Two algorithms to find the nth to last element of a singly linked list

This is one of frequently asked questions on the programming interview. There are two kinds of solution: iteration-based and recursion-based.

Data structure

We first define a toy class for the single linked list.

class LinkedListNode {

  int            data;
  LinkedListNode next;
  
  LinkedListNode(int data, LinkedListNode next) {
    this.data = data;
    this.next = next;
  }
}

Iteration-based algorithm

The iteration-based solution is quite tricky but I really like it. In Cracking the Coding Interview (4ed), the solution uses two pointers p1 and p2. Her algorithm first increaments p2 by (n-1) times, and then moves both p1 and p2 until p2.next reaches the tail of the list. As the result, p1 points to the nth to last element. Because of the copyright, I won’t reproduce her code in this post. If you are interested, please see page 106 for the solution.

Recursion-based algorithm

The recursion version is straightforward too. We first recursively call a function until we reach the tail of the list. Then we start to count from 0 and increment the counter when a called function is returned. Essentially, it counts the number of popped function calls on the call stack. When the counter equals to n, we record the element, which is the nth to the last.

An easier way to count the number of times we have returned to a recursive call is using a global variable. My solution attempted to avoid it by creating a class Record which stores the returned element (null if not) and the counter.

class Record {

  LinkedListNode node;
  Integer        i;

  Record(LinkedListNode node, int i) {
    this.node = node;
    this.i = i;
  }
}

Then I used a helper function for the recursive purpose.

private static Record nthToLastRurHelper(
    LinkedListNode head, 
    int n) {
  if (head == null) {
    // tail
    return new Record(null, 0);
  }
  Record record = nthToLastRurHelper(head.next, n);
  record.i++;
  if (record.i == n) {
    record.node = head;
    return record;
  } else {
    return record;
  }
}

To find the nth to last element, call

static LinkedListNode nthToLastRur(LinkedListNode head, int n) {
  return nthToLastRurHelper(head, n).node;
}

Test cases

Attached is a snippet code for the testing. The code creates a 10-element linked list, then tests two cases. Both cases should return true.

// create a list with 10 elements
LinkedListNode head = null;
for(int i=10; i>0; i--) {
  head = new LinkedListNode(i, head);
}
    
// return true
System.out.println(nthToLastRur(head, 2).data == 9);
// return true
System.out.println(nthToLastRur(head, 12) == null);