ALGORITHM READING NOTE

Graph Depth-First Search

DFS explores one path as deeply as possible before backtracking. It can be implemented recursively or with an explicit stack.

TYPEAlgorithmCATEGORYGraphsDEPTHBeginnerTYPICAL COMPLEXITYO(V+E)

SHORT INTERVIEW ANSWER

Start with this mental model

DFS explores one path as deeply as possible before backtracking. It can be implemented recursively or with an explicit stack.

SIMPLE EXPLANATION

How it works, without unnecessary jargon

Mark a node visited before exploring neighbors to avoid cycles.

Across a graph represented by adjacency lists, traversal is O(V + E).

EXECUTION

Read the algorithm as a sequence of decisions

Define directed/undirected and weighted/unweighted assumptions.

Choose the graph representation.

Track algorithm state and handle disconnected/cyclic cases explicitly.

A small example to keep in mind

Read a tiny input by hand and write down the state after every important operation. For Graph Depth-First Search, the goal is to make the invariant visible rather than to memorize code.

READABLE JAVASCRIPT IMPLEMENTATIONJavaScript

function dfs(graph, start) {
  const seen = new Set();
  function visit(node) {
    if (seen.has(node)) return;
    seen.add(node);
    for (const next of graph[node] ?? []) visit(next);
  }
  visit(start);
  return seen;
}

How to read this code

Do not memorize the syntax. Follow the state that changes on each line and connect it to the invariant described above.

COMPLEXITY

O(V+E)

Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.

WHEN TO USE IT

Good fit

Connectivity
Cycle/SCC building blocks
Backtracking-style graph exploration

COMMON MISTAKES

What usually goes wrong

Forgetting disconnected components.
Mixing weighted and unweighted shortest-path algorithms.
Not protecting against revisits/cycles.

HOW TO EXPLAIN IT IN AN INTERVIEW

A professional answer shape

State the visited-set requirement and O(V + E). Compare with BFS when shortest unweighted paths are needed.

Problem→Core idea→Invariant / state→Big-O→Trade-off

QUICK INTERVIEW CHECK

What problem does Graph Depth-First Search solve?

DFS explores one path as deeply as possible before backtracking. It can be implemented recursively or with an explicit stack.

What should I mention about complexity?

Its typical cost here is O(V+E), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.

What is the most common mistake?

Forgetting disconnected components.

Continue readingGraph representationDFS/BFSPriority queues

function dfs(graph, start) { const seen = new Set(); function visit(node) { if (seen.has(node)) return; seen.add(node); for (const next of graph[node] ?? []) visit(next); } visit(start); return seen; }