[LeetCode] 23. Merge k Sorted Lists 合并k个有序链表
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Merge k sorted linked lists and return it as one sorted list. Analyze and describe its complexity.
Example:
Input: [ 1->4->5, 1->3->4, 2->6 ] Output: 1->1->2->3->4->4->5->6
与21. Merge Two Sorted Lists的拓展,这道题要合并k个有序链表。
解法1: 两两合并。1和2合并,结果在和3合并,以此类推,直到结束。时间复杂度为:2n + 3n + ... + kn = [(k+1)*k/2-1]*n = O(nk^2),空间复杂度为O(1)
解法2: 分治法Divide and Conquer,也就是二分法。每次将所有的list两两之间合并,直到所有list合并成一个。时间复杂度:2n * k/2 + 4n * k/4 + ... + (2^x)n * k/(2^x) = O(nklogk),如果用迭代空间复杂度为O(1),用递归则空间复杂度为O(logk)。
解法3: 最小堆MinHeap/priority queue,取每个Linked List的最小节点放入一个heap中,排序成最小堆,取出堆顶最小的元素,放入合并的list中,然后将该节点在其list中的下一个节点插入heap,循环上面步骤,以此类推直到全部节点都经过heap。由于heap的大小为始终为k,而每次插入的复杂度是logk,一共插入了nk个节点。时间复杂度为O(nklogk),空间复杂度为O(k)。
Python: Merge two by two, Time: O(nk^2), Space: O(1)
class Solution(object): def mergeKLists(self, lists): def mergeTwoLists(l1, l2): curr = dummy = ListNode(0) while l1 and l2: if l1.val < l2.val: curr.next = l1 l1 = l1.next else: curr.next = l2 l2 = l2.next curr = curr.next curr.next = l1 or l2 return dummy.next if not lists: return None left, right = 0, len(lists) - 1; while right > 0: if left >= right: left = 0 else: lists[left] = mergeTwoLists(lists[left], lists[right]) left += 1 right -= 1 return lists[0]
Python: Divide and conquer, Time: O(nklogk), Space: O(logk)
class Solution: def mergeKLists(self, lists): def mergeTwoLists(l1, l2): curr = dummy = ListNode(0) while l1 and l2: if l1.val < l2.val: curr.next = l1 l1 = l1.next else: curr.next = l2 l2 = l2.next curr = curr.next curr.next = l1 or l2 return dummy.next def mergeKListsHelper(lists, begin, end): if begin > end: return None if begin == end: return lists[begin] return mergeTwoLists(mergeKListsHelper(lists, begin, (begin + end) / 2), \\ mergeKListsHelper(lists, (begin + end) / 2 + 1, end)) return mergeKListsHelper(lists, 0, len(lists) - 1)
Python: Heap, Time: O(nklogk), Space: O(k)
import heapq class Solution: def mergeKLists(self, lists): dummy = ListNode(0) current = dummy heap = [] for sorted_list in lists: if sorted_list: heapq.heappush(heap, (sorted_list.val, sorted_list)) while heap: smallest = heapq.heappop(heap)[1] current.next = smallest current = current.next if smallest.next: heapq.heappush(heap, (smallest.next.val, smallest.next)) return dummy.next
C++: Merge two by two
class Solution { public: ListNode *mergeKLists(vector<ListNode *> &lists) { ListNode *ret = NULL; for(int i=0; i<lists.size(); i++) ret = merge2Lists(ret, lists[i]); return ret; } ListNode* merge2Lists(ListNode *h1, ListNode *h2) { ListNode *dummy = new ListNode(0), *tail = dummy; while(h1 && h2) { if(h1->val<=h2->val) { tail->next = h1; h1 = h1->next; } else { tail->next = h2; h2 = h2->next; } tail = tail->next; } tail->next = h1 ? h1 : h2; return dummy->next; } };
C++: Divide and Conque
class Solution { public: ListNode *mergeKLists(vector<ListNode *> &lists) { if(lists.empty()) return NULL; int end = lists.size()-1; while(end>0) { int begin = 0; while(begin<end) { lists[begin] = merge2Lists(lists[begin], lists[end]); begin++; end--; } } return lists[0]; } ListNode* merge2Lists(ListNode *h1, ListNode *h2) { ListNode *dummy = new ListNode(0), *tail = dummy; while(h1 && h2) { if(h1->val<=h2->val) { tail->next = h1; h1 = h1->next; } else { tail->next = h2; h2 = h2->next; } tail = tail->next; } tail->next = h1 ? h1 : h2; return dummy->next; } };
C++: priority queque
class Solution { public: struct compNode { bool operator()(ListNode *p, ListNode *q) const { return p->val>q->val; } }; ListNode *mergeKLists(vector<ListNode *> &lists) { priority_queue<ListNode*, vector<ListNode*>, compNode> pq; ListNode *dummy = new ListNode(0), *tail = dummy; for(int i=0; i<lists.size(); i++) if(lists[i]) pq.push(lists[i]); while(!pq.empty()) { tail->next = pq.top(); tail = tail->next; pq.pop(); if(tail->next) pq.push(tail->next); } return dummy->next; } };
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