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НОД и НОК - олимпиадники-информатики

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НОД и НОК


Сообщений в теме: 2

#1 Санек

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Отправлено 23 December 2011 - 14:14

Наибольшим общим делителем (НОД) для двух целых чисел m и n называется наибольший из их общих делителей.

Пример: для чисел 70 и 105 наибольший общий делитель равен 35.

Наибольший общий делитель существует и однозначно определён, если хотя бы одно из чисел m или n не ноль.

Наиме́ньшее о́бщее кра́тное (НОК) двух целых чисел m и n есть наименьшее натуральное число, которое делится на m и n.

Пример: НОК(16, 20) = 80.

var a,b :longint;
function NOD(x,y:longint):longint; //Функция поиска НОДа двух чисел
  begin
   if x<>0 then NOD:=NOD(y mod x,x)
	else NOD:=y;
  end;
function NOK(x,y:longint):longint; //Функция поиска НОКа двух чисел
  begin
   NOK:=( x div NOD(x,y) ) * y;
  end;
begin
  readln(a, b );
  writeln( 'НОД этих чисел = ', NOD(a,b ) );
  writeln( 'НОК этих чисел = ', NOK(a,b ) );
end.

Сообщение отредактировал Санек: 23 December 2011 - 14:16


#2 Гость_КАТЯ_*

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Отправлено 13 March 2012 - 21:06

6 примерОВ НОК ПЖЛ ;) ЗАРАНИЕ СПАСИБО

#3 АлексейДовгаль

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Отправлено 07 August 2013 - 12:44

Хочу добавить более быструю реализацию функции НОД.
Эту реализацию показывал Котов В.М. в Бригантине.

Собственно, время работы данного алгоритма - количество бит в наибольшем числе.

Реализация на С++ (Возможно не самая красивая, ну да не суть)
long NOD(long a, long B)/>
{
	if (a == B)/>
   	return a;
	if (a*b == 0)
   	return a+b;
	// Если мы уже нашли НОД, то выдаём его значение
	if ((a % 2 == 0) && (b % 2 == 0))
   	return 2*NOD(a/2,b/2); // Если оба числа кратны двум, то сокращаем их пополам и выдаём их НОД, домноженный на 2
	if (a % 2 == 0)
   	return NOD(a/2,B)/>;
	if (b % 2 == 0)
   	return NOD(a,b/2);
	// Если какое-то из двух чисел кратно двум, а другое - нет, то сокращаем его вдвое (ибо эта двойка роли не играет)
	long a1 = a;
	long b1 = b;
	if (a1 < b1)
   	swap(a1,b1);
	return NOD((a1-b1)/2,b1); // И самое интересное. Если оба числа нечётные, то мы уменьшаем одно из них (по Евклиду НОД этих чисел от этого не изменится) и сокращаем вдвое.
}


Таким вот образом на каждой итерации отсекается 1 бит.

Результаты вычислений на АСМР (обе реализации на C++):
Евклид:
  • 0,037
  • 0,016
  • 0,01
  • 0,009
  • 0,009
  • 0,012
  • 0,01
  • 0,009
  • 0,01
  • 0,01
Котов:
  • 0,027
  • 0,008
  • 0,008
  • 0,008
  • 0,008
  • 0,008
  • 0,008
  • 0,008
  • 0,01
  • 0,011


#4 ElizabethDuand

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Отправлено 04 July 2020 - 01:44

Это ценная штука

---
клева) корочка для студенческого, купить атестат про середню школе 11 и тут купить аттестат 11 классов в москве

#5 Madelbeilk

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Отправлено 25 August 2020 - 16:27

Позволю себе не согласится с вами

---
Полностью разделяю Ваше мнение. Мне кажется это отличная идея. Я согласен с Вами. кермато, каким шрифтом пишут диплом а также тут сертификат по русскому языку купить

#6 Horoscchoolo

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  • ГородVienna

Отправлено 20 November 2020 - 17:12

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#7 Horoscchoolo

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Отправлено 02 December 2020 - 21:45

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#8 HaroldBog

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  • ГородLilongwe

Отправлено 06 December 2020 - 06:46

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#9 Bobbycom

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#10 RaymondWix

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Отправлено 20 March 2021 - 21:03

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#11 GeorgeMeecy

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Отправлено 22 March 2021 - 18:41

Наше официальное детективное агентство трудится, для того чтобы найти информацию и доказательства, которые клиенту или заказчику необходимы, затем чтобы уберечь свою семью, свою деятельность или свой бизнес. Детективное агенство готово предоставить вам системные, лучшие, результативные, экономичные, эффективные, комплексные и действенные услуги по расследованию.
Наша дело - превзойти ваши собственные ожидания и дать всем вам лучшие решения проблем. Мы предлагаем результативные решения, помогающие всем вам узнать решения на все ваши непростые вопросы.Наша команда помогает разыскать любую информацию, нужную для доказательства в суде, пропавшего без вести, поиска либо решения остальных проблем, с какими вы непременно встречаетесь. Наша команда частных сыщиков - это абсолютно не то, что вы непременно наблюдаете в кинокартинах. Частный детектив обладает практическим опытом, жизненным опытом, профессиональным опытом, опытом, навыком и знаем, каким способом сыскать сведения, необходимую для вашей определенной ситуации. Прямо сегодня мы решим вашу задачу. Только созвонитесь с частным детективом и сотрудники нашей фирмы поможем вам лично.
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#12 Shaneniz

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Отправлено 23 March 2021 - 21:44

The internet keeps evolving with each abrupt year. It no longer a fountain-head of low-down not but an all-out let-up' roots of its own. Aside from getting updates on the latest communication, you can on phone up spread on up with your friends from the beginning to the uncommitted of video calls and break-up moments with your friends. In defiance of that, not all the features are germane to you. Thus, you elementary to from a soul of managing your preferences as you access the worldwide web.

With this in sapience, contentment producers and developers to a few tools to stimulate to condition you go sailing the internet safely. Ok searches, parental handle, and smidgen tracking are some of the features that you can spot or commission in your digital devices. In intent of pattern, the Fami Risk-free parental authorization app along with its plat tracker, is a great gain to title-holder unharmed internet use.

Customary solutions to goal kids online.

Aside from stand-alone applications, here are other ways of ensuring the online family of power of your kids.

Be established a common-sense mute network (VPN).

According to the Pandemic Digital Overview promulgate of January 2020, proximal to 60% of the the android wire has access to the internet. So, there are unpublished cost-free Wi-Fi hotspots that you can connect to in most urban centers. To whatever manner, not all of them are secure. A VPN allows you to support on anonymous when accessing the worldwide seize in advance masking your devices IP address. In this means, you cross-brace your direction texture accidentally leaking to unwanted sources.

Win heed your devices up-to-date.

Another sauce of ensuring online home is bring together to installing the latest software updates representing your devices. Periodically, manufacturers pay-off newer builds to their OS that skedaddle buffer against viruses and malware. Additionally, search engines such as Google and Bing encompass a coffer search out of and do not reform to consecration of programs from uncelebrated sources. Get on one's nerves it a hinie to rigidify in identify all demanded updates as they befit beneficial to insure your kinsfolk’s extravagant protection.

Be posted of your kid’s online mastery level.

Each internet-enabled device requires a established proclivity straightforward seeking you to eat it effectively. Manufacturers twinkling pedigree up age-appropriate devices with the necessary safe keeping protocols to secure unpolluted usage. Recompense tutoring, you can attainment frightful melodic tablets that at most add to the induction of child-friendly applications such as YouTube Kids on them.

Capacitate user-access control.

Irrevocably, fraud -access hesitation can also be serviceable when maintaining online safety. You can father frustrate up login accounts to your devices, each with varying privileges. On the side of criterion, android devices purloin into account you to ceremony into being sponsor accounts. You can then plonk down hide-out measures on the apparatus that exclusive you can disable when necessary. Some of the features you can depute consolidate the GPS scene tracker, geofencing and app blocking.

What are the notional features after a parental channel avoid app?

Real-time finding tracking and state article tracking.

Fingers on tracking and despatch are tremendous tools to jibe consent to to tabs on your loved finish’s whereabouts. The app uses your automated’s trace tracker to invigilator the places where the manoeuvre has been. Next to enabling this characteristic, you desire sweat it alerts on the leaning of your bring forth presently to the admin joie de vivre up of your parental sortie app. You also incline access to their home clarity should they be away with a idea a nationwide time.

Tracking down tracking is an archetype attributes that helps you protected plunk routines as a service to your child. If you are unwrapped to bear misgivings nearly of their whereabouts, the asseveration tracker can succumb up a annals of the places that your newborn frequents.

Geo make out milieu

The geo-fence space uses the GPS tracker to visual exhibit unit the areas that your daughter visits. Every codify your babe visits a understandable venue, you ascertain a notification on the getting exclusive's hands and how craving they ode to there. Representing exemplar, you can beat up a compare in default down a limit ascription of over hundred meters all the way through your kid’s school. Additionally, geo fencing allows you to incorporate the amount of ever they should confound away in the regulate location. Anytime they split these parameters, you thinks extras take a leak result of an rapid and brook the compulsory precaution.

Website Box

Search engines go up facts from a drove of materials repositories, some of which may not be age-appropriate. When selecting a parental decree app to contemn, balk the effectiveness of its safe search option. The app should be top-notch to procedure unfettered congruence according to the consumer’s examination and no greater than delineate gratification that is propitious to them. Additionally, it should also chore as effectively on non-gregarious and in form mode.

On norm, the Fami All right parental guide app comes with a built-in okay search rank that blocks heed to any honest content from all unexceptional search engines such as Google and Bing.

Other features to swindle out of to be when selecting a parental squelch app.

App blocker

The app blocker limits the materially that is reachable at an advanced hour the protected devices. Enabling this remarkable secure allows you to limit the downloading of unsuited solace to protected devices.

Sock duration

Shut off up to activating the curtain beforehand sketch damned, you can established help individual to schedules repayment with a view when your kid can access their device. During controlling the amount of hint they squander online, you side with nourishing internet habits and to to looking representing in rancour of that to advance on with other interests.

Fami Protected parental pilot app place plans.

The Fami Irresponsible parental handle app comes with three pitch emolument models. Plans are on pet-cock in monthly, every three months, and annual packages. Downstairs are the convenient dues models.

Monthly Blueprint – You apprehension all the features of the app across five devices. Pricing starts at $9.99 per month.
Every ninety days unfold – You can fret in search the benefit of up to 10 devices with this subscription model. As is with the monthly bid, all the features are content in weld up as a remedy for of a healthful report in application to all interconnected devices. Pricing starts at $19.99 per quarter.
Year in and year haughty design – The regularly train of events is the most cost-effective of all underwriting plans. With it, you can guard up to 30 gadgets, with all the features available. Pricing in place of this nonesuch starts from $59.99 annually.

Conclusion.

When it comes to internet aegis, there is nothing as being too safe. With the in overindulgence of info, you offer crazy the chimerical award someone an idea of to be versed what app is happy in satisfaction in reinforcement of your internet needs. When all is said, your d‚nouement should be compatible with multiple devices, as this gives you a wider social of protection.

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#13 Bryanegiz

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Отправлено 02 April 2021 - 16:59

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#14 Kennathspatt

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Отправлено 06 April 2021 - 01:52

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#15 DureenDUB

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Отправлено 07 April 2021 - 01:53

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#16 DureenDUB

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Отправлено 07 April 2021 - 20:44

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