LeetCode-Merge K Sorted Lists

https://leetcode-cn.com/problems/merge-k-sorted-lists/

又是拖了一天才开始做 Orz。
首先,用最笨的办法,每次从三个数字里面挑出来一个最小的,添加到一个新的序列里去。复杂度为 O(kN),所以如我所料的超时了。

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# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None

class Solution:
def mergeKLists(self, lists):
"""
:type lists: List[ListNode]
:rtype: ListNode
"""
if len(lists)==0:
return None
start=ListNode(0)
l=start
while True:
now=-1
v=sys.maxsize
for i,li in enumerate(lists):
if li!=None and li.val<v:
v=li.val
now=i
if now!=-1:
nowLi=lists[now]
l.next=nowLi
lists[now]=nowLi.next
l=l.next
else:
break
return start.next

接下来的思路和之前 Merge Two Sorted Lists很像 ,将序列两两进行合并。

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class Solution:
def mergeKLists(self, lists):
"""
:type lists: List[ListNode]
:rtype: ListNode
"""
if len(lists)==0:
return None
s=ListNode(0)
s.next=lists[0]
for i in range(1,len(lists)):
start=s
while lists[i]!=None:
l=lists[i]
lists[i]=lists[i].next
while start!=None and start.next!=None and l.val>start.next.val:
start=start.next
if start.next!=None and l.val<=start.next.val:
l.next=start.next
start.next=l
start=start.next
else:
start.next=l
break

return s.next

但是在文末的很变态的 test case 下,还是超时了。


现在只能看看 solution 了。

Solution 中的第一个方法居然是直接将所有数字排序,排序结束后重新生成各个 Node。这样。。居然还挺快(排序复杂度 O(NlogN)),空间复杂度也就是 O(N),完全可接受,真的是好办法。

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class Solution(object):
def mergeKLists(self, lists):
"""
:type lists: List[ListNode]
:rtype: ListNode
"""
self.nodes = []
head = point = ListNode(0)
for l in lists:
while l:
self.nodes.append(l.val)
l = l.next
for x in sorted(self.nodes):
point.next = ListNode(x)
point = point.next
return head.next

第二种方法和我的第一种方法一样,由于复杂度太高,没法 Accept,所以根本没提供代码。不过它提供了使用了 PriorityQueue 的代码。

这段代码的设计也比较巧妙,利用优先队列可以排序的特性,现将队列中分别插入这几个 List 的头部,然后每出一个最小的,就将当前这个 List 前进一位,并插入队列中进行排序,然后再次输出。

这个算法使用了小根堆,的时间复杂度可以到 O(Nlogk),空间复杂度可以到 O(K)。

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from Queue import PriorityQueue

class Solution(object):
def mergeKLists(self, lists):
"""
:type lists: List[ListNode]
:rtype: ListNode
"""
head = point = ListNode(0)
q = PriorityQueue()
for l in lists:
if l:
q.put((l.val, l))
while not q.empty():
val, node = q.get()
point.next = ListNode(val)
point = point.next
node = node.next
if node:
q.put((node.val, node))
return head.next

Solution 中的第三种方法是我上面的第二种方法,复杂度和第一种一样高(只是简化了几个步骤,复杂度没变)。

最后一个方法是上一种方法的变种,它使用了分治的思路可以将几个 List 两两合并,可以参考图

这样,每一轮合并的序列都比之前有序,时间复杂度就会降低为 O((2N)*(K / 2)+(4N) *(K/4)+(8N)*(K/8)+...+(2^logK*N)*(K/(2 ^logK)))=O(logK*KN)

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class Solution(object):
def mergeKLists(self, lists):
"""
:type lists: List[ListNode]
:rtype: ListNode
"""
amount = len(lists)
interval = 1
while interval < amount:
for i in range(0, amount - interval, interval * 2):
lists[i] = self.merge2Lists(lists[i], lists[i + interval])
interval *= 2
return lists[0] if amount > 0 else lists

def merge2Lists(self, l1, l2):
head = point = ListNode(0)
while l1 and l2:
if l1.val <= l2.val:
point.next = l1
l1 = l1.next
else:
point.next = l2
l2 = l1
l1 = point.next.next
point = point.next
if not l1:
point.next=l2
else:
point.next=l1
return head.next

所以,在思考的时候还是要多积累,不一定非要追求那么好的空间复杂度,有时候可以为了时间,牺牲一些空间(Solution 中的第一种方案)。

附注:变态的 test case

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