ALGORITHMUS-LESENOTIZ

Bellman–Ford Algorithm

Bellman–Ford computes single-source shortest paths even with negative edge weights, and can detect a reachable negative-weight cycle.

TYPAlgorithmusKATEGORIEGraphsTIEFEFortgeschrittenTYPISCHE KOMPLEXITÄTO(VE)

KURZE INTERVIEWANTWORT

Beginne mit diesem mentalen Modell

Bellman–Ford computes single-source shortest paths even with negative edge weights, and can detect a reachable negative-weight cycle.

EINFACHE ERKLÄRUNG

So funktioniert es – ohne unnötigen Jargon

Relax every edge V−1 times because a simple shortest path uses at most V−1 edges.

A further successful relaxation indicates a reachable negative cycle.

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 Bellman–Ford Algorithm, the goal is to make the invariant visible rather than to memorize code.

LESBARE JAVASCRIPT-IMPLEMENTIERUNGJavaScript

function bellmanFord(vertices, edges, start) {
  const dist = Array(vertices).fill(Infinity);
  dist[start] = 0;
  for (let i = 1; i < vertices; i++) {
    for (const [u, v, w] of edges) {
      if (dist[u] !== Infinity && dist[u] + w < dist[v]) {
        dist[v] = dist[u] + w;
      }
    }
  }
  return dist;
}

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(VE)

Do not quote this complexity mechanically.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

Use the algorithm only when its graph assumptions match the problem.

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

Compare it with Dijkstra: Bellman–Ford is slower O(VE) but supports negative weights and negative-cycle detection.

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

SCHNELLER INTERVIEW-CHECK

What problem does Bellman–Ford Algorithm solve?

Bellman–Ford computes single-source shortest paths even with negative edge weights, and can detect a reachable negative-weight cycle.

Was sollte ich zur Komplexität erwähnen?

Its typical cost here is O(VE), 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 bellmanFord(vertices, edges, start) { const dist = Array(vertices).fill(Infinity); dist[start] = 0; for (let i = 1; i < vertices; i++) { for (const [u, v, w] of edges) { if (dist[u] !== Infinity && dist[u] + w < dist[v]) { dist[v] = dist[u] + w; } } } return dist; }