• push：每次插入元素到堆的末尾。然后up调整该元素

  • pop：移除堆顶的元素，然后将堆尾的元素放到堆顶，down调整堆顶元素

  • down：自上而下调整，使得整个堆仍然是小根堆

  • up：自下而上调整，使得整个堆仍然是小根堆

  • 注意，以上两个函数只能使得调整的那个元素到达正确位置，因此使用前要求其他元素作为根在正确位置

力扣23. 合并 K 个升序链表

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/**
 * Definition for singly-linked list.
 * struct ListNode {
 *     int val;
 *     ListNode *next;
 *     ListNode() : val(0), next(nullptr) {}
 *     ListNode(int x) : val(x), next(nullptr) {}
 *     ListNode(int x, ListNode *next) : val(x), next(next) {}
 * };
 */
class Solution {
public:
    ListNode* mergeKLists(vector<ListNode*>& lists) {
        vector<ListNode*> heap;
        heap.push_back(NULL);
        int n = 0;
        auto down = [&](this auto&& down, int u) -> void{
            int t = u;
            if (2 * u <= n && heap[2 * u]->val < heap[t]->val) t = 2 * u;
            if (2 * u + 1 <= n && heap[2 * u + 1]->val < heap[t]->val) t = 2 * u + 1;
            if (t != u) {
                swap(heap[t], heap[u]);
                down(t);
            } 
            return ;
        };
        auto up = [&](this auto&& up, int u) -> void{
            int t = u;
            if (u / 2 >= 1 && heap[u / 2]->val > heap[t]->val) {
                swap(heap[u / 2], heap[t]);
                up(u / 2);
            }
            return ;
        };

        auto push = [&](ListNode* x) -> void {
            heap.push_back(x);
            n++;
            up(n);
        };
        auto top = [&]()->ListNode* {
            if (n < 1) return NULL; 
            return heap[1];
        };
        auto pop = [&]()->void {
            swap(heap[1], heap[n]);
            n--;
            down(1);
        };

        ListNode* dummy = new ListNode(0);
        ListNode* head = dummy;
        for (auto list: lists) {
            ListNode* head = list;
            while (head) {
                push(head);
                ListNode* nodeTmp = head->next;
                head->next = NULL;
                head = nodeTmp;
            }
        }
        while (n >= 1) {
            head->next = top();
            head = head->next;
            pop();
        }
        return dummy->next;
    }
};