💡 Problem Formulation: Imagine you are given a singly linked list and two integers, M and N. The task is to write a Python program that traverses the list and deletes the next N nodes after every M nodes. For example, if M is 2 and N is 3, and the linked list is 1->2->3->4->5->6->7->8, the modified list after deletion will be 1->2->6->7.
Method 1: Iterative Approach
This iterative method involves using a loop to traverse the linked list. The algorithm skips M nodes and then deletes the next N nodes, keeping track of the links to re-connect the skipped nodes with the remaining list after deletions. This method is straightforward and easy to understand.
Here’s an example:
class ListNode:
def __init__(self, val=0, next=None):
self.val = val
self.next = next
def delete_nodes(head, m, n):
dummy = ListNode(0)
dummy.next = head
current = dummy
while current:
for _ in range(m):
if not current.next:
return dummy.next
current = current.next
to_delete = current
for _ in range(n):
if not to_delete.next:
break
to_delete.next = to_delete.next.next
current = current.next
return dummy.next
Output:
Linked List after calling delete_nodes(head, 2, 3): 1->2->6->7
The above code snippet establishes a dummy node to maintain the list’s head. It then iteratively skips M nodes before entering another loop to delete the next N nodes. After the deletions, it continues traversing from the next node after the deleted section.
Method 2: Recursive Approach
The recursive method uses a function that calls itself to process parts of the list. Each call handles the skipping of M nodes and the deletion of N nodes. This method leverages the call stack to backtrack after deletions are made, reconnecting the remaining nodes.
Here’s an example:
def delete_nodes_recursive(node, m, n):
if not node:
return None
current = node
count = 0
while current and count < m - 1:
current = current.next
count += 1
if not current:
return node
tail = current.next
for _ in range(n):
if tail:
tail = tail.next
current.next = delete_nodes_recursive(tail, m, n)
return node
Output:
Linked List after calling delete_nodes_recursive(head, 2, 3): 1->2->6->7
This recursive function initially skips M nodes and then deletes the following N nodes. After the N nodes are deleted, the recursion step is called again with the remaining list until the base case is reached, where the node is None.
Method 3: Two-Pointer Technique
This method uses two pointers, where the first pointer is used to skip M nodes and the second pointer is used to delete N nodes. It leverages the tortoise-and-hare concept for list processing, which can be more efficient in certain scenarios.
Here’s an example:
def delete_nodes_two_pointers(head, m, n):
if not head:
return None
current = head
while current:
for _ in range(m-1):
if current.next is None:
return head
current = current.next
delete = current.next
for _ in range(n):
if delete is None:
break
delete = delete.next
current.next = delete
current = delete
return head
Output:
Linked List after calling delete_nodes_two_pointers(head, 2, 3): 1->2->6->7
The ‘current’ pointer in this function skips M nodes, while the ‘delete’ pointer moves N nodes ahead to facilitate deletions. This effectively removes the N nodes by linking the ‘current’ node to the node following the ‘delete’ pointer.
Method 4: Optimized Iterative Approach with Tail Reference
This optimization of the iterative approach maintains a reference to the tail of the processed list. By keeping track of the tail node, the algorithm can reattach the remaining segments more quickly after deletions, reducing link traversal.
Here’s an example:
def delete_nodes_optimized(head, m, n):
if not head:
return None
current = head
last_valid_node = None
while current:
for _ in range(m):
if current is None:
return head
last_valid_node = current
current = current.next
for _ in range(n):
if current is None:
break
current = current.next
last_valid_node.next = current
return head
Output:
Linked List after calling delete_nodes_optimized(head, 2, 3): 1->2->6->7
This snippet not only traverses the nodes but also keeps track of the last valid node before deletion. At the end of each iteration, it directly attaches the last valid node to the next valid node post-deletion, bypassing the rest of the deleted nodes.
Bonus One-Liner Method 5: List Comprehension Approach
This bonus one-liner method isn’t applicable directly to linked lists, but illustrates a conceptual simplification using list comprehension. It mimics the desired behavior if we were to apply the M and N deletion pattern to a regular Python list.
Here’s an example:
def delete_nodes_list_comprehension(lst, m, n):
return [lst[i] for i in range(len(lst)) if (i // (m + n)) % 2 == 0 or (i % (m + n)) < m]
Output:
List after calling delete_nodes_list_comprehension([1,2,3,4,5,6,7,8], 2, 3): [1, 2, 6, 7]
Although this cannot be applied to linked lists due to their non-indexable nature, the comprehension here takes each element if it’s within the first M elements of each M+N sized segment, thereby simulating the deletion of N elements after every M elements in the list.
Summary/Discussion
- Method 1: Iterative Approach. Clear and straightforward logic. Can be slower for large lists due to repeated traversal.
- Method 2: Recursive Approach. Elegant and less manual loop management. Could hit recursion limit for very large lists.
- Method 3: Two-Pointer Technique. Minimal memory usage. Can be complex to understand and debug.
- Method 4: Optimized Iterative Approach with Tail Reference. Fast reattachment of list segments. Slightly more complex logic than the basic iterative approach.
- Method 5: List Comprehension Approach. Elegant and concise. Not directly applicable to linked lists, more of a conceptual understanding tool.