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Merge K Sorted Lists

ID: 104; medium; 合并k个排序链表算法

Solution 1 (Java)

/**
* 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;
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 leftHalf = mergeHelper(lists, start, mid);
ListNode rightHalf = mergeHelper(lists, mid + 1, end);
return mergeTwoLists(leftHalf, rightHalf);
}
// from Merge Two Sorted Lists
private ListNode mergeTwoLists(ListNode l1, ListNode l2) {
ListNode dummy = new ListNode(0);
ListNode cur = dummy;
while (l1 != null && l2 != null) {
if (l1.val < l2.val) {
cur.next = l1;
l1 = l1.next;
} else {
cur.next = l2;
l2 = l2.next;
}
cur = cur.next;
}
if (l1 == null) cur.next = l2;
if (l2 == null) cur.next = l1;
return dummy.next;
}
}

Notes

  • This solution uses divide and conquer.
  • Let k be the number of lists and n be the number of nodes in a list on average, then the time complexity is O(nk * log(k)). Also, the recursion uses the stack space, which is O(n).

Solution 2 (Java)

/**
* 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;
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 cur = dummy;
while (!heap.isEmpty()) {
ListNode head = heap.poll();
cur.next = head;
cur = cur.next;
if (head.next != null)
heap.add(head.next);
}
return dummy.next;
}
private Comparator<ListNode> ListNodeComparator = new Comparator<ListNode>() {
public int compare(ListNode left, ListNode right) {
return left.val - right.val;
}
};
}

Notes

  • This solution uses a minimum heap with the size of the lists. Each time, we grab a node from each list and add the smallest one to the linked list by the property of the min heap.

Solution 3 (Java)

/**
* 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> newLists = new ArrayList<ListNode>();
for (int i = 0; i + 1 < lists.size(); i+=2) {
ListNode twoMergedLists = mergeTwoLists(lists.get(i), lists.get(i+1));
newLists.add(twoMergedLists);
}
if (lists.size() % 2 == 1) {
newLists.add(lists.get(lists.size() - 1));
}
lists = newLists;
}
return lists.get(0);
}
// from Merge Two Sorted Lists
private ListNode mergeTwoLists(ListNode l1, ListNode l2) {
ListNode dummy = new ListNode(0);
ListNode cur = dummy;
while (l1 != null && l2 != null) {
if (l1.val < l2.val) {
cur.next = l1;
l1 = l1.next;
} else {
cur.next = l2;
l2 = l2.next;
}
cur = cur.next;
}
if (l1 == null) cur.next = l2;
if (l2 == null) cur.next = l1;
return dummy.next;
}
}

Notes

  • This solution is straightforward. We simply merge the lists two by two, which is similar to a playoffs elimination table.
  • Be careful if the number of lists is odd.