額，直接上代碼：

typedef struct Node
{
    int data;
    struct Node *next;
}Node;

void circle_init(Node *head, const int len);
void circle_kill(Node *head, int num, const int len);
void circle_print(Node *head);
void circle_des(Node *head);

int main()
{
    int len;
    int num;
    Node head = {0, &head};
    
    printf(
 
"輸入人數：");
    scanf("%d", &len);
    
    circle_init(&head, len); 
    circle_print(&head);
    
    printf("輸入num：");
    scanf("%d", &num);
    
    circle_kill(&head, num, len);
    
    //circle_des(&head);
    return 0;
}

void circle_init(Node *head, const int len)
{
    
 
int i = 0;
    Node *p = head;
    
    for(i=0; i<len; i++)
    {
        p->next = (Node *)malloc(sizeof(Node));
        p = p->next;
        p->data = i + 1;
        p->next = head->next;
    }
    
}

void circle_kill(Node *head, int num, const int len)
{
    Node *p = head->next;
    Node 
 
*temp = NULL;
    int left = len;
    int i = 0;
    do {
        num = num % left;
        for(i=1; i<num-1; i++)
        {
            p = p->next;
        }
        temp = p->next;
        p->next = temp->next;
        p = temp->next;
        printf("%d ", temp->data);
        free(temp);
        left -= 1; 
    }while(left != 1);
    
    printf("%d ", p->data);
    free(p);
    head->next = head;
    
}

void circle_print(Node *head)
{
    Node *p = head->next;
    printf("鏈表：\n");
    
    do {
        printf("%d ", p->data);
        p = p->next;
    }while(p != head->next);
    
    printf("\n");
}

void circle_des(Node *head)
{
    Node *p = head->next;
    Node *temp = NULL;
    
    
    do {
        temp = p->next;
        free(p);
        p = temp;
    }while(p->next != head->next);
    free(p);
    head->next = head;
}

約瑟夫問題