約瑟夫環的實現

#約瑟夫環的實現

##概述 約瑟夫環（約瑟夫問題）是一個數學的應用問題：已知n我的（以編號1，2，3...n分別表示）圍坐在一張圓桌周圍。從編號爲k的人開始報數，數到m的那我的出列；他的下一我的又從1開始報數，數到m的那我的又出列；依此規律重複下去，直到圓桌周圍的人所有出列。一般解決這類問題時咱們把編號從0~n-1，最後結果+1即爲原問題的解。

##解法 ###模擬法

#include<stdio.h>
#include<stdlib.h>
struct_Node
{
          int  data;
          struct_Node*next;
};
typedef struct_Node node_t;
typedef struct_Linklist
{
       node_t*phead;
       node_t*ptail;
       int len;
}Linklist;

staticnode_t*GetNode(inti)//新建並初始化節點
{
          node_t*pNode;
          pNode=(node_t*)malloc(sizeof(node_t));
         if(!pNode)
         {
             printf("Error,thememoryisnotenough!\n");
             exit(-1);
          }
          pNode->data=i;
          pNode->next=NULL;
          return pNode;
}

voidinit_list(Linklist*plist)//用第一個節點初始化循環單鏈表
{
          node_t*p;
          p=GetNode(1);
         //printf("TheNewNodeis:%d\n",p->data);//****TEST****
         plist->phead=p;
         plist->ptail=p;
         p->next=plist->phead;
         plist->len=1;
}

static void Create_List(Linklist*plist,intn)//把其他數據添加到循環單鏈表中
{
          int i=0;
          node_t*pNew;
         for(i=2;i<=n;i++)
         {
                pNew=GetNode(i);
                 /********TEST********
                 printf("TheNewNodeis:%d\n",pNew->data);
                 ********TEST********/
                  plist->ptail->next=pNew;
                  plist->ptail=pNew;
                  pNew->next=plist->phead;
                  plist->len++;
          }
          printf("Completesthee-waycirculationchaintablethefoundation!\n");
}

voidPrint_List(Linklist*plist)//輸出鏈表內容
{
         node_t*pCur=plist->phead;
         do
         {
                  printf("The%dperson.\n",pCur->data);
                  pCur=pCur->next;
           }while(pCur!=plist->phead);
           printf("ThelengthoftheList:%d\n",plist->len);
}
 
約瑟夫迴環函數實現
 
voidjoseph(Linklist*plist,intm)//約瑟夫迴環函數實現
{
       node_t*pPre=plist->ptail;
       node_t*pCur=plist->phead;
       int  i;
       while(plist->len!=1)
       {
            i=0;
            while(i<m-1)
            {
                      pPre=pPre->next;
                      i++;
            }
            pCur=pPre->next;
            pPre->next=pCur->next;
           free(pCur);
           plist->len--;
         }
        printf("Thelastoneis:%d\n",pPre->data);
}

int main()
{
        int n=0;
        printf("Please input the Length of the Circlelist:");
        scanf("%d",&n);
        int m=0;
        printf("Please input the Stoppoint:");
        scanf("%d",&m);
        LinklistpList;
        init_list(&pList);
        Create_List(&pList,n);
        Print_List(&pList);
        joseph(&pList,m);
        return 0;
}

###數學法

#include <iostream>
#include <list>
using std::cout;
using std::endl;
using std::cin;
using std::list;
 
int main()
{
    int total  = 0;
    cout << "Please input total number of people : ";
    cin >> total;
 
    int number = 0;
    cout << "Please input selected number : ";
    cin >> number;
 
    /* If number = 3
     * f(1) = 0
     * f(2) = 1 = (f(1) + 3) % 2
     * f(3) = 1 = (f(2) + 3) % 3
     * f(4) = 0 = (f(3) + 3) % 4
     * f(5) = 3 = (f(4) + 3) % 5
     * ...
     * f(n) = x = (f(n-1) + 3) % n
     * */
 
      int last = 0; // f(1) = 0
      for(int i = 2; i <= total; ++i)
      {
        last = (last + number) % i;
      }
      cout << "The last one is : " << last + 1 << endl;
      return 0;
}

---

##參考文章 http://baike.baidu.com/link?url=e-a03N1jkfyo9IGe5lXHPKpSK9WoqXU29gTLGlzaILz8SgYmCu7uv2w7vNA56qy3NwpaGyYDfl9WKG94Y5U5o_