Decide target via subsequence plus/multiply expression
Overview
This question evaluates a candidate's ability to design and implement combinatorial search and expression-evaluation logic, covering backtracking, pruning heuristics, reverse-search reasoning, correctness conditions for arithmetic operations, and handling 32-bit integer overflow when selecting subsequences and placing '+' and '*' with strict left-to-right evaluation. It is asked in the coding & algorithms domain to assess algorithmic problem-solving and complexity analysis, testing both practical implementation skills and conceptual understanding of search space pruning, time/space trade-offs, and edge-case reasoning.
Given a sequence of positive 32-bit integers A and an integer target, determine whether there exists a subsequence of A (preserving order, using each element at most once) and a placement of '+' and '' operators between the chosen numbers such that, with equal precedence and strict left-to-right evaluation, the resulting value equals target. For example, for A = [1, 9, 8, 7, 10, 3, 1] and target = 25, one valid expression is 83+1. Implement a function that returns true/false and, if true, also returns one valid expression. Discuss: (
- a backtracking search that enforces left-to-right evaluation without normal operator precedence; (
- pruning heuristics (e.g., stop when partial value already exceeds reasonable bounds, avoid repeating equivalent states, and early termination rules); (
- a reverse search from the target using subtraction and division where subtraction continues only if the remainder stays >= 0 and division only when the current target is exactly divisible by the chosen number—explain correctness conditions and ordering; (
- time and space complexity, and worst-case behavior; (
- dealing with 32-bit overflow for intermediate results and other edge cases.