剑指OFFER系列之62----圆圈中最后剩下的数字

题目描述：0,1，…, n-1这n个数字围成一圈，从0开始报数，每次从圈中删除第m个数字。求圈中最后剩下的数字。

struct ListNode{
	int val;
	ListNode* next;
	ListNode(): val(-1), next(nullptr){}
	ListNode(int x): val(x), next(nullptr){}
};

// math method
int joesphus(int n, int m){
	if(n < 1 || m < 1){
		return -1;
	}
	int ans = 0; 
	for(int i = 2; i <= n; i++){
		ans = (ans + m) % i;
	}
	return ans;
}

// recurisive
int joesphusII(int n, int m){
	if(n < 1 || m < 1){
		return -1;
	}
	if(n == 1){
		return 0;
	}
	return (joesphusII(n - 1, m) + m) % n;
}

// recurent list
int joesphusIII(int n, int m){
	if(n < 1 || m < 1){
		return -1;
	}
	ListNode* head = new ListNode(0);
	ListNode* pre = head;
	for(int i = 1; i < n; i++){
		ListNode* tmp = new ListNode(i);
		pre -> next = tmp;
		pre = tmp;
	}
	pre -> next = head;
	while(n != 1){
		for(int i = 1; i < m - 1; i++){
			head = head -> next;
		}
		head -> next = head -> next -> next;
		head = head -> next;
		n--;
	}
	return head -> val;
}