循环链表和约瑟夫环

循环链表的实现

单链表只有向后结点，当单链表的尾链表不指向NULL，而是指向头结点时候，形成了一个环，成为单循环链表，简称循环链表。当它是空表，向后结点就只想了自己，这也是它与单链表的主要差异，判断node->next是否等于head。

代码实现分为四部分：

1. 初始化
2. 插入
3. 删除
4. 定位寻找

代码实现：

void ListInit(Node *pNode){
	int item;
	Node *temp,*target;
	cout<<"输入0完成初始化"<<endl;
	
	while(1){
		cin>>item;
		if(!item)
			return ;
		if(!(pNode)){ //当空表的时候，head==NULL 
			pNode = new Node ;
			if(!(pNode))
				exit(0);//未成功申请 
			pNode->data = item;
			pNode->next = pNode;
		}
		else{
			//
			for(target = pNode;target->next!=pNode;target = target->next)
				;
			temp = new Node;
			if(!(temp))
				exit(0);
			temp->data = item;
			temp->next = pNode;
			target->next = temp;
		}
	}
} 
void ListInsert(Node *pNode,int i){ //参数是首节点和插入位置 
	Node *temp;
	Node *target;
	int item;
	cout<<"输入您要插入的值:"<<endl;
	cin>>item;
	if(i==1){
		temp = new Node;
		if(!temp)
			exit(0);
		temp->data = item;
		for(target=pNode;target->next != pNode;target = target->next)
		;
		temp->next = pNode;
		target->next = temp;
		pNode = temp;
	}
	else{
		target = pNode;
		for (int j=1;j<i-1;++j)
			target = target->next;
		temp = new Node;
		if(!temp)
			exit(0);
		temp->data = item;
		temp->next = target->next;
		target->next = temp;
	}
}
void ListDelete(Node *pNode,int i){
	Node *target,*temp;
	if(i==1){
		for(target=pNode;target->next!=pNode;target=target->next)
		;
		temp = pNode;//保存一下要删除的首节点 ,一会便于释放 
		pNode = pNode->next;
		target->next = pNode;
		delete temp; 
	}
	else{
		target = pNode;
		for(int j=1;j<i-1;++j)
			target = target->next;
		temp = target->next;//要释放的node
		target->next = target->next->next;
		delete temp; 
	}
}
int ListSearch(Node *pNode,int elem){ //查询并返回结点所在的位置 
	Node *target;
	int i=1;
	for(target = pNode;target->data!=elem && target->next!= pNode;++i)
		target = target->next;
	if(target->next == pNode && target->data!=elem)
		return 0;
	else return i;
}

---

约瑟夫问题

约瑟夫环（约瑟夫问题）是一个数学的应用问题：已知n个人（以编号1，2，3...n分别表示）围坐在一张圆桌周围。从编号为k的人开始报数，数到m的那个人出列；他的下一个人又从1开始报数，数到m的那个人又出列；依此规律重复下去，直到圆桌周围的人全部出列。这类问题用循环列表的思想刚好能解决。

注意：编写代码的时候，注意报数为m = 1的时候特殊情况

#include<iostream>
#include<cstdio>
using namespace std;
typedef struct Node{
	int data;
	Node *next;
};

Node *Create(int n){
	Node *p = NULL, *head;
	head = new Node;
	if (!head)
		exit(0);
	p = head; // p是当前指针 
	int item=1;
	if(n){
		int i=1;
		Node *temp;
		while(i<=n){
			temp = new Node;
			if(!temp)
				exit(0);
			temp->data = i++;
			p->next = temp;
			p = temp; 
		}
		p->next = head->next;
	}
	delete head;
	return p->next;
}
void Joseph(int n,int m){
	//n为总人数，m为数到第m个的退出
	m = n%m;
	
	Node *start = Create(n);
	
	if(m){//如果取余数后的m!=0，说明 m!=1 
		while(start->next!=start){
			Node *temp = new Node;
			if(!temp)
				exit(0);
			for(int i=0;i<m-1;i++) // m = 3%2 = 1
				start = start->next;
			temp = start->next;
			start->next = start->next->next;
			start = start->next;
			cout<<temp->data<<" ";
			delete temp;
		}
	}
	else{
		for(int i=0;i<n-1;i++){
			Node *temp = new Node;
			if(!temp)
				exit(0);	
			cout<<start->data<<" ";
			temp = start;
			start = start->next;
			delete temp;
		}
	}
	cout<<endl;
	cout<<"The last person is:"<<start->data<<endl;
}
int main(){
	Joseph(3,1);
	Joseph(3,2);
	return 0;
}