Clarify that this is a variation of the 'Target Sum' problem where concatenation is allowed, which adds complexity. Use recursion with memoization (DP) to explore all possibilities: at each step, either concatenate the current number with the next, or apply '+' or '-' and move to the next number. Track the current index, current sum, and previous operand to handle concatenation correctly.
Pro tip: Mention that without concatenation, the problem can be solved with subset sum DP, but concatenation makes it a stateful DFS. Also, discuss potential optimizations like pruning when the remaining maximum possible sum can't reach the target.
Confirm that concatenation is allowed and that numbers are used in the given order. Ask about constraints (e.g., list size, number ranges) to determine if exponential brute force is acceptable.
Define a function dfs(index, current_sum, previous_operand) that processes the list from index onward. At each step, decide whether to concatenate the next number to the previous operand or to apply '+' or '-'.
When concatenating, update the previous operand by multiplying by 10 and adding the new digit, and adjust the current sum accordingly. This requires tracking the last operand's value and its sign.
Use a memo table (e.g., HashMap) keyed by (index, current_sum, previous_operand) to avoid recomputing overlapping subproblems. Note that previous_operand can be large, so consider using a string key or limiting memoization.
Discuss time complexity (exponential without memo, but memoization reduces it) and space complexity. Handle edge cases like empty list, single number, and leading zeros in concatenation.
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