138. Copy List with Random Pointer

Problem Statement

link: https://leetcode.com/problems/copy-list-with-random-pointer/ https://leetcode.cn/problems/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:

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

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

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

Solution Approach

Use a hashmap to maintain a mapping between the original and copied nodes to facilitate the deep copy process.

Algorithm

1. Initialization: Start with a hashmap to track visited nodes. This ensures no cycles and helps in completing random pointer assignments.
2. Deep Copy: For each node in the original list, create its copy, save the mapping in the hashmap, and move to its next and random nodes recursively.
3. Assigning Next and Random: For each newly created node, set its next and random pointers by consulting the hashmap. If the corresponding node isn’t copied yet, recurse and then assign.

Implement

    class Solution:
      def __init__(self):
          self.visited = {None: None}

      def copyRandomList(self, head: 'Optional[Node]') -> 'Optional[Node]':
          if head in self.visited:
              return self.visited[head]
          res = Node(head.val)
          self.visited[head] = res
          res.next = self.copyRandomList(head.next)
          res.random = self.copyRandomList(head.random)
          return res
 

    
    

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