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I'd seen the LC 282 version before so I jumped straight into a backtracking approach and felt pretty good.
Use backtracking to explore all possible ways to partition the digit string into numbers and insert operators between them. At each step, build the current expression and evaluate it left-to-right, pruning branches that cannot reach the target. Collect all valid expressions that evaluate to the target.
Pro tip: Emphasize the importance of pruning and handling edge cases like leading zeros and multi-digit numbers. Also, mention that since operators have no precedence, the evaluation is straightforward and can be done incrementally.
Clarify that operators are evaluated left-to-right with no precedence, and that multi-digit numbers cannot have leading zeros. Identify that we need to return all valid expressions.
Recursively choose the next number (1 or more digits) from the remaining string, ensuring no leading zeros. At each step, try inserting '+', '-', or '*' (or no operator for the first number) and update the current evaluated value.
Since evaluation is left-to-right, maintain the current value and update it as you append operators and numbers. Prune branches where the current value cannot possibly reach the target (e.g., if all remaining operations are multiplication by positive numbers, etc.).
When the entire string is consumed, check if the evaluated value equals the target. If so, add the expression to the result list. Return all such expressions.
Discuss time complexity (exponential in worst case) and potential optimizations like memoization or pruning based on bounds. Mention that the number of expressions can be large, so pruning is crucial.
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