This one messed me up more than I expected.
Model the problem as a state-space search where each state represents the current expression value and the number of x's used, then use BFS to find the minimum number of operators to reach the target. Since division yields exact rationals and order of operations applies, represent values as fractions and carefully handle operator precedence by considering the expression as a sequence of terms combined by + and -, with each term being a product/division chain.
Pro tip: Clarify with the interviewer whether the expression must use exactly a given number of x's or if any number is allowed, as this drastically changes the problem; also discuss the trade-off between BFS for optimality and potential exponential blow-up, suggesting pruning or bidirectional search for large targets.
Ask about the allowed number of x's, the range of x and target, and whether the expression must be fully evaluated with standard precedence. Confirm that division is exact and no parentheses are allowed.
Represent the current value as a rational number (numerator/denominator) to handle exact division. Also track the number of x's used and possibly the current 'term' value to respect operator precedence.
Use BFS to explore expressions in increasing number of operators, ensuring the first time the target is reached gives the minimum. Alternatively, use dynamic programming or meet-in-the-middle if the search space is large.
When building expressions left-to-right, maintain the value of the current additive term separately. For example, when encountering *, /, update the current term; when encountering +, -, finalize the term and start a new one.
Prune states that cannot possibly reach the target (e.g., using bounds or modular arithmetic). Consider bidirectional BFS or A* with a heuristic to reduce search space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.