Why does Dijkstra's algorithm fail with negative edges?

A strong answer

A strong candidate frames Why does Dijkstra's algorithm fail with negative edges? around the exact memory layout, compiler semantics, and hardware execution model covered in Dijkstra's algorithm. Explain the proof Dijkstra relies on, give a counterexample, and say what to use instead.

Breadth-first search finds shortest paths when every edge counts the same. Real networks have weights: driving times, latencies, costs. A path with more edges can then be shorter in total, and BFS's rings of edge counts no longer match distance.

Edsger Dijkstra's 1959 algorithm handles any graph whose weights are non-negative. It keeps a tentative distance for every vertex, initially infinite except the start, and improves those estimates by relaxing edges: if the distance to u plus the edge's weight beats the current estimate for v, the estimate for v drops. The question is in which order to relax.

In a production interview, always connect the specification rule to its concrete runtime consequence: state what lives on the stack versus the heap or static storage segment, how the compiler or operating system validates alignments, lifetimes, and error codes, and what happens under adversarial or boundary inputs (such as zero-length buffers, integer overflow, concurrent mutation, or partial I/O). Backing your explanation with a small trace of register/memory state transitions immediately separates senior systems engineers from candidates who only memorized syntax.

What the interviewer is listening for

• Mastery of core invariant: Run Dijkstra's algorithm with a min-heap and lazy deletion of stale entries.
• Mastery of core invariant: Explain why a popped vertex's distance is final when all weights are non-negative.
• Mastery of core invariant: State its cost, recover paths, and adapt it to bottleneck problems.
• Hardware and ABI awareness: Explaining how sizes, alignments, calling conventions, or kernel boundaries behave on real 64-bit targets rather than relying on implementation-defined assumptions.
• Defensive engineering: Naming the exact compiler flags (-Wall -Wextra -Werror), static analyzers, or runtime sanitizers (-fsanitize=address,undefined,thread) that verify correctness in CI.

Common mistakes

• Explaining only surface syntax without tracing the underlying memory addresses, ownership lifetime, or kernel/user-space state transitions.
• Assuming undefined behavior (such as signed overflow, uninitialized reads, strict-aliasing violations, or dangling pointers) will "just work" because it passed an unoptimized -O0 debug build.
• Ignoring return codes, partial reads/writes, alignment padding, or cleanup paths when an allocation or syscall fails midway through a function.