双向约瑟夫问题

待我称王封你为后i 2022-06-02 08:56 12阅读 0赞

约瑟夫问题是一个经典的问题，我们不妨将这个经典问题进行扩展，变成一个双向的约瑟夫问题。

已知 n 个人（不妨分别以编号 1，2，3，...，n 代表 ）围坐在一张圆桌周围，首先从编号为 k 的人从 1 开始顺时针报数，1, 2, 3, ...，记下顺时针数到 m 的那个人，同时从编号为 k 的人开始逆时针报数，1, 2, 3, ...，数到 m 后，两个人同时出列。然后从出列的下一个人又从 1 开始继续进行双向报数，数到 m 的那两个人同时出列，...；。依此重复下去，直到圆桌周围的人全部出列。直到圆桌周围只剩一个人为止。

如果双向报数报到 m 时落在同一个人身上，那本次出列的只有一个人。

例如：5,1,2。则总共5个人，从1开始顺时针报数，数到2，定位编号2；同时从1开始报数数到2，定位编号5；2和5同时出列。然后继续开始报数，顺时针报数3,4，定位到4；逆时针报数4,3，定位3；4和3同时出列。最后剩余的为编号1。输出为：2-5,4-3,1,。

如果输入：6,2,3。则输出：4-6,2,1-3,5,。其中第2次只输出一个2，表示第二次双向报数时，恰好都落在编号2上，所以只有一个编号出列。

### **输入：** ###

n,k,m

### **输出：** ###

按照出列的顺序依次输出编号。同时出列编号中间用减号"-”连接。

### 非法输入的对应输出如下 ###

输入：n、k、m任一个为0  
输出：n,m,k must bigger than 0.

输入：k>n  
输出：k should not bigger than n.

<table style="width:1615px; margin-bottom:20px; background-color:transparent"> 
 <thead> 
  <tr> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> &nbsp;</th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 测试输入<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=input&amp;lang=zh_cn" title="关于“测试输入”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“测试输入”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 期待的输出<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=expectedoutput&amp;lang=zh_cn" title="关于“期待的输出”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“期待的输出”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 时间限制<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=timelimit&amp;lang=zh_cn" title="关于“时间限制”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“时间限制”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 内存限制<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=memlimit&amp;lang=zh_cn" title="关于“内存限制”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“内存限制”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 额外进程<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=nproc&amp;lang=zh_cn" title="关于“{$a} 个额外进程”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“{$a} 个额外进程”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 测试用例 1</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64755&amp;test=82435&amp;type=in&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">1,0,0↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64755&amp;test=82435&amp;type=out&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">n,m,k&nbsp;must&nbsp;bigger&nbsp;than&nbsp;0.↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 1秒</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 64M</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 0</td> 
  </tr> 
  <tr> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 测试用例 2</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64755&amp;test=82436&amp;type=in&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">1,2,1↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64755&amp;test=82436&amp;type=out&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">k&nbsp;should&nbsp;not&nbsp;bigger&nbsp;than&nbsp;n.↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 1秒</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 64M</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 0</td> 
  </tr> 
  <tr> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 测试用例 3</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64755&amp;test=82437&amp;type=in&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">5,1,2↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64755&amp;test=82437&amp;type=out&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">2-5,4-3,1,↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 1秒</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 64M</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 0</td> 
  </tr> 
  <tr> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 测试用例 4</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64755&amp;test=82438&amp;type=in&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">6,2,3↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64755&amp;test=82438&amp;type=out&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">4-6,2,1-3,5,↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 1秒</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 64M</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 0</td> 
  </tr> 
 </tbody> 
</table>

#include<stdio.h> 
    #include<stdlib.h> 
    int n, k, m; 
     
    typedef struct node 
    { 
       int data; 
      struct node*next; 
      struct node*pre; 
    }*ptrnode, node; 
     
     
    ptrnode head = NULL, tail = NULL; 
     
    ptrnode creatList() 
    { 
       for (int i = 1; i <= n; i++) 
        { 
           ptrnode pnew = (ptrnode)malloc(sizeof (struct node)); 
        pnew->data = i; 
         if (head == NULL) 
              head = tail = pnew; 
        else 
           { 
              tail->next = pnew; 
              pnew->pre = tail; 
               tail = pnew; 
               head->pre = pnew; 
           } 
       } 
      tail->next = head; 
    } 
     
    /*void solve() 
    { 
      struct node *p, *q, *p1, *pp, *qq; 
     int i; 
     int count = 0; 
     p1 = head; 
     for (i = 1; i <= k - 1; i++) 
            p1 = p1->next; 
      p = q = p1; 
        while (count < n){ 
          for (i = 1; i <= m - 1; i++) 
                p = p->next; 
            printf("%d", p->data); 
          for (i = 1; i <= m - 1; i++) 
                q = q->pre; 
         if (q->data == p->data){ 
             count++; 
               printf(","); 
               pp = p->pre; 
                pp->next = p->next; 
              p->next->pre = pp; 
               free(p); 
               p = pp->next; 
               q = pp; 
            } 
          else{ 
              printf("-%d,", q->data); 
                count += 2; 
                pp = p->pre; 
                pp->next = p->next; 
              p->next->pre = pp; 
               free(p); 
               p = pp->next; 
               qq = q->next; 
               qq->pre = q->pre; 
                q->pre->next = qq; 
               if (q == p) 
                    p = p->next; 
                free(q); 
               q = qq->pre; 
            } 
      } 
      printf("\n"); 
    }*/ 
     
    int main() 
    { 
        //freopen("4.txt", "r", stdin); 
        scanf("%d,%d,%d", &n, &k, &m); 
     if (m < 1 || k < 1 || n < 1) 
      { 
          printf("n,m,k must bigger than 0.\n"); 
         return 0; 
      } 
      else if (k>n) 
       { 
          printf("k should not bigger than n.\n"); 
       } 
      else 
       { 
          creatList(); 
           //solve(); 
         /*ptrnode start1 = head; 
           while (start1->data != k) 
               start1 = start1->next; 
          ptrnode start2 = start1; 
           int count = 0; 
         ptrnode p1, p2; 
            while (1) 
          { 
              count++; 
               if (count == m - 1) 
                { 
                  p1 = start1->next; 
                  p2 = start2->pre; 
                   if (p1 == p2) 
                  { 
                      printf("%d,",p1->data); 
                     n--; 
                       start1->next = p1->next; 
                     p1->next->pre = start1; 
                      //start2 = p2->pre; 
                     //free(p1); 
                    } 
                  else 
                   { 
                      printf("%d-%d,",p1->data,p2->data); 
                      n -= 2; 
                        start1->next = p1->next; 
                     p1->next->pre = start1; 
                      //free(p1); 
                        p2->pre->next = p2->next; 
                     p2->next->pre = p2->pre; 
                      //free(p2); 
                    } 
                  count = 0; 
                 if (n <=0) 
                      break; 
             } 
              start1 = start1->next; 
              start2 = start2->pre; 
           } 
          printf("\n");*/ 
            /*if (n == 1) 
              printf("%d,\n", start1->next->data); 
         else 
               printf("%d-%d,\n", start1->data,start2->data); 
               */ 
         ptrnode start1 = head; 
         while (start1->data != k) 
               start1 = start1->next; 
          ptrnode start2 = start1; 
           int i; int start = 1; 
          while (n--) 
            { 
              for (i = start; i < m; i++) 
             { 
                  start1 = start1->next; 
                  if (start1->data == 0) 
                      i--; 
               } 
              for (i =start; i < m; i++) 
              { 
                  start2 = start2->pre; 
                   if (start2->data == 0) 
                      i--; 
               } 
              printf("%d", start1->data); 
             start1->data = 0; 
               if (start1 != start2) 
              { 
                  printf("-%d", start2->data); 
                    start2->data = 0; 
                   n--; 
               } 
              start = 0; 
             printf(","); 
           } 
          printf("\n"); 
      } 
           return 0; 
    }