I stared at this for a bit before the constraint clicked: if 'a' and 'b' are on the same card, you can't use both.
Model the problem as a bipartite matching or flow problem where cards are matched to characters in the target string. Use backtracking with pruning or maximum bipartite matching to determine if a valid assignment exists. Discuss time/space complexity and potential optimizations.
Pro tip: Clarify constraints upfront (e.g., target length vs. number of cards, duplicate letters) to choose the right algorithm. Mention that if each card can be used at most once and each character needs a distinct card, it's a matching problem, not just a frequency count.
Ask about constraints: Can cards be reused? Are there duplicate letters? What are the input sizes? Confirm that each card can contribute at most one letter and each card can be used only once.
Represent each card as a node with two possible letters, and each character in the target string as a demand. This is a bipartite matching problem between cards and target positions.
For small inputs, use backtracking with pruning (e.g., sort cards by flexibility). For larger inputs, use maximum bipartite matching (Hopcroft-Karp) or max flow.
State the time and space complexity of your approach. For matching, it's O(E√V) where V is cards + target length, E is edges (at most 2 per card).
Walk through edge cases (e.g., target longer than cards, duplicate letters). Discuss optimizations like early termination or greedy heuristics if applicable.
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