新学链表，高手帮忙找找错~~~

/*设计一个单向链表。从标准输入读取若干整数，建立链表，
每次读入的数放入链表结尾。当用户输入 0时，结束链表的建立工作。然后从前往后依次输出链表节点中的内容*/

#include<iostream>
using namespace std;
typedef struct node
{
    int elem;
    struct node *next;
}Node;
int main()
{
    Node *head, *p, *last, *q;
    head = last = NULL;
    p = new Node;
    if(p == NULL)
        cout<<"there is no space"<<endl;
    cout<<"please input integers to build the link:";
    cin>>p->elem;
    p->next = NULL;
    if(p->elem == 0)
    {
        head = last = p;
    }
    else
    while(p->elem != 0)
    {
        last->next = p;
            p->next = NULL;
            last = p;
            p = new Node;
            if(p == NULL)
                cout<<"there is not space"<<endl;
            cin>>p->elem;
    }
    q = head;
    cout<<"Link elements:";
    while(q != NULL)
    {
        cout<<q->elem<<" ";
        q = q->next;
    }
    delete p;
    return 0;
}