Here is a detailed Markdown blog post for the problem "Find n/k th node in Linked list":

Find n/k th node in Linked list

Summary

Given a linked list and two integers n and k, find the n/kth node from the beginning of the linked list. This problem requires understanding of linked lists, traversal, and basic arithmetic operations.

Detailed Explanation

To solve this problem, we will use a simple approach: traverse the linked list until we reach the desired node. We will keep track of the current node and increment a counter whenever we move to the next node.

Here is a step-by-step breakdown:

1. Initialize a variable count to 0 and a pointer current to the head of the linked list.
2. Traverse the linked list until count is greater than or equal to n/k.
3. Increment count by 1 for each node visited.
4. When count is greater than or equal to n/k, return the current node.

To ensure we reach the correct node, we can maintain an additional variable k_count to keep track of how many nodes have been traversed so far. We increment this counter whenever we move to the next node and reset it when we find a new multiple of k. This ensures that we don't miss any nodes.

Here's a diagram illustrating the traversal:

Head -> Node 1 -> Node 2 -> ... -> Node n/k
          ^     ^
          |     |
         k_count = 0

Time complexity: O(n) as we need to traverse the linked list once. Space complexity: O(1) as we only use a constant amount of space to store the variables.

Optimized Solutions

Java