Reverse Nodes in k-Group

Clarify the problem 

The "Reverse Nodes in k-Group" problem requires reversing the linked list in groups of size k. The input is a linked list and an integer k. The output is the modified linked list where each group of k nodes is reversed. The constraint is that we should not use any predefined functions or imports.

Analyze the problem 

To solve the problem, we need to break down the linked list into groups of size k and reverse each group individually. We'll iterate through the linked list, keeping track of the start and end of each group. Then, we'll reverse the nodes within each group using a technique called "reverse linked list in place." The problem constraints state that we should not use any predefined functions or imports, so we'll implement the solution from scratch.

Design an algorithm 

To solve the problem, we can use the following algorithm:

  1. Create a dummy node and set its next pointer to the head of the linked list. This dummy node will help handle the case when the first group needs to be reversed.
  2. Initialize pointers curr and prev to the dummy node.
  3. While curr is not None, iterate through the linked list:
    • Move the curr pointer k steps forward. If there are fewer than k nodes remaining, break the loop.
    • Initialize pointers start and end to the curr node.
    • Reverse the nodes within the group by iteratively reversing the pointers between start and end.
    • Set the prev node's next pointer to the new start of the reversed group.
    • Set prev to the end of the reversed group.
    • Set curr to prev's next node.
  4. Return the dummy node's next pointer as the modified linked list.

Explain your approach 

The approach is to use a dummy node to handle the case when the first group needs to be reversed. We'll use iterative pointer manipulation to break down the linked list into groups of size k and reverse each group individually. We'll perform the reversal using the "reverse linked list in place" technique. Finally, we'll return the modified linked list.

Write clean and readable code 

Let's implement the algorithm in Python:

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next


def reverseKGroup(head, k):
    # Create a dummy node and set its next pointer to the head
    dummy = ListNode(0)
    dummy.next = head

    # Initialize pointers
    curr = dummy
    prev = dummy

    while curr:
        # Move curr pointer k steps forward
        for _ in range(k):
            curr = curr.next
            if not curr:
                return dummy.next

        # Initialize pointers for the group
        start = prev.next
        end = curr.next

        # Reverse the nodes within the group
        prev.next = reverseLinkedList(start, k)
        start.next = end

        # Update prev and curr for the next iteration
        prev = start
        curr = start

    return dummy.next


def reverseLinkedList(head, k):
    prev = None
    curr = head

    while k > 0:
        next_node = curr.next
        curr.next = prev
        prev = curr
        curr = next_node
        k -= 1

    return prev

Test your code 

Let's test the code with an example test case and explain the chosen test case:

This test case is chosen to demonstrate the reversal of the linked list in groups of size 2.

# Test case
# Input: 1 -> 2 -> 3 -> 4 -> 5 -> None, k = 2
# Output: 2 -> 1 -> 4 -> 3 -> 5 -> None
head = ListNode(1)
head.next = ListNode(2)
head.next.next = ListNode(3)
head.next.next.next = ListNode(4)
head.next.next.next.next = ListNode(5)

reversed_list = reverseKGroup(head, 2)
while reversed_list:
    print(reversed_list.val, end=" -> ")
    reversed_list = reversed_list.next
print("None")

Optimize if necessary 

The given algorithm already uses an iterative approach to reverse the linked list in groups of size k. Further optimization might involve reducing the number of pointer manipulations or optimizing the reverseLinkedList function. However, since the problem constraints prohibit using any predefined functions or imports, there are limitations to optimization within these constraints.

Handle error cases 

The algorithm assumes that the input linked list is valid and the value of k is a positive integer. If an invalid input is provided, such as a non-linked list or a negative value of k, the behavior is undefined. You can add error handling code at the beginning of the reverseKGroup function to handle such cases and return an appropriate error message or value.

Discuss complexity analysis 

The time complexity of the algorithm is O(N), where N is the number of nodes in the linked list. This is because we traverse each node once to reverse the groups. The space complexity is O(1) since we use a constant amount of additional space to store the pointers and temporary variables.


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