[issue17930] Search not needed in combinations_with_replacement

[Tim Peters]

New submission from Tim Peters:

Each time thru, CWR searches for the rightmost position not containing the maximum index.  But this is wholly determined by what happened the last time thru - search isn't really needed.  Here's Python code:

def cwr2(iterable, r):
    pool = tuple(iterable)
    n = len(pool)
    if not n and r:
        return
    indices = [0] * r
    yield tuple(pool[i] for i in indices)
    j = r-1 if n > 1 else -1
    while j >= 0:
        newval = indices[j] + 1
        indices[j:] = [newval] * (r - j)
        yield tuple(pool[i] for i in indices)
        j = r-1 if newval < n-1 else j-1

There `j` is the rightmost position not containing the maximum index.  A little thought suffices to see that the next j is either r-1 (if newval is not the maximum index) or j-1 (if newval is the maximum index:  since the indices vector is non-decreasing, if indices[j] was r-2 then indices[j-1] is also at most r-2).

I don't much care if this goes in, but Raymond should find it amusing so assigning it to him ;-)

----------
assignee: rhettinger
components: Extension Modules
keywords: easy
messages: 188686
nosy: rhettinger, tim_one
priority: low
severity: normal
stage: needs patch
status: open
title: Search not needed in combinations_with_replacement
type: performance
versions: Python 2.7, Python 3.5

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Python tracker <report at bugs.python.org>
<http://bugs.python.org/issue17930>
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