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Let <code>dp[i]</code> denote the minimum cost to make <code>s</code> equal to the prefix of <code>target</code> of length <code>i</code>.
<code>dp[i] = min(costs[k] + dp[j])</code>, where <code>j > i</code> and <code>words[k] == target[i..j]</code>.
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Variations of string construction and minimum-cost dynamic programming problems frequently appear in FAANG-style interviews. They test understanding of DP state transitions, string matching, and optimization techniques.
A dynamic programming array is the core data structure for tracking minimum costs. For faster substring matching, a hash map or Trie can be used to store available strings and quickly check valid transitions.
The optimal approach usually involves dynamic programming. You track the minimum cost required to build each prefix of the target string and update it whenever a valid substring match is found. This ensures the target is constructed with the smallest total cost.
Dynamic programming works well because the problem has overlapping subproblems and optimal substructure. The minimum cost to build the full string depends on the minimum cost of building its prefixes.