[LeetCode] 23. Merge k Sorted Lists ☆☆

Merge k sorted linked lists and return it as one sorted list. Analyze and describe its complexity.

解法1：

　　采用递归的方法，不管合并几个，归根到底还是需要两两合并。

　　首先想到的是前两个先合并，然后再跟第三个合并，然后第四个。。。。但是这种做法效率不高。

　　换个思路，采用分治法，对数量超过2的任务进行拆分，直到最后只有一个或两个链表再进行合并。代码如下：

/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
public class Solution {
    public ListNode mergeKLists(ListNode[] lists) {
        if (lists == null || lists.length == 0) {
            return null;
            
        } else if (lists.length == 1) {
            return lists[0];
            
        } else {
            ListNode res = new ListNode(0);
            ListNode last = res;
            
            int mid = lists.length / 2;
            ListNode one = mergeKLists(Arrays.copyOfRange(lists, 0, mid));
            ListNode two = mergeKLists(Arrays.copyOfRange(lists, mid, lists.length));
            
            while (one != null && two != null) {
                if (one.val < two.val) {
                    last.next = one;
                    one = one.next;
                } else {
                    last.next = two;
                    two = two.next;
                }
                last = last.next;
            }
            
            last.next = one != null ? one : two;
            return res.next;
        }
        
    }
}

或者：

/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
public class Solution {
    public ListNode mergeKLists(ListNode[] lists) {
        if (lists == null || lists.length == 0) {
            return null;
        }
        
        int n = lists.length;
        while (n > 1) {
            int k = (n + 1) / 2;
            for (int i = 0; i < n / 2; i++) {
                lists[i] = mergeTwoLists(lists[i], lists[i + k]);
            }
            n = k;
        }
        return lists[0];
    }
    
    public ListNode mergeTwoLists(ListNode list1, ListNode list2) {
        ListNode head = new ListNode(0);
        ListNode last = head;
        
        while (list1 != null && list2 != null) {
            if (list1.val < list2.val) {
                last.next = list1;
                list1 = list1.next;
            } else {
                last.next = list2;
                list2 = list2.next;
            }
            last = last.next;
        }
        
        last.next = list1 != null ? list1 : list2;
        return head.next;
    }
}

解法2:

　　采用小根堆的方法，先将k个链表的首节点加入堆中，每次会自动输出最小的节点，将该节点加入到最终结果的链表中，然后将其下一个元素（如果不为null）加入堆中，直到最终堆为空，即输出了全部元素。代码如下：

/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
public class Solution {
    private Comparator<ListNode> ListNodeComparator = new Comparator<ListNode>() {
        public int compare(ListNode left, ListNode right) {
            if (left == null) {
                return 1;  // 这样操作的原因是，确保堆顶（最小节点）不会为null
            } else if (right == null) {
                return -1;  // 这样操作的原因是，确保堆顶（最小节点）不会为null
            } // 因为下面操作中确保堆中不会有null，所以这两个判断不要亦可
            return left.val - right.val;
        }
    };
    
    public ListNode mergeKLists(ListNode[] lists) {
        if (lists == null || lists.length == 0) {
            return null;
        }
        
        Queue<ListNode> heap = new PriorityQueue<ListNode>(lists.length, ListNodeComparator);
        for (ListNode node : lists) {
            if (node != null) {
                heap.add(node);
            }
        }
        
        ListNode dummy = new ListNode(0);
        ListNode last = dummy;
        while (!heap.isEmpty()) {
            last.next = heap.poll();
            last = last.next;
            if (last.next != null) {
                heap.add(last.next);
            }
        }
        return dummy.next;
    }
}