LeetCode The Hard Way
0100 - 0199

0148 - Sort List (Medium)

https://leetcode.com/problems/sort-list/

Problem Statement

Given the head of a linked list, return the list after sorting it in ascending order.

Example 1:

Input: head = [4,2,1,3]
Output: [1,2,3,4]

Example 2:

Input: head = [-1,5,3,4,0]
Output: [-1,0,3,4,5]

Example 3:

Input: head = []
Output: []

Constraints:

  • The number of nodes in the list is in the range [0, 5 * 10^4].
  • -10^5 <= Node.val <= 10^5

Follow up: Can you sort the linked list in O(n logn) time and O(1) memory (i.e. constant space)?

Approach 1: Recursive Merge Sort

  • Find the middle node and cut the head reference till middle node
  • Keep reducing the nodes size to smaller for comparison (same as like merge sort)
  • Once we reduce nodes size to 1, merge the nodes in sorted (ascending) order.
  • Keep merging the nodes till last, to build the sorted list.

Time Complexity: O(nlog(n))O(n log(n)), where nn - # of nodes in the list

Space complexity: O(n)O(n), nn - recursive call stack

/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode() {}
 *     ListNode(int val) { this.val = val; }
 *     ListNode(int val, ListNode next) { this.val = val; this.next = next; }
 * }
 */
class Solution {
    public ListNode sortList(ListNode head) {
        if (Objects.isNull(head) || Objects.isNull(head.next)) {
            return head;
        }
        // Middle node
        ListNode mid = middleNode(head);
        // Keep traversing left to get the smallest nodes for comparison (smallest we can get is 1 node)
        ListNode left = sortList(head);
        // Starting from middle, to find the smallest nodes for comparison
        ListNode right = sortList(mid);
        // Compare the list and return the merged nodes
        return mergeTwoLists(left, right);
    }

    public ListNode middleNode(ListNode head) {
        ListNode midPrev = null;
        //
        while (head != null && head.next != null) {
            midPrev = (midPrev == null) ? head : midPrev.next;
            head = head.next.next;
        }
        ListNode mid = midPrev.next;
        // Cut the reference to the next pointer (mid), so that head remains from start to mid.
        midPrev.next = null;
        return mid;
    }

    public ListNode mergeTwoLists(ListNode list1, ListNode list2) {
        // Base case
        if (Objects.isNull(list1) && Objects.isNull(list2)) {
            return list1;
        }
        if (Objects.isNull(list1)) {
            return list2;
        }
        if (Objects.isNull(list2)) {
            return list1;
        }
        ListNode head = new ListNode();
        ListNode node = head;
        while (Objects.nonNull(list1) && Objects.nonNull(list2)) {
            if (list1.val <= list2.val) {
                node.next = list1;
                list1 = list1.next;
            } else {
                node.next = list2;
                list2 = list2.next;
            }
            node = node.next;
        }
        // If either of half is not empty then append it
        node.next = Objects.nonNull(list1) ? list1 : list2;
        return head.next;
    }
}
# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, val=0, next=None):
#         self.val = val
#         self.next = next
class Solution:
    def sortList(self, head):
        # Base case
        if not head or not head.next:
            return head

        # split the list into two halfs
        slow, fast = head, head.next
        while fast and fast.next:
            slow = slow.next
            fast = fast.next.next
        start = slow.next
        slow.next = None

        # Sort left portion
        left = self.sortList(head)
        # Sort right portion
        right = self.sortList(start)
        # Merge them and return
        return self.merge(left, right)

    def merge(self, list1, list2):
        tail = dummy = ListNode()
        # while list1 and list2 are not empty
        while list1 and list2:
            # Find smaller value
            if list1.val < list2.val:
                tail.next = list1
                list1 = list1.next
            else:
                tail.next = list2
                list2 = list2.next
            tail = tail.next
        # it's possible that one of two lists are not empty
        if list1:
            tail.next = list1
        if list2:
            tail.next = list2

        return dummy.next
/**
 * Definition for singly-linked list.
 * function ListNode(val, next) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.next = (next===undefined ? null : next)
 * }
 */
/**
 * @param {ListNode} head
 * @return {ListNode}
 */
var sortList = function (head) {
  // base case
  if (!head || !head.next) return head;
  // split the list into two halfs
  // two pointers
  let slow = head;
  let fast = head.next;
  while (fast && fast.next) {
    slow = slow.next;
    fast = fast.next.next;
  }
  let start = slow.next;
  slow.next = null;
  // sort left portion
  let left = sortList(head);
  // sort right portion
  let right = sortList(start);
  // merge them and return
  return merge(left, right);
};
// merge sort function
function merge(list1, list2) {
  let tail = (dummy = new ListNode());
  // while list1 and list2 are not empty
  while (list1 && list2) {
    // find smaller value
    if (list1.val < list2.val) {
      tail.next = list1;
      list1 = list1.next;
    } else {
      tail.next = list2;
      list2 = list2.next;
    }
    tail = tail.next;
  }
  // it's possible that one of two lists are not empty
  if (list1) tail.next = list1;
  if (list2) tail.next = list2;
  return dummy.next;
}
/**
 * Definition for singly-linked list.
 * struct ListNode {
 *     int val;
 *     ListNode *next;
 *     ListNode() : val(0), next(nullptr) {}
 *     ListNode(int x) : val(x), next(nullptr) {}
 *     ListNode(int x, ListNode *next) : val(x), next(next) {}
 * };
 */
class Solution {
public:
    ListNode* sortList(ListNode* head) {
        // base case
        if (head == NULL || head->next == NULL) return head;
        // split list into two halfs
        // slow and fast pointer
        ListNode* slow = head;
        ListNode* fast = head->next;
        while (fast && fast->next) {
            slow = slow->next;
            fast = fast->next->next;
        }
        ListNode* start = slow->next;
        slow->next = NULL;
        // sort left portion
        ListNode* left = sortList(head);
        // sort right portion
        ListNode* right = sortList(start);
        // merge left and right portion
        return merge(left, right);
    }
    // merge sort function
    ListNode* merge(ListNode* list1, ListNode* list2) {
        ListNode* dummy = new ListNode(0);
        ListNode* tail = dummy;
        // while both lists are not empty
        while (list1 && list2) {
            // find smaller value
            if (list1->val < list2->val) {
                tail->next = list1;
                list1 = list1->next;
            } else {
                tail->next = list2;
                list2 = list2->next;
            }
            tail = tail->next;
        }
        // it's possible that one of two lists are not empty
        if (list1) tail->next = list1;
        if (list2) tail->next = list2;
        return dummy->next;
    }
};

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