A linked list is given such that each node contains an additional random pointer which could point to any node in the list or null.

Return a deep copy of the list.

O(n) time, O(n) extra space

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/**
 * Definition for singly-linked list with a random pointer.
 * class RandomListNode {
 *     int label;
 *     RandomListNode next, random;
 *     RandomListNode(int x) { this.label = x; }
 * };
 */
public class Solution {
    public RandomListNode copyRandomList(RandomListNode head) {
        Map<RandomListNode, RandomListNode> oldToNew = new HashMap<>();
        RandomListNode cur = head;
        while (cur != null) {
            oldToNew.put(cur, new RandomListNode(cur.label));
            cur = cur.next;
        }
        cur = head;
        while (cur != null) {
            oldToNew.get(cur).next = oldToNew.get(cur.next);
            oldToNew.get(cur).random = oldToNew.get(cur.random);
            cur = cur.next;
        }
        return oldToNew.get(head);
    }
}

O(n) time, O(1) extra space

Except the space needed for the new list

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public class Solution {
    public RandomListNode copyRandomList(RandomListNode head) {
        RandomListNode cur = head, next, prev;
        // copy the nodes one by one, into the old new
        // old-new-old-new-old-new...
        while (cur != null) {
            next = cur.next;
            cur.next = new RandomListNode(cur.label);
            cur.next.next = next;
            cur = next;
        }
        // copy random node
        cur = head;
        while (cur != null) {
            if (cur.random != null)
                cur.next.random = cur.random.next;
            cur = cur.next.next;
        }
        // split new nodes from old ones
        RandomListNode newHead = new RandomListNode(0);
        prev = newHead;
        while (head != null) {
            prev.next = head.next;
            head.next = head.next.next;
            head = head.next;
            prev = prev.next;
        }
        return newHead.next;
    }
}

Recursive solution with a global variable

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public class Solution {
    Map<RandomListNode, RandomListNode> oldToNew = new HashMap<>();
    public RandomListNode copyRandomList(RandomListNode head) {
        if (head == null) return null;
        if (oldToNew.containsKey(head)) return oldToNew.get(head);
        RandomListNode result = new RandomListNode(head.label);
        oldToNew.put(head, result);
        result.next = copyRandomList(head.next);
        result.random = copyRandomList(head.random);
        return result;
    }
}