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Talk:Hamming numbers: Difference between revisions
→"Cyclic generator variant #1" not efficient: new section
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::Thank ''you'' for getting inspired and making this page happen! :) The book in question is "A Discipline of Programming", Prentice-Hall, [http://web.cecs.pdx.edu/~cs410aph/Lectures/Smalltalk%20II/Dijkstra%20on%20Hamming's%20Problem.pdf chap. 17 "An Exercise Attributed to R.W.Hamming"], [http://i.imgur.com/tPygG.gif pg. 132]. -- [[User:WillNess|WillNess]] 17:40, 29 August 2012 (UTC)
== "Cyclic generator variant #1" not efficient ==
The Python [[Hamming numbers#Cyclic generator variant #1.|Cyclic generator variant #1.]] that is said to be much simpler, is not really equivalent to the other solutions. I compared it to another version, measuring how many times the <code>merge</code> iterator is advanced:
<lang python>from itertools import tee, chain, groupby, islice
import heapq
count = 0
def merge(*args):
global count
for x in heapq.merge(*args):
count += 1
yield x
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 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(), 100))
print count</lang>
<lang python>from itertools import tee, chain, groupby, islice
import heapq
count = 0
def merge(*args):
global count
for x in heapq.merge(*args):
count += 1
yield x
def hamming_numbers():
last = 1
yield last
a,b,c = tee(hamming_numbers(), 3)
for n in merge((2*i for i in a), (3*i for i in b), (5*i for i in c)):
if n != last:
yield n
last = n
print list(islice(hamming_numbers(), 100))
print count</lang>
The results I get:
{| class="wikitable"
|-
! number of items printed !! raymonds_hamming !! hamming_numbers
|-
| 20 || 28 || 59
|-
| 100 || 201 || 670
|-
| 1,000 || 2,506 || 17,822
|-
| 10,000 || 27,634 || 420,168
|-
| 100,000 || 288,851 || 9,429,734
|}
The new "Cyclic generator variant #1" version seems to be much, much worse. --[[User:Spoon!|Spoon!]] 20:52, 12 October 2012 (UTC)
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