 +1,44 @@
+from math import factorial
+import functools
+
+def memoize(func):
+    cache = {}
+    def memoized(key):
+        # Returned, new, memoized version of decorated function
+        if key not in cache:
+            cache[key] = func(key)
+        return cache[key]
+    return functools.update_wrapper(memoized, func)
+
+
+@memoize
+def fact(n):
+    return factorial(n)
+
+def cat_direct(n):
+    return fact(2*n) // fact(n + 1) // fact(n)
+
+@memoize
+def catR1(n):
+    return ( 1 if n == 0
+             else sum( catR1(i) * catR1(n - 1 - i)
+                       for i in range(n) ) )
+
+@memoize
+def catR2(n):
+    return ( 1 if n == 0
+             else ( ( 4 * n - 2 ) * catR2( n - 1) ) // ( n + 1 ) )
+
+
+if __name__ == '__main__':
+    def pr(results):
+        fmt = '%-10s %-10s %-10s'
+        print ((fmt % tuple(c.__name__ for c in defs)).upper())
+        print (fmt % (('='*10,)*3))
+        for r in zip(*results):
+            print (fmt % r)
+
+
+    defs = (cat_direct, catR1, catR2)
+    results = [ tuple(c(i) for i in range(15)) for c in defs ]
+    pr(results)