LeetCode 138: Copy List with Random Pointer — Python Solution

Solve LeetCode 138: Copy List with Random Pointer in Python with a node-to-copy map approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Create one copy per original node, then wire next and random pointers by looking up their copied targets.

Algorithm

1. Create one copy per original node, then wire next and random pointers by looking up their copied targets.
2. Maintain this invariant: The map contains the unique clone for every original node before any cloned edge is assigned.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

LeetCode provides the list, tree, or graph node definition used by the method.

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def copyRandomList(self, head):
        if not head:
            return None
        copies = {}
        current = head
        while current:
            copies[current] = Node(current.val)
            current = current.next
        current = head
        while current:
            copies[current].next = copies.get(current.next)
            copies[current].random = copies.get(current.random)
            current = current.next
        return copies[head]

Why this is correct

The proof follows the maintained state: The map contains the unique clone for every original node before any cloned edge is assigned. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(n) space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Random pointers may be null, self-referential, or point backward.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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