## digitalmars.D.learn - O(1) sum

- helxi (1/1) Jun 11 2017 Is it possible to sum an array in O(1)?
- Stefan Koch (6/7) Jun 11 2017 No.
- Biotronic (11/18) Jun 11 2017 On a multi-core system we can do better:
- Stefan Koch (3/22) Jun 12 2017 Biotronic how do you arrive at O(log(N)) ??
- H. S. Teoh via Digitalmars-d-learn (24/41) Jun 12 2017 His stated presupposition is arbitrary parallelism, which I assume means
- =?UTF-8?Q?Ali_=c3=87ehreli?= (4/5) Jun 12 2017 It's possible to maintain the sum as elements are added and removed.

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 2017

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: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. -- BiotronicIs 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 2017

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:Biotronic how do you arrive at O(log(N)) ?? And which logarithm ?On Monday, 12 June 2017 at 01:02:58 UTC, helxi 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. -- BiotronicIs 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 12 2017

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:[...]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.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. -- BiotronicBiotronic how do you arrive at O(log(N)) ?? And which logarithm ?

Jun 12 2017

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 2017