index.md

138. Copy List with Random Pointer

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

Construct a deep copy of the list. The deep copy should consist of exactly n brand new nodes, where each new node has its value set to the value of its corresponding original node. Both the next and random pointer of the new nodes should point to new nodes in the copied list such that the pointers in the original list and copied list represent the same list state. None of the pointers in the new list should point to nodes in the original list.

For example, if there are two nodes X and Y in the original list, where X.random --> Y, then for the corresponding two nodes x and y in the copied list, x.random --> y.

Return the head of the copied linked list.

The linked list is represented in the input/output as a list of n nodes. Each node is represented as a pair of [val, random_index] where:

• val: an integer representing Node.val
• random_index: the index of the node (range from 0 to n-1) that the random pointer points to, or null if it does not point to any node.

Your code will only be given the head of the original linked list.

Example 1:

Input: head = [[7,null],[13,0],[11,4],[10,2],[1,0]] Output: [[7,null],[13,0],[11,4],[10,2],[1,0]]

Example 2:

Input: head = [[1,1],[2,1]] Output: [[1,1],[2,1]]

Example 3:

Input: head = [[3,null],[3,0],[3,null]] Output: [[3,null],[3,0],[3,null]]

Constraints:

• 0 <= n <= 1000
• -10^4 <= Node.val <= 10^4
• Node.random is null or is pointing to some node in the linked list.

Solution

# Definition for a Node.
class Node:
    def __init__(self, x: int, next: 'Node' = None, random: 'Node' = None):
        self.val = int(x)
        self.next = next
        self.random = random

class Solution:
    def copyRandomList(self, head: 'Optional[Node]') -> 'Optional[Node]':
        if not head:
            return None

        # Step 1: Create a copy of each node and insert it right next to the original node
        current = head
        while current:
            copy = Node(current.val, current.next)
            current.next = copy
            current = copy.next

        # Step 2: Set the random pointers for the copied nodes
        current = head
        while current:
            if current.random:
                current.next.random = current.random.next
            current = current.next.next

        # Step 3: Separate the original list and the copied list
        original = head
        copy = head.next
        copy_head = copy
        while original:
            original.next = original.next.next
            copy.next = copy.next.next if copy.next else None
            original = original.next
            copy = copy.next

        return copy_head

Thoughts

Time complexity: O(n), where n is the number of nodes in the linked list. We traverse the list three times: once to create the copies, once to set the random pointers, and once to separate the lists.

Space complexity: O(1), as we don't use any extra space proportional to the number of nodes in the list.