Merge K Sorted Lists

Merge k Sorted Lists

Heap

Description

Leetcode: Merge k Sorted Lists | LeetCode OJ Lintcode: Merge k Sorted Lists

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

Example

Example 1

Input:   [2->4->null, null, -1->null]
Output:  -1->2->4->null

Example 2

Input: [2->6->null, 5->null, 7->null]
Output: 2->5->6->7->null

Example 3

Input:
[
  1->4->5,
  1->3->4,
  2->6
]
Output: 1->1->2->3->4->4->5->6

题解思路

归并k个已排序链表，可以分解问题拆解成为，重复k次，归并2个已排序链表。不过这种方法会在LeetCode中TLE（超出时间限制）。总共需要k次merge two sorted lists的合并过程。

改进方法：

1. 使用merge sort中的二分的思维，将包含k个链表的列表逐次分成两个部分，再逐次对两个链表合并，这样就有 log(k)次合并过程，每次均使用merge two sorted lists的算法。时间复杂度O(nlog(k))，不需要额外空间，因此空间复杂度O(1)。

2. 使用Priority Queues。这样保持每次取出的节点中是当前最小的，依次加入新的链表，从而得到合并的结果。时间复杂度O(nlogk)，空间复杂度O(k) 是PriorityQueue的空间。

源代码

• Divide and Conquer

/**
 * Definition for ListNode.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int val) {
 *         this.val = val;
 *         this.next = null;
 *     }
 * }
 */
public class Solution {
    public ListNode mergeTwoLists(ListNode l1, ListNode l2) {
        ListNode dummy = new ListNode(0);
        ListNode lastNode = dummy;

        while (l1 != null && l2 != null) {
            if (l1.val < l2.val) {
                lastNode.next = l1;
                l1 = l1.next;
            } else {
                lastNode.next = l2;
                l2 = l2.next;
            }
            lastNode = lastNode.next;
        }

        if (l1 != null) {
            lastNode.next = l1;
        } else {
            lastNode.next = l2;
        }

        return dummy.next;
    }
    /**
     * @param lists: a list of ListNode
     * @return: The head of one sorted list.
     */
    public ListNode mergeKListsNaive(List<ListNode> lists) {
        if (lists == null || lists.size() == 0) {
            return null;
        }
        if (lists.size() == 1) {
            return lists.get(0);
        }

        int listSize = lists.size();

        ListNode base = lists.get(0);

        for (int i = 1; i < listSize; i++) {
            base = mergeTwoLists(base, lists.get(i));
        }
        return base;
    }
    /**
     * @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;
         }
         if (lists.size() == 1) {
             return lists.get(0);
         }
         if (lists.size() == 2) {
             return mergeTwoLists(lists.get(0), lists.get(1));
         }
         return mergeTwoLists(
            mergeKLists(lists.subList(0, lists.size()/2)),
            mergeKLists(lists.subList(lists.size()/2, lists.size()))
         );
     }
}

• Divide & Conquer Another implementation

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) {
        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;
    }
}

• Heap*

public class Solution {
    private Comparator<ListNode> ListNodeComparator = new Comparator<ListNode>() {
        public int compare(ListNode left, ListNode right) {
            if (left == null) {
                return 1;
            } else if (right == null) {
                return -1;
            }
            return left.val - right.val;
        }
    };

    public ListNode mergeKLists(ArrayList<ListNode> lists) {
        if (lists == null || lists.size() == 0) {
            return null;
        }

        Queue<ListNode> heap = new PriorityQueue<ListNode>(lists.size(), ListNodeComparator);
        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 (!heap.isEmpty()) {
            ListNode head = heap.poll();
            tail.next = head;
            tail = head;
            if (head.next != null) {
                heap.add(head.next);
            }
        }
        return dummy.next;
    }
}