Approach

To effectively answer the question "How do you partition a linked list around a value x, ensuring that all nodes with values less than x come before nodes with values greater than or equal to x?", follow this structured framework:

1. Understand the Problem: Clearly define what is meant by partitioning a linked list.

2. Identify Input and Output: Specify the input (the linked list and the value x) and the desired output (the rearranged linked list).

3. Outline the Algorithm: Develop a step-by-step approach to solve the problem.

4. Consider Edge Cases: Think through possible scenarios, including empty lists or all nodes being less than or greater than x.

5. Provide Time and Space Complexity: Assess the efficiency of your solution.

Key Points

• Clarity: Demonstrate a clear understanding of linked lists and the partitioning process.

• Logical Flow: Make sure your thought process is logical and easy to follow.

• Efficiency: Highlight the importance of a solution that operates in O(n) time complexity with O(1) space complexity when possible.

• Technical Terms: Use appropriate terminology (e.g., pointers, nodes, linked lists) to convey professionalism and expertise.

Standard Response

Here’s a structured response to the interview question:

To partition a linked list around a value x, ensuring that all nodes with values less than x come before nodes with values greater than or equal to x, I would follow these steps:

• Initialize Two New Lists: Create two separate linked lists:

• less_head: To store nodes with values less than x.

• greater_head: To store nodes with values greater than or equal to x.

• Iterate Through the Original List: Traverse the original linked list and for each node:

• If the node's value is less than x, append it to the less_head list.

• If the node's value is greater than or equal to x, append it to the greater_head list.

• Combine the Two Lists: After the traversal, connect the end of the lesshead list to the head of the greaterhead list.

• Handle Edge Cases: Ensure that if either list is empty, the other list is returned directly.

• Return the New List: Finally, return the combined list starting from less_head.

Here is a sample implementation in Python:

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

def partition(head: ListNode, x: int) -> ListNode:
 less_head = ListNode(0) # Dummy node for less than x
 greater_head = ListNode(0) # Dummy node for greater than or equal to x
 less = less_head
 greater = greater_head

 current = head
 while current:
 if current.val < x:
 less.next = current
 less = less.next
 else:
 greater.next = current
 greater = greater.next
 current = current.next

 # Connect the two lists
 greater.next = None # Important to avoid cycles
 less.next = greater_head.next # Combine the two lists

 return less_head.next # Return the new head

Tips & Variations

Common Mistakes to Avoid

• Neglecting Edge Cases: Failing to handle cases where the linked list is empty or where all nodes belong to one partition.

• Incorrect Pointer Manipulation: Forgetting to set the next pointers correctly can lead to cycles or loss of data.

• Inefficient Solutions: Using extra space unnecessarily or not achieving linear time complexity.

Alternative Ways to Answer

• For a technical role, focus on the algorithm's complexity and provide a more in-depth explanation of pointer manipulation.

• In a managerial interview, emphasize teamwork and how you would approach problem-solving collaboratively.

Role-Specific Variations

• Technical Positions: Discuss potential optimizations or variations of the algorithm, such as in-place partitioning.

• Creative Roles: Illustrate how you would visualize the process or use diagrams to explain your thought process.

Follow-Up Questions

• "How would you modify your approach if the linked list was doubly linked?"

• "Can you explain how this solution scales with larger datasets?"

• "What would you do if the partition value x was not provided?"

• Interviewers may ask follow-up questions to delve deeper, such as:

This structured approach not only conveys your technical understanding but also demonstrates your ability to communicate complex ideas clearly and effectively, which is crucial in any job interview setting