Core data structures, complexity analysis, and tradeoff-focused problem solving.
I start with constraints, propose a baseline solution, then compare alternatives by time complexity, memory usage, and implementation risk. Interviewers usually value clear reasoning and pragmatic decision making more than jumping to the fanciest algorithm.
If k is much smaller than n or data is streaming, a heap usually gives better incremental performance and memory behavior. Full sorting is simpler and sometimes acceptable when n is small or when ordered output for all elements is already needed.
I define invariants early, test edge cases manually, and walk through a small example that exercises cycles or disconnected components. This demonstrates both correctness thinking and the ability to catch subtle implementation mistakes.