详解约瑟夫环问题及其相关的C语言算法实现

#include <stdio.h> 
  #include <stdlib.h> 
  #include <string.h> 
    
  typedef struct lnode 
  { 
    int pos; 
    struct lnode *next; 
  } lnode; 
    
    
  /** 
   * 构建循环链表&&循环遍历 
   */ 
  void create_ring(lnode **root, int loc, int n) 
  { 
    lnode *pre, *current, *new; 
    current = *root; 
    pre = NULL; 
    
    while (current != NULL) { 
      pre = current; 
      current = current->next; 
    } 
    
    new = (lnode *)malloc(sizeof(lnode)); 
    new->pos = loc; 
    new->next = current; 
    
    if (pre == NULL) { 
      *root = new; 
    } else { 
      pre->next = new; 
    } 
    
    // 循环链表 
    if (loc == n) { 
      new->next = *root; 
    } 
  } 
    
  /** 
   * 约瑟夫环 
   */ 
  void kickoff_ring(lnode *head, int p) 
  { 
    int i; 
    lnode *pre, *pcur; 
    pre = pcur = head; 
    
    while (pcur->next != pcur) { 
      for (i = 1; i < p; i ++) { 
        pre = pcur; 
        pcur = pcur->next; 
      } 
    
      printf("%d ", pcur->pos); 
      pre->next = pcur->next; 
      free(pcur); 
      pcur = pre->next; 
    } 
    printf("%d\n", pcur->pos); 
    free(pcur); 
  } 
    
    
  void print_ring(lnode *head) 
  { 
    lnode *cur;  
    cur = head; 
    
    while (cur->next != head) { 
      printf("%d ", cur->pos); 
      cur = cur->next; 
    } 
    printf("%d\n", cur->pos); 
  } 
    
  int main() 
  { 
    int i, p, n; 
    lnode *head; 
    
    while (scanf("%d %d", &n, &p) != EOF) { 
      // 构建循环链表 
      for (i = 1, head = NULL; i <= n; i ++) 
        create_ring(&head, i, n); 
    
      // 约瑟夫环 
      if (p != 1)  
        kickoff_ring(head, p); 
      else 
        print_ring(head); 
    } 
    
    return 0; 
  } 

 #include <stdio.h> 
  #include <stdlib.h> 
   
  int main() 
  { 
    int i, index, p, n, remain, delete[3001], flag[3001] = {0}; 
   
    while (scanf("%d %d", &n, &p) != EOF) { 
      remain = n; 
      index = 0; 
      while (remain >= 1) { 
        for (i = 0; i < n; i ++) { 
          if (flag[i] == 0) { 
            // 报数 
            index ++; 
            // 报p者退出圈外 
            if (index == p) { 
              // 退出圈外 
              flag[i] = 1; 
              // 重新报数 
              index = 0; 
              delete[remain - 1] = i + 1; 
              remain --; 
            }   
          }   
        } 
      } 
   
      // 输出每个退出人的序号 
      for (i = n - 1; i >= 0; i --) { 
        if (i == 0) { 
          printf("%d\n", delete[i]); 
        } else { 
          printf("%d ", delete[i]); 
        } 
      } 
    } 
   
    return 0; 
  } 

#include <stdio.h> 
   
  int main(void) 
  { 
    int i, n, m, last; 
   
    while (scanf("%d", &n) != EOF && n != 0) { 
      // 接收报数 
      scanf("%d", &m); 
   
      // 约瑟夫环问题 
      for (i = 2, last = 0; i <= n; i ++) { 
        last = (last + m) % i; 
      } 
      printf("%d\n", last + 1); 
    } 
   
    return 0; 
  }