Some optimization problems have a monotonic feasibility predicate. Search the smallest or largest feasible value instead of explicit sorted elements.
Before you start
You should know arrays, loops and basic complexity notation. Start with a small input you can trace by hand. State what each variable means and which invariant is maintained, then use that invariant to explain correctness before discussing performance or writing a more compact solution.
The practical goal is to reason through this situation: Increasing machine capacity can turn an impossible schedule feasible. Read the walkthrough first, then try the interview exercise before opening its answer. The important part is explaining the decision and its consequences, rather than remembering a definition alone.
Step-by-step walkthrough
Step 1: Define feasible capacity
The predicate must mean a candidate can satisfy the original constraints.
Step 2: Prove monotonicity
A solution at capacity c must remain valid at larger capacities.
Step 3: Bound the answer
Use a justified minimum and maximum, then search the first feasible value.
Worked scenario
Increasing machine capacity can turn an impossible schedule feasible.
A schedule fits at capacity ten. If increased capacity never removes an option, it also fits at eleven. This gives a false-then-true feasibility boundary. A greedy feasibility checker still needs its own correctness proof; binary search cannot repair a predicate that misclassifies candidates.
Common mistake
A non-monotonic feasibility test invalidates binary search.
Verify the behavior
Compare the optimized search with exhaustive capacities on small instances.
Interview exercise
Prove feasibility monotonicity.
Answer and reasoning
Show that any solution under capacity c also works under larger capacity, then bound the searchable answer range.
Continue learning
Compare the scenario with the Data Structures and Algorithms interview questions and test your understanding with the Data Structures and Algorithms MCQs. For terminology and implementation details, consult the reference material.