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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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