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LetsGit.IT/Categories/Algorithms
Algorithmshard

Why doesn’t Dijkstra work with negative edge weights, and what can you use instead?

Tags
#dijkstra#bellman-ford#negative-weights#graphs
Back to categoryPractice quiz

Answer

Dijkstra assumes that once a node has the smallest known distance, it will never improve later — negative edges break this assumption. Use Bellman–Ford for negative weights (and it can detect negative cycles).

Advanced answer

Deep dive

Expanding on the short answer — what usually matters in practice:

  • Context (tags): dijkstra, bellman-ford, negative-weights, graphs
  • Complexity: compare typical operations (average vs worst-case).
  • Invariants: what must always hold for correctness.
  • When the choice is wrong: production symptoms (latency, GC, cache misses).
  • Explain the "why", not just the "what" (intuition + consequences).
  • Trade-offs: what you gain/lose (time, memory, complexity, risk).
  • Edge cases: empty inputs, large inputs, invalid inputs, concurrency.

Examples

A tiny example (an explanation template):

// Example: discuss trade-offs for "why-doesn’t-dijkstra-work-with-negative-edge-wei"
function explain() {
  // Start from the core idea:
  // Dijkstra assumes that once a node has the smallest known distance, it will never improve l
}

Common pitfalls

  • Too generic: no concrete trade-offs or examples.
  • Mixing average-case and worst-case (e.g., complexity).
  • Ignoring constraints: memory, concurrency, network/disk costs.

Interview follow-ups

  • When would you choose an alternative and why?
  • What production issues show up and how do you diagnose them?
  • How would you test edge cases?

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