ALGORITHMUS-LESENOTIZ

Graph Depth-First Search

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

TYPAlgorithmusKATEGORIEGraphsTIEFEEinsteigerTYPISCHE KOMPLEXITÄTO(V+E)

KURZE INTERVIEWANTWORT

Beginne mit diesem mentalen Modell

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

EINFACHE ERKLÄRUNG

So funktioniert es – ohne unnötigen Jargon

Mark a node visited before exploring neighbors to avoid cycles.

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

AUSFÜHRUNG

Lies den Algorithmus als Folge von Entscheidungen

Define directed/undirected and weighted/unweighted assumptions.

Choose the graph representation.

Track algorithm state and handle disconnected/cyclic cases explicitly.

Ein kleines Beispiel als Orientierung

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.

LESBARE JAVASCRIPT-IMPLEMENTIERUNGJavaScript

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;
}

So liest du diesen Code

Lerne die Syntax nicht auswendig. Folge dem Zustand, der sich in jeder Zeile ändert, und verbinde ihn mit der oben beschriebenen Invariante.

KOMPLEXITÄT

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Do not quote this complexity mechanically.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.

WANN EINSETZEN

Gut geeignet

Connectivity
Cycle/SCC building blocks
Backtracking-style graph exploration

HÄUFIGE FEHLER

Was typischerweise schiefgeht

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

SO ERKLÄRST DU ES IM INTERVIEW

Struktur einer professionellen Antwort

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

Problem→Kernidee→Invariante / Zustand→Big-O→Trade-off

SCHNELLER 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.

Was sollte ich zur Komplexität erwähnen?

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.

Was ist der häufigste Fehler?

Forgetting disconnected components.

WeiterlesenGraph 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; }