104. 合并k个排序链表

描述

合并k个排序链表，并且返回合并后的排序链表。尝试分析和描述其复杂度。

样例

给出3个排序链表[2->4->null,null,-1->null]，返回 -1->2->4->null

代码

1.分治 + 归并排序的思想，NlogK (合并两个链表时间复杂度为 N ，对链表组分治时间复杂度为 logK)，自顶向下分治一层层递归

/**
 * Definition for ListNode.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int val) {
 *         this.val = val;
 *         this.next = null;
 *     }
 * }
 */ 
public class Solution {
    /**
     * @param lists: a list of ListNode
     * @return: The head of one sorted list.
     */
    public ListNode mergeKLists(List<ListNode> lists) {
        if (lists.size() == 0) {
            return null;
        }
        return mergeHelper(lists, 0, lists.size() - 1);
    }
    
    private ListNode mergeHelper(List<ListNode> lists, int start, int end) {
        // 只有一条链表，返回链表头结点
        if (start == end) {
            return lists.get(start);
        }
        
        int mid = start + (end - start) / 2;
        ListNode left = mergeHelper(lists, start, mid);
        ListNode right = mergeHelper(lists, mid + 1, end);
        return mergeTwoLists(left, right);
    }
    
    private ListNode mergeTwoLists(ListNode list1, ListNode list2) {
        ListNode dummy = new ListNode(0);
        ListNode tail = dummy;
        while (list1 != null && list2 != null) {
            if (list1.val < list2.val) {
                tail.next = list1;
                tail = list1;
                list1 = list1.next;
            } else {
                tail.next = list2;
                tail = list2;
                list2 = list2.next;
            }
        }
        if (list1 != null) {
            tail.next = list1;
        } else {
            tail.next = list2;
        }
        
        return dummy.next;
    }
}

2. heap 时间复杂度NlogK
   PriorityQueue

PriorityQueue是基于优先堆的一个无界队列，本质是一个堆，这个优先队列中的元素可以默认自然排序或者通过提供的Comparator（比较器）在队列实例化的时排序。Java默认从小到大顺序，Cpp默认从大到小顺序。

public class Solution {
    // 自定义Comparator，Comparator方法第一个参数减去第二个参数就是从小到大排序
    private Comparator<ListNode> ListNodeComparator = new Comparator<ListNode>() {
        public int compare(ListNode left, ListNode right) {
            return left.val - right.val;
        }
    };
    
    public ListNode mergeKLists(List<ListNode> lists) {
        if (lists == null || lists.size() == 0) {
            return null;
        }
        
        // 可直接确定PriortyQueue的大小为lists.size()
        // 用最小堆实现PriorityQueue
        Queue<ListNode> heap = new PriorityQueue<ListNode>(lists.size(), ListNodeComparator);
        // K个链表的表头加入heap
        for (int i = 0; i < lists.size(); i++) {
            if (lists.get(i) != null) {
                heap.add(lists.get(i));
            }
        }
        
        ListNode dummy = new ListNode(0);
        ListNode tail = dummy;
        // while执行N次，N是所有结点个数
        // 此处是本算法的精髓
        while (!heap.isEmpty()) {
            // head即为堆的弹出当前最小值结点
            ListNode head = heap.poll();
            tail.next = head;
            tail = head;
            // head结点所在链表在head后仍有结点，加入heap，和其余结点比较
            if (head.next != null) {
                heap.add(head.next);
            }
        }
        return dummy.next;
    }
}

3. merge two by two 时间复杂度NlogK，自底向上归并

/**
 * Definition for ListNode.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int val) {
 *         this.val = val;
 *         this.next = null;
 *     }
 * }
 */ 
public class Solution {
    /**
     * @param lists: a list of ListNode
     * @return: The head of one sorted list.
     */
    public ListNode mergeKLists(List<ListNode> lists) {  
        if (lists == null || lists.size() == 0) {
            return null;
        }
        
        while (lists.size() > 1) {
            List<ListNode> new_lists = new ArrayList<ListNode>();
            // 每两条链表相互合并，合并后链表加入new_lists
            // 合并完一轮后list = new_lists，继续两两合并，直到只剩一个链表
            for (int i = 0; i + 1 < lists.size(); i += 2) {
                ListNode merged_list = merge(lists.get(i), lists.get(i+1));
                new_lists.add(merged_list);
            }
            // 某一轮合并链表个数为奇数时，最后一个链表直接加入new_lists
            if (lists.size() % 2 == 1) {
                new_lists.add(lists.get(lists.size() - 1));
            }
            lists = new_lists;
        }
        
        return lists.get(0);
    }
    
    // 合并两个链表
    private ListNode merge(ListNode a, ListNode b) {
        ListNode dummy = new ListNode(0);
        ListNode tail = dummy;
        while (a != null && b != null) {
            if (a.val < b.val) {
                tail.next = a;
                a = a.next;
            } else {
                tail.next = b;
                b = b.next;
            }
            tail = tail.next;
        }
        
        if (a != null) {
            tail.next = a;
        } else {
            tail.next = b;
        }
        
        return dummy.next;
    }
}