joseph问题

1.Joseph描述:

原始的Joseph问题的描述如下：有n个人围坐在一个圆桌周围，把这n个人依次编号为1，…，n。从编号是start的人开始报数，数到第num个人出列，然后从出列的下一个人重新开始报数，数到第num个人又出列，…，如此反复直到所有的人全部出列为止。比如当n=6，start=1，num=5的时候，出列的顺序依次是5，4，6，2，3，1。

2.instance analysis

#include <stdio.h>
#include <stdlib.h>

typedef int DATATYPE;

typedef struct node
{
	DATATYPE data;
	struct node *next;
}LoopList;

LoopList *create_empty_looplist()
{
	LoopList *head;

	head = (struct node *)malloc(sizeof(struct node));
	head->next = head;

	return head;
}

int insert_head_looplist(LoopList *head,DATATYPE data)
{
	struct node *temp;

	temp = (struct node *)malloc(sizeof(struct node));
	temp->data = data;

	temp->next = head->next;
	head->next = temp;

	return 0;
}

LoopList *cut_head_looplist(LoopList *head)
{
	struct node *p = head;
	
	//找到尾部节点
	while(p->next != head) p = p->next;

	//删除头节点
	p->next = head->next;

	free(head);
	head = NULL;

	return p->next;
}

int printf_looplist(LoopList *head)
{
	struct node *p = head->next;

	while(p != head)
	{
		printf("%d ",p->data);
		p = p->next;
	}

	printf("\n");

	return 0;
}

int _printf_looplist(LoopList *head)
{
	struct node *p = head->next;
	
	printf("%d ",head->data);

	while(p != head)
	{
		printf("%d ",p->data);
		p = p->next;
	}

	printf("\n");

	return 0;
}

void joseph(int n,int k,int m)
{
	int i = 0;
	struct node *temp,*p;
	LoopList *L = create_empty_looplist();

	for(i = n;i > 0;i --)
	{
		insert_head_looplist(L,i);
	}

	p = cut_head_looplist(L);
		
	//找到第K个人
	for(i = 0;i < k -1;i ++)
	{
		p = p->next;
	}

	while(p->next != p)
	{
		//找到要删除节点的前一节点
		for(i = 0;i < m - 2;i ++)
		{
			p = p->next;
		}

		//删除 
		temp = p->next;
		printf("%d ",temp->data);
		p->next = temp->next;
		free(temp);

		//从一个节点开始计数
		p = p->next;
	}

	printf("%d\n",p->data);
	free(p);

	return;
}

int main(int argc, const char *argv[])
{
	joseph(8,3,4);

	return 0;
}