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Clone Graph – Solution & Complexity

Interview solutions
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Clone Graph

Solution Walkthrough

  1. Step 1: Recognize the Pattern

    The key pattern is: DFS copies each vertex and adjacency row once. Identify the state and invariant before coding.

  2. Step 2: Build the Algorithm

    Advance one state transition at a time. Mark or update state before exploring dependent work.

  3. Step 3: Check Edge Cases

    Test empty or minimal input, skewed shapes, duplicates where allowed, and impossible outcomes.

  4. Step 4: Solution and Complexity

    Time: O(V + E). Space: O(V + E).

    def clone_graph(adjacency: list[list[int]]) -> list[list[int]]:
    clone = [[] for _ in adjacency]
    seen = set()
    def visit(node):
        if node in seen: return
        seen.add(node)
        clone[node] = adjacency[node].copy()
        for neighbor in adjacency[node]:
            visit(neighbor - 1)
    if adjacency: visit(0)
    return clone
Learn the Graph Traversal pattern: recognition cues, invariant, and ordered practice →

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See also

Practice Clone Graph online (run code in the browser)Pacific Atlantic Water Flow solution (medium)Accounts Merge solution (medium)Course Schedule II solution (medium)Longest Increasing Path in a Matrix solution (hard)All coding interview problems
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