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LeetCode - Remove Duplicates from Sorted List II

Problem statement

Given the head of a sorted linked list, delete all nodes that have duplicate numbers, leaving only distinct numbers from the original list. Return the linked list sorted as well.

Problem statement taken from: https://leetcode.com/problems/remove-duplicates-from-sorted-list-ii

Example 1:

Container

Input: head = [1, 2, 3, 3, 4, 4, 5]
Output: [1, 2, 5]

Example 2:

Container

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

Constraints:

- The number of nodes in the list is in the range [0, 300].
- -100 <= Node.val <= 100
- The list is guaranteed to be sorted in ascending order.

Explanation

Using Hash Map

We can use a simple hash map to solve the problem. We store the node value as the hash map key. The value of each key will be the number of times a key appears in the list.

We then iterate over this hash map and create a new list for keys that appear only once.

A C++ snippet of this logic will look as below:

ListNode* removeDuplicates(ListNode* head) {
    map<int, int> map;

    map<int, int> map;

    while(head != NULL) {
        map[head->val]++;
        head = head->next;
    }

    ListNode* prev = new ListNode(0);

    for(auto it: map) {
        if(it.second == 1) {
            ListNode* cur = new ListNode(it.first);
            prev->next = cur;
            prev = cur;
        }
    }
}

The time-complexity of the function is O(N), and the space complexity is O(N).

Using Sentinel

The Example 1 can be solved by using two pointers. Things become tricky for Example 2. We do come across these cases a lot when dealing with linked lists. To solve such kinds of issues, we use Sentinel Node. These nodes are used as pseudo head or tail to deal with edge cases like Example 2.

To solve this problem, we will use a sentinel head to ensure the situation deletes the list head never happens.

The input list is sorted, and we should compare the node value with its next node. We use a predecessor pointer that points to the last node before the sub-list of duplicates. Once the duplicate sub-list ends, we point predecessors next to the non-duplicate node.

Let's check the algorithm:

- set sentinel = ListNode(0)
  point sentinel->next = head
  set predecessor = sentinel

- loop while head != NULL
    // if the sub-list is duplicate
  - if head->next != NULL && head->val == head->next->val

    loop while head->next != NULL && head->val == head->next->val
      - move head = head->next

    // point predecessor's next to the non-duplicate node
    - set predecessor->next = head->next

  - else
    - set predecessor = predecessor->next
  - end if

  - set head = head->next
- end while

// return the new head.
- return sentinel-next

The time-complexity of this function is O(N), and the space complexity is O(1).

Let's check our solutions in C++, Golang, and Javascript.

C++ solution

class Solution {
public:
    ListNode* deleteDuplicates(ListNode* head) {
        ListNode* sentinel = new ListNode(0);
        sentinel->next = head;
        ListNode* predecessor = sentinel;

        while(head != NULL) {
            if(head->next != NULL && head->val == head->next->val) {
                while(head->next != NULL && head->val == head->next->val) {
                    head = head->next;
                }

                predecessor->next = head->next;
            } else {
                predecessor = predecessor->next;
            }

            head = head->next;
        }

        return sentinel->next;
    }
};

Golang solution

func deleteDuplicates(head *ListNode) *ListNode {
    sentinel := &ListNode{
        Val: 0,
        Next: head,
    }

    predecessor := sentinel

    for head != nil {
        if head.Next != nil && head.Val == head.Next.Val {
            for head.Next != nil && head.Val == head.Next.Val {
                head = head.Next
            }

            predecessor.Next = head.Next
        } else {
            predecessor = predecessor.Next
        }

        head = head.Next
    }

    return sentinel.Next
}

Javascript solution

var deleteDuplicates = function(head) {
    let sentinel = new ListNode(0, head);
    let predecessor = sentinel;

    while(head != null) {
        if(head.next != null && head.val == head.next.val) {
            while(head.next != null && head.val == head.next.val) {
                head = head.next;
            }

            predecessor.next = head.next;
        } else {
            predecessor = predecessor.next;
        }

        head = head.next;
    }

    return sentinel.next;
};

Let's dry-run our algorithm to see how the solution works.

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

Step 1: ListNode* sentinel = new ListNode(0)

        sentinel->next = head
        sentinel = [0, 1, 1, 1, 2, 3]

        ListNode* predecessor = sentinel
        predecessor = [1, 1, 1, 2, 3]

Step 2: loop while head != NULL
        1 != NULL
        true

        if head->next != NULL && head->val == head->next->val
           1 != NULL && 1 == 1
           true

           loop while head->next != NULL && head->val == head->next->val
                head = head->next

            head = [1, 2, 3]

            predecessor->next = head->next
            predecessor = [2, 3]

        head = head->next
        head = [2, 3]
        sentinel = [0, 2, 3]

Step 3: loop while head != NULL
        2 != NULL
        true

        if head->next != NULL && head->val == head->next->val
           2 != NULL && 2 == 3
           false

        else
           predecessor = predecessor->next
           predecessor = [3]

        head = head->next
        head = [3]
        sentinel = [0, 2, 3]

Step 4: loop while head != NULL
        3 != NULL
        true

        if head->next != NULL && head->val == head->next->val
           NULL != NULL
           false

        else
           predecessor = predecessor->next
           predecessor = NULL

        head = head->next
        head = NULL
        sentinel = [0, 2, 3]

Step 5: loop while head != NULL
        NULL != NULL
        false

Step 6: return sentinel->next
        sentinel = [0, 2, 3]
        sentinel->next = [2, 3]

We return the answer as [2, 3].
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