June 2018 Update

Task/Hamming-numbers/Python/hamming-numbers-3.py

@@ -1,25 +1,16 @@
-from itertools import tee, chain, groupby, islice
-from heapq import merge
+from heapq import heappush, heappop
+from itertools import islice
 
-def raymonds_hamming():
-    # Generate "5-smooth" numbers, also called "Hamming numbers"
-    # or "Regular numbers".  See: http://en.wikipedia.org/wiki/Regular_number
-    # Finds solutions to 2**i * 3**j * 5**k  for some integers i, j, and k.
+def h():
+    heap = [1]
+    while True:
+        h = heappop(heap)
+        while heap and h==heap[0]:
+            heappop(heap)
+        for m in [2,3,5]:
+            heappush(heap, m*h)
+        yield h
 
-    def deferred_output():
-        for i in output:
-            yield i
-
-    result, p2, p3, p5 = tee(deferred_output(), 4)
-    m2 = (2*x for x in p2)                          # multiples of 2
-    m3 = (3*x for x in p3)                          # multiples of 3
-    m5 = (5*x for x in p5)                          # multiples of 5
-    merged = merge(m2, m3, m5)
-    combined = chain([1], merged)                   # prepend a starting point
-    output = (k for k,g in groupby(combined))       # eliminate duplicates
-
-    return result
-
-print list(islice(raymonds_hamming(), 20))
-print islice(raymonds_hamming(), 1689, 1690).next()
-print islice(raymonds_hamming(), 999999, 1000000).next()
+print list(islice(h(), 20))
+print list(islice(h(), 1690, 1691))
+print list(islice(h(), 999999, 1000000)) # runtime 9.5 sec on i5-3570S