substantially fewer array-element compares. This is best practice as of
Kntuh Volume 3 Ed 2, and the code is actually simpler this way (although
the key idea may be counter-intuitive at first glance! breaking out of
a loop early loses when it costs more to try to get out early than getting
out early saves).
Also added a comment block explaining the difference and giving some real
counts; demonstrating that heapify() is more efficient than repeated
heappush(); and emphasizing the obvious point thatlist.sort() is more
efficient if what you really want to do is sort.
Added new heapify() function, which transforms an arbitrary list into a
heap in linear time; that's a fundamental tool for using heaps in real
life <wink>.
Added heapyify() test. Added a "less naive" N-best algorithm to the test
suite, and noted that this could actually go much faster (building on
heapify()) if we had max-heaps instead of min-heaps (the iterative method
is appropriate when all the data isn't known in advance, but when it is
known in advance the tradeoffs get murkier).
Tim Peters
Guido van Rossum