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Re: SortedMap question?

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On 11/25/2012 3:21 PM, Arne Vajhøj wrote:
> On 11/25/2012 3:16 PM, Joshua Cranmer wrote:
>> And we always use merge sort or heap sort instead of all the other
>> sorts... oh wait.
>
> I don't see the point here. Those have the same big O not
> worse than quick sort.

We tend to use quicksort as often as merge sort, if not more, and 
quicksort has O(N^2) worst-case time. As mentioned earlier, 
quicksorts--including Java's implementation--often use insertion sort 
for very small arrays (when you get down to 7-16 or so). Heapsort tends 
to be extremely rare, despite being an O(n lg n) in-place sort, since 
maintaining the heap tends to come with a relatively oppressive constant 
factor.

Insertion sort, our favorite O(N^2) sort, is actually a very common 
sorting algorithm, especially if you realize that keeping an array 
sorted as you add elements to it tends to end up being an insertion sort.

Radix sort, which is O(N) for fixed-size elements (like primitive 
integers), is quite rare in practice despite being asymptotically better 
than quicksort or mergesort. A bucket sort would actually be 
asymptotically superior in Java for bytes, shorts, and chars, too (256 
or 64K integer arrays are not onerous in memory usage in modern computers).

>> I read a paper which said you could use log space to see if an
>> undirected graph was connected. The hidden constant is 3^16, and it
>> looks like you'd need a much larger constant to actually make it more
>> usable.
>
> And that contradicts it being rare?

No, it's asymptotically better space-wise than BFS or DFS (which are 
both linear in space). But I highly doubt anyone has even bothered to 
write an implementation in any computer language (the paper itself 
didn't specify the whole algorithm concisely).

-- 
Beware of bugs in the above code; I have only proved it correct, not 
tried it. -- Donald E. Knuth

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SortedMap question? Knute Johnson <nospam@rabbitbrush.frazmtn.com> - 2012-11-24 15:23 -0800
  Re: SortedMap question? Joerg Meier <joergmmeier@arcor.de> - 2012-11-25 00:57 +0100
    Re: SortedMap question? David Lamb <dalamb@cs.queensu.ca> - 2012-11-25 08:49 -0500
      Re: SortedMap question? David Lamb <dalamb@cs.queensu.ca> - 2012-11-25 08:59 -0500
        Re: SortedMap question? "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2012-11-25 14:02 +0000
          Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 14:20 -0500
        Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 14:24 -0500
          Re: SortedMap question? David Lamb <dalamb@cs.queensu.ca> - 2012-11-25 21:25 -0500
            Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 22:24 -0500
            Re: SortedMap question? Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-11-26 15:45 -0800
              Re: SortedMap question? Eric Sosman <esosman@comcast-dot-net.invalid> - 2012-11-26 20:29 -0500
    Re: SortedMap question? Eric Sosman <esosman@comcast-dot-net.invalid> - 2012-11-25 09:02 -0500
      Re: SortedMap question? Martin Gregorie <martin@address-in-sig.invalid> - 2012-11-25 17:47 +0000
        Re: SortedMap question? Knute Johnson <nospam@rabbitbrush.frazmtn.com> - 2012-11-25 16:25 -0800
          Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 19:36 -0500
            Re: SortedMap question? Eric Sosman <esosman@comcast-dot-net.invalid> - 2012-11-25 22:58 -0500
          Re: SortedMap question? Lew <lewbloch@gmail.com> - 2012-11-25 16:53 -0800
          Re: SortedMap question? Martin Gregorie <martin@address-in-sig.invalid> - 2012-11-26 02:20 +0000
      Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 14:20 -0500
        Re: SortedMap question? Eric Sosman <esosman@comcast-dot-net.invalid> - 2012-11-25 14:44 -0500
          Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 16:18 -0500
            Re: SortedMap question? Eric Sosman <esosman@comcast-dot-net.invalid> - 2012-11-25 17:35 -0500
              Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 19:58 -0500
              Re: SortedMap question? Jim Janney <jjanney@shell.xmission.com> - 2012-11-26 12:45 -0700
                Re: SortedMap question? Joshua Cranmer <Pidgeot18@verizon.invalid> - 2012-11-26 14:26 -0600
        Re: SortedMap question? Joshua Cranmer <Pidgeot18@verizon.invalid> - 2012-11-25 14:16 -0600
          Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 16:21 -0500
            Re: SortedMap question? Joshua Cranmer <Pidgeot18@verizon.invalid> - 2012-11-25 17:07 -0600
              Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-25 20:05 -0500
          Re: SortedMap question? "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2012-11-26 01:34 +0000
            Re: SortedMap question? Joshua Cranmer <Pidgeot18@verizon.invalid> - 2012-11-25 20:36 -0600
              Re: SortedMap question? "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2012-12-15 12:27 +0000
  Re: SortedMap question? Robert Klemme <shortcutter@googlemail.com> - 2012-11-25 01:36 +0100
  Re: SortedMap question? Arne Vajhøj <arne@vajhoej.dk> - 2012-11-24 20:00 -0500
  Re: SortedMap question? markspace <-@.> - 2012-11-24 17:34 -0800
    Re: SortedMap question? Robert Klemme <shortcutter@googlemail.com> - 2012-11-25 15:28 +0100
      Re: SortedMap question? Martin Gregorie <martin@address-in-sig.invalid> - 2012-11-25 17:49 +0000
  Re: SortedMap question? "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2012-11-25 14:00 +0000

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