Josephus Problem
Autor: Wladimir Araújo Tavares | Publicado: 2013-08-05T12:09:00-07:00

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Flávio Josephus foi um
historiador judeu famoso do
primeiro século, no momento da destruição do Segundo Templo. Durante
a guerra judaico-romana, ele ficou
preso em uma caverna com um grupo
de 40 soldados cercados pelos romanos. A lenda
diz que eles preferia o suicídio
do que serem capturados então os judeus decidiram
formar um círculo e, procedendo à
sua volta, para matar cada
terceira pessoa restante até que ninguém foi deixado. Josephus, não queria de morrer, rapidamente encontrou
o local seguro no círculo e assim permaneceu vivo.



Você pode tentar repetir o feito de Flávio no seguinte jogo:

http://www.cut-the-knot.org/recurrence/flavius.shtml

Uma maneira simples de resolver este problema é utilizar a estrutura de dados fila e realizar uma simulação para descobrir qual é a posição do último a morrer no círculo formado.
&nbsp;&nbsp; 
Resultado

input:
		
10 3


output:
		
morreu 3
morreu 6
morreu 9
morreu 2
morreu 7
morreu 1
morreu 8
morreu 5
morreu 10
Sobrevivente 4
&nbsp;
&nbsp;



Outra maneira é definir a estrutura recursiva do problema:f(n,k) = sobrevivente em um círculo com n pessoas e salto k começando na pessoa 1.f(n,k) = ( k-1 + f(n-1,k)) %n + 1f(1,k) = 1O valor k-1 é adicionado ao valor de f(n-1,k) justamente para ajustar o círculo na posição k-1, lembrando que f(n-1,k) devolve a posição com relação primeiro, e o valor +1 é para ajustar corretamente na posição k.