A strong answer
A strong candidate frames Detect a currency arbitrage opportunity around the exact memory layout, compiler semantics, and hardware execution model covered in Negative edges and Bellman-Ford. Model exchange rates as a graph, turn profitable loops into negative cycles with logarithms, and find them with Bellman-Ford.
Negative weights sound unnatural for distances, but they appear whenever an edge can give something back: a step in a process that releases energy, a trade that earns a rebate, a task that reduces later costs. They also appear by transformation. Converting money along a chain of exchange rates multiplies the rates; taking the negative logarithm of each rate turns the product into a sum, and a loop that ends with more money than it started with becomes a cycle whose weights add up to less than zero.
Dijkstra's algorithm breaks on such graphs. Its proof relied on the fact that a detour through a farther vertex can never come back cheaper, and a negative edge can do exactly that. The last step of the trace above shows how: Dijkstra would settle vertex 1 at distance 2 before discovering that going through vertex 2 and its −4 edge costs only 1.
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: Explain why negative weights break Dijkstra's algorithm.
- Mastery of core invariant: Run Bellman-Ford and explain why V − 1 rounds of relaxation suffice.
- Mastery of core invariant: Detect negative cycles, and use the round structure for shortest paths with at most k edges.
- 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
-O0debug build. - Ignoring return codes, partial reads/writes, alignment padding, or cleanup paths when an allocation or syscall fails midway through a function.