猴子选大王的四种VB解法

题目:

一堆猴子编号依次是1，2，3 ...n ,这群猴子（n个）按照1到n的顺序围坐一圈，从第1开始报数，报双数的猴子离开此圈，这样依次下来，直到圈中只剩下最后一只猴子，则该猴子为大王。

解法:

1.集合的方法(O(2N)):

Function Monkeyking(ByVal n As Long) As Long Dim all As New Collection, i As Long For i = 1 To n all.Add i Next While all.Count > 1 all.Add all(1) all.Remove 1 all.Remove 1 Wend Monkeyking = all(1) End Function

2.直接循环取模(O(N)):

Function Monkeyking(ByVal n As Long) As Long Dim i As Long, K As Long For i = 2 To n K = (K + 2) Mod i Next Monkeyking = K + 1 End Function

3.递归(O(LOG N)):

Function Monkeyking(ByVal n As Long) As Long If n = 1 Then Monkeyking = 1: Exit Function Monkeyking = 2 * (Monkeyking(n \ 2) + (n And 1)) - 1 End Function

4. 公式:

Function Monkeyking(ByVal n As Long) As Long Monkeyking = 2 * (n - 2 ^ Int(Log(n) / Log(2))) + 1 End Function

以上四种方法不仅代码越来越短,而且效率越来越高.