LC 138 - Copy List with Random Pointer

Question

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
• -104 <= Node.val <= 104
• Node.random is null or is pointing to some node in the linked list.

Links

Question here and solution here

Solution

concept

The main problem here is when we traverse the linked list and make copies along the way, it is possible that this node might point to a random node that has been created. The key concept is to make 2 passes:

1. first pass is to create all the nodes first, and store them in a hashmap with key = old node and value is the new node
2. we will then make all the connection in the second pass

code

"""
# 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:
	"""
	hashmap + 2 pass
	"""
    def copyRandomList(self, head: 'Optional[Node]') -> 'Optional[Node]':
        old_to_copy = {None : None} # old node: new copy, if cur.next = None, we need it to return None
        cur = head
        # create all nodes and store them in hashmap
        while cur:
            old_to_copy[cur] = Node(cur.val)
            cur = cur.next

        # link all the nodes
        cur = head
        while cur:
            copy = old_to_copy[cur]
            copy.next = old_to_copy[cur.next]
            copy.random = old_to_copy[cur.random]
            cur = cur.next
        
        return old_to_copy[head]

Complexity

time: $O(n)$
space: $O(n)$