← Confluent Interview Insights
Took me longer than it should have to strip away the robot framing and see this as a subset-sum reachability problem.
Model the problem as a reachability question over possible running sums, using a set to track all achievable totals after each operation. Since the order is unknown, consider all permutations, but optimize by recognizing that the set of reachable sums after processing a subset of operations depends only on which operations are included, not their order. Use dynamic programming or BFS over subsets to determine if the target is reachable.
Pro tip: Clarify whether operations can be reordered arbitrarily or if some constraints exist; if arbitrary, the problem reduces to subset sum with signs, which is NP-hard in general. Mention that for small N, brute force is fine, but for large N, you need to discuss complexity and potential approximations.
Restate the problem: given N integers (positive/negative), can we order them so that at some point the running sum equals the target? Note that the running sum starts at 0 and changes by each operation.
Recognize that the order matters only in that we can choose any permutation. The set of possible running sums after k operations is the set of sums of any k-element subset of the operations, but with signs as given. This is equivalent to: does there exist a subset of operations whose sum equals the target, and can that subset be placed first in some order? Actually, any subset can be placed first, so the problem reduces to: is there a subset of the operations whose sum equals the target?
Since we can order operations arbitrarily, we can choose any subset to be the first k operations. The running sum after those k operations is the sum of that subset. Thus, the question becomes: does any subset of the given integers sum to the target? This is the classic subset sum problem.
For small N, use brute force or dynamic programming (pseudo-polynomial). For large N, note that subset sum is NP-complete, so no polynomial-time solution is known. Mention possible optimizations like meet-in-the-middle for N up to ~40, or DP if the target is small.
Handle cases like target=0 (empty subset always works), all positive/negative numbers, and large values. Clarify if N is small enough for exponential algorithms or if approximation is acceptable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.