用回朔的办法解递归 L(m)=L(-1)+n =L(n-2)+(n-1)+n =L(n-3)+(m-2)+(n-1)+n =L(0)+1+2+..+(n-2)t(n-1)tn L(m=n(n+)/2+1
用回朔的办法解递归 L(n) = L(n-1)+n = L(n-2)+(n-1)+n = L(n-3)+(n-2)+(n-1)+n = …… = L(0)+1+2+……+(n-2)+(n-1)+n L(n) = n(n+1)/2 + 1
递归思维：Josephus问题 Live or die,it's a problem! Legend has it that Josephus wouldn't have lived to become famous without his mathematical talents.During the Jewish Roman war,he was among a band of 41 Jewish rebels trapped in a cave by the Romans.Preferring suicide to capture,the rebels decided to form a circle and,proceeding around it,to kill every third remaining person until no one was left.But Josephus,along with an unindicted co-conspirator,wanted none of this suicide nonsense;so he quickly calculated where he and his friend should stand in the vicious circle. We use a simpler version: “every second
递归思维：Josephus 问题 ◼ Live or die, it’s a problem! ◼ Legend has it that Josephus wouldn't have lived to become famous without his mathematical talents. During the Jewish Roman war, he was among a band of 41 Jewish rebels trapped in a cave by the Romans. Preferring suicide to capture, the rebels decided to form a circle and, proceeding around it, to kill every third remaining person until no one was left. But Josephus, along with an unindicted co-conspirator, wanted none of this suicide nonsense; so he quickly calculated where he and his friend should stand in the vicious circle. We use a simpler version: “every second
试试看：n=10 一及 survivor J(10)=5
试试看：n=10 1 8 7 6 2 4 5 10 3 9 1 7 5 9 3 1 7 5 9 3 survivor J(10)=5
For 2n Persons (n=1,2,3,...) 2- 2n-1 2n-1X-XLX3 2n- 5 n persons left\ k+1 下一轮将如何进行？它和上一轮有什么相同之处？
For 2n Persons (n=1,2,3,... ) 1 2n 2 2n-1 3 k+1 k k-1 1 2n-1 3 2n-3 5 k+3 k+1 k-1 n persons left 下一轮将如何进行？它和上一轮有什么相同之处？
For 2n Persons (n=1,2,3,...) 2-1-1x3 2n-3X 5将“第二轮”的问 题看做规模为n的/ 问题 假设在规模为n 的问题中，解 是m:J(n)=m -k-1 k+1 规模为n的问题中，解是m,这个m在2n规模问题中，位置在哪里？
For 2n Persons (n=1,2,3,... ) 1 2n-1 3 2n-3 5 k+3 k+1 k-1 1 2 3 m+1 m m-1 将“第二轮”的问 题看做规模为n的 问题 规模为n的问题中，解是m，这个m在2n规模问题中，位置在哪里？ 假设在规模为n 的问题中，解 是m：J(n)=m