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digitalmars.D.learn - O(1) sum

reply helxi <brucewayneshit gmail.com> writes:
Is it possible to sum an array in O(1)?
Jun 11
next sibling parent reply Stefan Koch <uplink.coder googlemail.com> writes:
On Monday, 12 June 2017 at 01:02:58 UTC, helxi wrote:
 Is it possible to sum an array in O(1)?
No. If you want to sum the elements you have to at-least look at all the elements. So it'll always be O(N). it's the best you can do.
Jun 11
parent reply Biotronic <simen.kjaras gmail.com> writes:
On Monday, 12 June 2017 at 01:36:04 UTC, Stefan Koch wrote:
 On Monday, 12 June 2017 at 01:02:58 UTC, helxi wrote:
 Is it possible to sum an array in O(1)?
No. If you want to sum the elements you have to at-least look at all the elements. So it'll always be O(N). it's the best you can do.
On a multi-core system we can do better: auto nums = iota(10_000_000.0f); auto sum = taskPool.reduce!"a + b"(nums); Given arbitrary parallelism (yeah, right!), this will be O(log(N)). For real-world systems, it might give a speed-up for large arrays, but won't reduce the big-O complexity. Of course, there will also be overhead to such a solution, so there is a limit to how much one'd actually benefit from it. -- Biotronic
Jun 11
parent reply Stefan Koch <uplink.coder googlemail.com> writes:
On Monday, 12 June 2017 at 06:15:07 UTC, Biotronic wrote:
 On Monday, 12 June 2017 at 01:36:04 UTC, Stefan Koch wrote:
 On Monday, 12 June 2017 at 01:02:58 UTC, helxi wrote:
 Is it possible to sum an array in O(1)?
No. If you want to sum the elements you have to at-least look at all the elements. So it'll always be O(N). it's the best you can do.
On a multi-core system we can do better: auto nums = iota(10_000_000.0f); auto sum = taskPool.reduce!"a + b"(nums); Given arbitrary parallelism (yeah, right!), this will be O(log(N)). For real-world systems, it might give a speed-up for large arrays, but won't reduce the big-O complexity. Of course, there will also be overhead to such a solution, so there is a limit to how much one'd actually benefit from it. -- Biotronic
Biotronic how do you arrive at O(log(N)) ?? And which logarithm ?
Jun 12
parent "H. S. Teoh via Digitalmars-d-learn" <digitalmars-d-learn puremagic.com> writes:
On Mon, Jun 12, 2017 at 06:16:06PM +0000, Stefan Koch via Digitalmars-d-learn
wrote:
 On Monday, 12 June 2017 at 06:15:07 UTC, Biotronic wrote:
[...]
 On a multi-core system we can do better:
 
 auto nums = iota(10_000_000.0f);
 auto sum = taskPool.reduce!"a + b"(nums);
 
 Given arbitrary parallelism (yeah, right!), this will be O(log(N)).
 For real-world systems, it might give a speed-up for large arrays,
 but won't reduce the big-O complexity. Of course, there will also be
 overhead to such a solution, so there is a limit to how much one'd
 actually benefit from it.
 
 --
   Biotronic
Biotronic how do you arrive at O(log(N)) ?? And which logarithm ?
His stated presupposition is arbitrary parallelism, which I assume means arbitrary number of CPUs or cores that can run in parallel, so then you can divide the array of N elements into N/2 pairs, sum each pair in parallel, which gives you N/2 subtotals after one iteration, then you recursively repeat this on the subtotals until you're left with the final total. The complexity would be O(log_2(N)) iterations, assuming that the constant factor hidden by the big-O covers the overhead of managing the parallel summing operations across the arbitrary number of cores. You can also get logarithms of a different base if you divided the initial array, say, into triplets or j-tuplets, for some constant j. Then you'd get O(log_j(N)). (Of course, with a slightly larger constant factor, assuming that each CPU core only has binary summation instructions. But if your instruction set has multiple-summation instructions you may be able to get a higher j at little or no additional cost. Assuming you can produce a machine with an unlimited number of cores in the first place.) Of course, his comment "yeah, right!" indicates that he's aware that this is an unrealistic scenario. :-) T -- Notwithstanding the eloquent discontent that you have just respectfully expressed at length against my verbal capabilities, I am afraid that I must unfortunately bring it to your attention that I am, in fact, NOT verbose.
Jun 12
prev sibling parent =?UTF-8?Q?Ali_=c3=87ehreli?= <acehreli yahoo.com> writes:
On 06/11/2017 06:02 PM, helxi wrote:
 Is it possible to sum an array in O(1)?
It's possible to maintain the sum as elements are added and removed. Then, accessing it would be O(1). Ali
Jun 12