Priority queue and Heap

I have seen lots of solutions confuse priority queue with heap. I find a good link and list the talk below.

Concept:

1.Heap is a kind of data structure. It is a name for a particular way of storing data that makes certain operations very efficient. We can use a tree or array to describe it.

   18
  /	 10	 16
/ \   / 9  5  8  12

18, 10, 16, 9, 5, 8, 12

2.Priority queue is an abstract datatype. It is a shorthand way of describing a particular interface and behavior, and says nothing about the underlying implementation.

A heap is a very good data structure to implement a priority queue. The operations which are made efficient by the heap data structure are the operations that the priority queue interface needs.

Implementation: c++

1.priority_queue:

struct compare {
    bool operator()(const ListNode* l, const ListNode* r) {
        return l->val > r->val;
    }
};
ListNode *mergeKLists(vector<ListNode *> &lists) { //priority_queue
    priority_queue<ListNode *, vector<ListNode *>, compare> q;
    for(auto l : lists) {
        if(l)  q.push(l);
    }
    if(q.empty())  return NULL;

    ListNode* result = q.top();
    q.pop();
    if(result->next) q.push(result->next);
    ListNode* tail = result;
    while(!q.empty()) {
        tail->next = q.top();
        q.pop();
        tail = tail->next;
        if(tail->next) q.push(tail->next);
    }
    return result;
}

2.make_heap:

static bool heapComp(ListNode* a, ListNode* b) {
        return a->val > b->val;
}
ListNode* mergeKLists(vector<ListNode*>& lists) { //make_heap
    ListNode head(0);
    ListNode *curNode = &head;
    vector<ListNode*> v;
    for(int i =0; i<lists.size(); i++){
        if(lists[i]) v.push_back(lists[i]);
    }
    make_heap(v.begin(), v.end(), heapComp); //vector -> heap data strcture

    while(v.size()>0){
        curNode->next=v.front();
        pop_heap(v.begin(), v.end(), heapComp);
        v.pop_back();
        curNode = curNode->next;
        if(curNode->next) {
            v.push_back(curNode->next);
            push_heap(v.begin(), v.end(), heapComp);
        }
    }
    return head.next;
}