How to find nth element from the end of a singly linked list?

Question

The following function is trying to find the nth to last element of a singly linked list.

For example:

If the elements are

Answer 1

Use two pointer pTemp and NthNode. Initially, both points to head node of the list. NthNode starts moving only after pTemp made n moves. From the both moves forward until pTemp reaches end of the list. As a result NthNode points to nth node from the end of the linked list.

public ListNode NthNodeFromEnd(int n){
    ListNode pTemp = head, NthNode = null;
   for(int count=1; count<n;count++){
     if(pTemp!=null){
       pTemp = pTemp.getNext();
     }
   }
   while(pTemp!=null){
     if(NthNode==null){
         NthNode = head;
     }
     else{
        NthNode = NthNode.getNext();
     }
     pTemp = pTemp.getNext();
   }
   if(NthNode!=null){
     NthNode = NthNode.getNext();
     return NthNode;
   }
return null;
}

Refer TextBook : "Data Structure and Algorithms Made Easy in Java"

Answer 2

Depending of the memory cost tolerance (O(k) in this solution) we could allocate an array of pointers of length k, and populate it with the nodes as a circular array while traversing the linked list.

When we finish traversing the linked list, the first element of the array (just be sure to calculate the 0-index properly as it's a circular array) we'll have the answer.

If the first element of the array is null, there's no solution to our problem.

Answer 3

No you dont know the length of the linkedlist ... You will have to go through once to get length of the likedlist so your approach is little in efficient;

Answer 4

What do you think regarding this approach.

1. Count length of the linkedlist.
2. Actual Node index from head = linkedlist length - given index;
3. Write a function to travesre from head and get the node at the above index.

Answer 5

---

First of all

As mention in comment, but to be more clear, the question is from:

<Cracking the coding interview 6th> | IX Interview Questions | 2. Linked Lists | Question 2.2.

It's a great book by Gayle Laakmann McDowell, a software engineer from Google, who has interviewed a lot people.

---

Approaches

(Assuming the linked list doesn't keep track of length), there are 2 approaches in O(n) time, and O(1) space:

• Find length first, then loop to the (len-k+1) element.
  This solution is not mentioned in the book, as I remember.
• Loop, via 2 pointer, keep them (k-1) distance.
  This solution is from the book, as the same in the question.

---

Code

Following is the implementation in Java, with unit test, (without using any advanced data structure in JDK itself).

KthToEnd.java

/**
 * Find k-th element to end of singly linked list, whose size unknown,
 * <p>1-th is the last, 2-th is the one before last,
 *
 * @author eric
 * @date 1/21/19 4:41 PM
 */
public class KthToEnd {
    /**
     * Find the k-th to end element, by find length first.
     *
     * @param head
     * @param k
     * @return
     */
    public static Integer kthToEndViaLen(LinkedListNode<Integer> head, int k) {
        int len = head.getCount(); // find length,

        if (len < k) return null; // not enough element,

        return (Integer) head.getKth(len - k).value; // get target element with its position calculated,
    }

    /**
     * Find the k-th to end element, via 2 pinter that has (k-1) distance.
     *
     * @param head
     * @param k
     * @return
     */
    public static Integer kthToEndVia2Pointer(LinkedListNode<Integer> head, int k) {
        LinkedListNode<Integer> p0 = head; // begin at 0-th element,
        LinkedListNode<Integer> p1 = head.getKth(k - 1); // begin at (k-1)-th element,

        while (p1.next != null) {
            p0 = p0.next;
            p1 = p1.next;
        }

        return p0.value;
    }

    static class LinkedListNode<T> {
        private T value;
        private LinkedListNode next;

        public LinkedListNode(T value) {
            this.value = value;
        }

        /**
         * Append a new node to end.
         *
         * @param value
         * @return new node
         */
        public LinkedListNode append(T value) {
            LinkedListNode end = getEnd();
            end.next = new LinkedListNode(value);
            return end.next;
        }

        /**
         * Append a range of number, range [start, end).
         *
         * @param start included,
         * @param end   excluded,
         */
        public void appendRangeNum(Integer start, Integer end) {
            KthToEnd.LinkedListNode last = getEnd();
            for (int i = start; i < end; i++) {
                last = last.append(i);
            }
        }

        /**
         * Get end element of the linked list this node belongs to, time complexity: O(n).
         *
         * @return
         */
        public LinkedListNode getEnd() {
            LinkedListNode end = this;
            while (end != null && end.next != null) {
                end = end.next;
            }

            return end;
        }

        /**
         * Count of element, with this as head of linked list.
         *
         * @return
         */
        public int getCount() {
            LinkedListNode end = this;
            int count = 0;
            while (end != null) {
                count++;
                end = end.next;
            }

            return count;
        }

        /**
         * Get k-th element from beginning, k start from 0.
         *
         * @param k
         * @return
         */
        public LinkedListNode getKth(int k) {
            LinkedListNode<T> target = this;
            while (k-- > 0) {
                target = target.next;
            }

            return target;
        }
    }
}

KthToEndTest.java

(unit test, using TestNG, or you change to JUnit / .., as wish)

import org.testng.Assert;
import org.testng.annotations.BeforeClass;
import org.testng.annotations.Test;

/**
 * KthToEnd test.
 *
 * @author eric
 * @date 1/21/19 5:20 PM
 */
public class KthToEndTest {
    private int len = 10;
    private KthToEnd.LinkedListNode<Integer> head;

    @BeforeClass
    public void prepare() {
        // prepare linked list with value [0, len-1],
        head = new KthToEnd.LinkedListNode(0);
        head.appendRangeNum(1, len);
    }

    @Test
    public void testKthToEndViaLen() {
        // validate
        for (int i = 1; i <= len; i++) {
            Assert.assertEquals(KthToEnd.kthToEndViaLen(head, i).intValue(), len - i);
        }
    }

    @Test
    public void testKthToEndVia2Pointer() {
        // validate
        for (int i = 1; i <= len; i++) {
            Assert.assertEquals(KthToEnd.kthToEndVia2Pointer(head, i).intValue(), len - i);
        }
    }
}

Tips:

• KthToEnd.LinkedListNode
  It's a simple singly linked list node implemented from scratch, it represents a linked list start from itself.
  It doesn't additionally track head / tail / length, though it has methods to do that.

Answer 6

You can just loop through the linkedlist and get the size. Once you have the size you can find the n'th term in 2n which is O(n) still.

public T nthToLast(int n) {
    // return null if linkedlist is empty
    if (head == null) return null;

    // declare placeholder where size of linkedlist will be stored
    // we are hoping that size of linkedlist is less than MAX of INT
    int size = 0;

    // This is O(n) for sure
    Node i = head;
    while (i.next != null) {
        size += 1;
        i = i.next;
    }

    // if user chose something outside the size of the linkedlist return null
    if (size < n)
        return null;

    // This is O(n) if n == size
    i = head;
    while(size > n) {
        size--;
        i = i.next;
    }

    // Time complexity = n + n = 2n
    // therefore O(n)

    return i.value;
}