Clone Graph
A medium Graph interview guide. Task statement, worked examples, intuition, and step-by-step solutions.
- Topic
- Graph
- Sheets
- 2
- Core for
- 12 roles
The problem
You are handed one node of a connected, undirected graph, where every node stores a value and a list of its neighbours. Build a completely new graph with the same values and the same connections, and return the new node that corresponds to the one you were given.
Example 1
- Input
- Node 1 with neighbors [Node2, Node4], Node2 with neighbors [Node1, Node3], Node3 with neighbors [Node2, Node4], Node4 with neighbors [Node1, Node3]
- Output
- A new graph with the same structure where no node references the original graph's nodes.
Example 2
- Input
- Node 1 with neighbor [Node2], Node2 with neighbors [Node1, Node3], Node3 with neighbor [Node2]
- Output
- A cloned graph with 3 nodes preserving all connections.
Constraints
- Number of nodes in [0, 100]
- 1 <= Node.val <= 100
- Node.val is unique
How to think about it
Updated 2026-09-29Copying a cyclic graph fails if you try to build trees recursively without memory. The moment you clone a node, register the pair in a lookup map before cloning its neighbors. Whenever an edge points back to an already visited vertex, wire to the existing clone instead of recursing into an infinite loop.
Approaches, worst first
DFS with clone dictionary
time O(V + E) · space O(V)
Pass the current node into a recursive function that checks a hash map of original-to-clone references. If absent, instantiate the clone immediately, insert it into the map, and fill its neighbor list by recursively cloning each neighbor.
BFS with queue and clone dictionaryWrite this one
time O(V + E) · space O(V)
Seed a queue with the starting node and pre-populate the dictionary with its clone. Dequeue vertices, creating and recording new neighbor clones on first sight while always appending the cloned neighbor to the current clone's adjacency list, avoiding call stack depth.
Where people lose marks · 3
- A null graph with 0 nodes must return null immediately; dereferencing `node.val` on an empty graph causes a null pointer crash.
- Appending the clone to the lookup map AFTER recursing on its neighbors causes infinite mutual recursion across undirected edges.
- Attempting to index clones by array index when node values might not start strictly from 0 or 1.
The theory behind it
Graph — the ground this problem stands on. All Graph problems
What Graph is
A graph is a network of individual points, called vertices or nodes, connected by lines called edges. Think of a subway transit map, an electrical circuit, or a web of social friends. Unlike a tree, a graph has no designated top node and no parent-child hierarchy. Connections can run one-way or both ways, and paths can loop back on themselves to form closed cycles.
When to reach for it
Reach for graph algorithms when inputs describe relationships, networks, flights between cities, course prerequisites, or clone networks. Signals include finding the shortest route across unweighted connections, ordering tasks that depend on earlier tasks, counting isolated clusters, or checking whether a path contains an infinite loop. Whenever problems present pairs of related entities and ask for reachability, distances, or dependencies, graph representations apply.
How the pattern works
First convert edge lists into an adjacency list, mapping each node to an array of its neighbors. Choose your exploration strategy based on the goal: use a queue and breadth-first search to find the shortest path in unweighted networks, or use recursion and depth-first search to explore full paths and detect cycles. Because graphs can have loops, always track visited nodes in a set or boolean array. Add nodes to the visited set at the moment they enter the queue so they are never visited twice.
More Graph problems
Target Roles
Core requirement for 12 roles:
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