Data commit

Task/Catalan-numbers/Python/catalan-numbers-1.py

@@ -0,0 +1,49 @@
+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)

Task/Catalan-numbers/Python/catalan-numbers-2.py

@@ -0,0 +1,47 @@
+'''Catalan numbers'''
+
+from itertools import accumulate, chain, count, islice
+
+
+# catalans3 :: [Int]
+def catalans3():
+    '''Infinite sequence of Catalan numbers
+    '''
+    def go(c, n):
+        return 2 * c * pred(2 * n) // succ(n)
+
+    return accumulate(
+        chain([1], count(1)), go
+    )
+
+
+# ------------------------- TEST -------------------------
+# main :: IO ()
+def main():
+    '''Catalan numbers, definition 3'''
+    print("Catalans 1-15:\n")
+    print(
+        '\n'.join([
+            f'{n:>10}' for n
+            in islice(catalans3(), 15)
+        ])
+    )
+
+
+# ----------------------- GENERIC ------------------------
+
+# pred :: Int -> Int
+def pred(n):
+    '''Predecessor function'''
+    return n - 1
+
+
+# succ :: Int -> Int
+def succ(n):
+    '''Successor function'''
+    return 1 + n
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()