June 2018 Update

Task/Hamming-numbers/Python/hamming-numbers-6.py

@@ -0,0 +1,38 @@
+from itertools import islice, chain, tee
+
+def merge(r, s):
+    # This is faster than heapq.merge.
+    rr = r.next()
+    ss = s.next()
+    while True:
+        if rr < ss:
+            yield rr
+            rr = r.next()
+        else:
+            yield ss
+            ss = s.next()
+
+def p(n):
+    def gen():
+        x = n
+        while True:
+            yield x
+            x *= n
+    return gen()
+
+def pp(n, s):
+    def gen():
+        for x in (merge(s, chain([n], (n * y for y in fb)))):
+            yield x
+    r, fb = tee(gen())
+    return r
+
+def hamming(a, b = None):
+    if not b:
+        b = a + 1
+    seq = (chain([1], pp(5, pp(3, p(2)))))
+    return list(islice(seq, a - 1, b - 1))
+
+print hamming(1, 21)
+print hamming(1691)[0]
+print hamming(1000000)[0]