fnds Posted April 28, 2008 at 02:57 PM Report Share #181930 Posted April 28, 2008 at 02:57 PM À uns dias tive esta ideia, já resolvi o problema 🙂 Título: - Fazer a divasão de dois números Objectivo: - Fazer um pequeno programa que faça a divisão de dois números reais finitos; - Os números podem ser decimais, e o separador pode ser "." e ","; - A divisão deve de ser até ao infinito; - O programa deve mostrar a periodicidade das dizimas infinitas. Exemplo de Input/Output: Input: 100 200 Output: 0,5 Input: 1 0,003 Output: 333,(3) Material de Apoio: - Nada. Restrições: - Não se pode usar funções/bibliotecas que façam a divisão por nós. Link to comment Share on other sites More sharing options...
Tharis Posted April 28, 2008 at 10:16 PM Report Share #182177 Posted April 28, 2008 at 10:16 PM - A divisão deve de ser até ao infinito; Até ao infinito? É estúpido... 1 / 2 = 0.5 / 2 = 0.25 / 2 = 0.125 / 2 = 0.625 ... e nunca mais acabava... (infinito) Outra coisa é não se diz deve de ser, mas deve ser... A seguir ao verbo dever não existe a proposição de.... Link to comment Share on other sites More sharing options...
djthyrax Posted April 28, 2008 at 10:24 PM Report Share #182189 Posted April 28, 2008 at 10:24 PM Podemos então usar as operações *, + e -? Não peças ajuda por PM! A tua dúvida vai ter menos atenção do que se for postada na secção correcta do fórum! Link to comment Share on other sites More sharing options...
Warrior Posted April 28, 2008 at 10:26 PM Report Share #182193 Posted April 28, 2008 at 10:26 PM http://www.dcc.fc.up.pt/oni/problemas/2005/qualificacao/probB.html É um problema "típico", já o resolvi algumas vezes, é um bom treino. Link to comment Share on other sites More sharing options...
Rui Carlos Posted April 28, 2008 at 10:34 PM Report Share #182197 Posted April 28, 2008 at 10:34 PM Até ao infinito? É estúpido... 1 / 2 = 0.5 / 2 = 0.25 / 2 = 0.125 / 2 = 0.625 ... e nunca mais acabava... (infinito) Outra coisa é não se diz deve de ser, mas deve ser... A seguir ao verbo dever não existe a proposição de.... Uma fracção, se for uma dízima infinita, é obrigatoriamente periódica. Só precisas de encontrar o período. Rui Carlos Gonçalves Link to comment Share on other sites More sharing options...
Tharis Posted April 28, 2008 at 11:18 PM Report Share #182226 Posted April 28, 2008 at 11:18 PM Uma fracção, se for uma dízima infinita, é obrigatoriamente periódica. Só precisas de encontrar o período. Mas isso é para uma dízima infinita. E para uma finita? Link to comment Share on other sites More sharing options...
Rui Carlos Posted April 28, 2008 at 11:35 PM Report Share #182234 Posted April 28, 2008 at 11:35 PM Mas isso é para uma dízima infinita. E para uma finita? Se quiseres resolver o problema de forma simples, procuras uma dízima infinita. Se encontrares um período, verificas se é realmente o valor correspondente à fracção (como? é só investigar um pouco), se não for, continuas à procura. Vais acabar por, ou encontrar um período válido, ou chegar a uma dízima periódica. Estudando um pouco de Teoria de Números, é capaz de se encontrar algumas propriedades úteis, mas agora não tenho tempo para ver isso. Rui Carlos Gonçalves Link to comment Share on other sites More sharing options...
djthyrax Posted April 28, 2008 at 11:58 PM Report Share #182235 Posted April 28, 2008 at 11:58 PM Se o numerador é multiplo do denominador, é só simplificar. Digo eu. Não peças ajuda por PM! A tua dúvida vai ter menos atenção do que se for postada na secção correcta do fórum! Link to comment Share on other sites More sharing options...
fnds Posted April 29, 2008 at 10:58 AM Author Report Share #182259 Posted April 29, 2008 at 10:58 AM Bem como eu não sabia que se uma dízima infinita é sempre periódica.... O que eu quero é um programa que de uma divisão retorne o período, como o da ONI. @Tharis, até ao infinito, ou seja sempre a acrescentar casas decimais, se o input for 1/3, o programa retorna 0,333333333.... e por ai fora. @djthyrax, podes usar o que quiseres 👍 Link to comment Share on other sites More sharing options...
Warrior Posted April 29, 2008 at 04:40 PM Report Share #182361 Posted April 29, 2008 at 04:40 PM fnds3000: é bastante mais útil fazer como o das ONI. Se for infinita, retorna #3, a indicar o 3 infinito. Link to comment Share on other sites More sharing options...
pedrosorio Posted April 29, 2008 at 09:02 PM Report Share #182430 Posted April 29, 2008 at 09:02 PM Bem como eu não sabia que se uma dízima infinita é sempre periódica.... E não é, apenas o é se for um número racional. Como todos os números fraccionários são racionais... Não respondo a dúvidas por mensagem. Link to comment Share on other sites More sharing options...
pcaldeira Posted April 29, 2008 at 09:25 PM Report Share #182441 Posted April 29, 2008 at 09:25 PM http://www.dcc.fc.up.pt/oni/problemas/2005/qualificacao/probB.html É um problema "típico", já o resolvi algumas vezes, é um bom treino. Já agora, podias dizer como resolveste/qual a forma mais eficiente de resolver isto? Link to comment Share on other sites More sharing options...
Warrior Posted April 30, 2008 at 01:00 AM Report Share #182535 Posted April 30, 2008 at 01:00 AM Implementar a divisão da "primária" consecutivamente. Quando encontras o resto 0, significa que arranjaste uma dizima finita, se encontras um resto cujo valor já tinhas encontrado anteriormente, então tens uma dízima infinita periódica, cujo período vai desde um dos restos ao outro. Facilmente ves qual é a parte que não se repete neste caso. Isto não é difícil de demonstrar/perceber, e até é bastante fácil de implementar. Link to comment Share on other sites More sharing options...
fnds Posted April 30, 2008 at 09:07 AM Author Report Share #182562 Posted April 30, 2008 at 09:07 AM Warrior, tens razão, eu só postei isto aqui porque não tinah conhecimento do da ONI, eu resolvi o problema como tu disses-te 👍 , vou optimizar o código, depois posto. Link to comment Share on other sites More sharing options...
fnds Posted April 30, 2008 at 08:15 PM Author Report Share #182716 Posted April 30, 2008 at 08:15 PM #!/usr/bin/python # -*- coding: utf-8 -*- # # Coded by Fábio Domingues (fnds) <fnds3000@gmail.com> from sys import stdout while 1: dividendo_str = raw_input('Dividendo: ') divisor_str = raw_input('Divisor: ') dividendo_str = dividendo_str.replace(',', '.') divisor_str = divisor_str.replace(',', '.') dividendo_str_virgula_pos = dividendo_str.find('.') if dividendo_str_virgula_pos <> -1: dividendo_str_virgula_pos = len(dividendo_str)-dividendo_str_virgula_pos-1 else: dividendo_str_virgula_pos = 0 divisor_str_virgula_pos = divisor_str.find('.') if divisor_str_virgula_pos <> -1: divisor_str_virgula_pos = len(divisor_str)-divisor_str_virgula_pos-1 else: divisor_str_virgula_pos = 0 if dividendo_str_virgula_pos >= divisor_str_virgula_pos: virgula_pos = dividendo_str_virgula_pos else: virgula_pos = divisor_str_virgula_pos dividendo = int(float(dividendo_str)*(10**virgula_pos)) divisor = int(float(divisor_str)*(10**virgula_pos)) quocientes = [] restos = [] while 1: quociente = dividendo/divisor resto = dividendo%divisor dividendo = resto*10 quocientes.append(quociente) if not resto: break if resto not in restos: restos.append(resto) else: quocientes.insert(restos.index(resto)+1, '(') quocientes.append(')') break if len(quocientes) > 1: quocientes.insert(1, ',') stdout.write('Quociente: ') for q in quocientes: stdout.write(str(q)) stdout.write('\n\n') Dividendo: 1 Divisor: 2 Resultado: 0,5 Dividendo: 123 Divisor: 321 Resultado: 0,(38317757009345794392523364485981308411214953271028037) Dividendo: 9494,5 Divisor: 9,2663 Resultado: 1024,(626873725219343211422034684825658569223962099219753299590991010 43566472054649644410390339186082902560892697193054401433150232563158973916234095 59371054250348035353916881603228904740835069013522117781638841824676515977250898 41684383195018507926572634168977909197845957933587300216915057790056441082201094 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10768051973279518254319415516441298036972685969588724733712485026385936134163582 01223789430517034846702567367773544996384749036832392648629981761868275363413660 25274381360413541543010694667774624175776739367385040415268230037879196658860602 39793660900251448798333747018766929626711848310544661839137519829921327822323904 90271197781207170067880383756191791761544521545816561086949483612660932626830558 04366359819992877416012863818352524740187561378327919450050181841727550370698121 148678544834507840238282809751464986024) 😉 (Peço desculpa pelo tamanho, não tenho culpa do programa ser bom 😁.) 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Psicopunk Posted April 30, 2008 at 10:59 PM Report Share #182744 Posted April 30, 2008 at 10:59 PM Há quem goste de reinventar a roda... sinceramente... Link to comment Share on other sites More sharing options...
pedrosorio Posted April 30, 2008 at 11:24 PM Report Share #182748 Posted April 30, 2008 at 11:24 PM Há quem goste de reinventar a roda... sinceramente... Não percebi essa... Não respondo a dúvidas por mensagem. Link to comment Share on other sites More sharing options...
fnds Posted May 1, 2008 at 04:14 PM Author Report Share #182837 Posted May 1, 2008 at 04:14 PM Nem eu, explica-te... Link to comment Share on other sites More sharing options...
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