kmp
\n## Intuition\n\nWhen faced with this problem, the first thought is to determine how to effectively break down the target string into substrings that match the
\n## Intuition\n\nWhen faced with this problem, the first thought is to determine how to effectively break down the target string into substrings that match the words in the provided list. A naive approach might involve trying all possible combinations of words, but this quickly becomes infeasible due to the exponential number of possibilities, especially with longer target strings.\n\nTo optimize, we can leverage the **Knuth-Morris-Pratt (KMP) algorithm** for efficient substring matching. By pre-processing each word to build a KMP table, we can rapidly identify how each word contributes to constructing the target string. This approach allows us to dynamically determine the minimum number of operations (i.e., word selections) required to build the target incrementally.\n\n---\n\n## Approach\n\nThe problem can be approached using dynamic programming combined with efficient string matching techniques. Here\'s a step-by-step breakdown of the strategy:\n\n1. **KMP Table Construction for Each Word:**\n   - For each word in `words`, build its KMP table. The KMP table helps in identifying the longest prefix of the word that matches a suffix of the current target substring. This is crucial for overlapping matches, ensuring we don\'t miss potential matches that can reduce the number of operations.\n\n2. **Building Match Tables:**\n   - Using the KMP tables, construct a match table for each word against the entire target string. This table records, for each position in the target, the length of the prefix of the word that matches the target up to that position.\n\n3. **Dynamic Programming to Determine Minimum Operations:**\n   - Initialize a dynamic programming (DP) table `tbl_min_ops`, where `tbl_min_ops[i]` represents the minimum number of operations needed to construct the target string up to the `i-th` character.\n   - Iterate through each character in the target string. For each position, consider all words and update the DP table based on the match tables. If a word matches a substring ending at the current position, update the minimum operations accordingly.\n   - If no word matches at a particular position, it\'s impossible to form the target, and the function returns `-1`.\n\n4. **Final Result:**\n   - After processing the entire target string, the last entry in the DP table will hold the minimum number of operations required to form the target. If it\'s not possible, `-1` is returned.\n\nThis method ensures that we efficiently explore all possible word matches while minimizing redundant computations, thanks to the preprocessing done by the KMP algorithm.\n\n---\n\n## Code\n\nHere\'s the Python implementation of the described approach:\n\n```python\nclass Solution:\n    def minValidStrings(self, words: List[str], target: str) -> int:\n        DEBUG_VIZ = False\n\n        def build_kmp_table(word):\n            tbl = [0] * len(word)\n            for i in range(1, len(word)):\n                tgt = word[i]\n                l = tbl[i - 1]\n                while l > 0 and word[l] != tgt:\n                    l = tbl[l - 1]\n                if word[l] == tgt:\n                    l += 1\n                tbl[i] = l\n            return tbl\n\n        def build_match_table(word, kmp_tbl):\n            tbl = []\n            l = 0\n            for ch in target:\n                if l == len(word):\n                    l = kmp_tbl[l - 1]\n                while l > 0 and word[l] != ch:\n                    l = kmp_tbl[l - 1]\n                if word[l] == ch:\n                    l += 1\n                tbl.append(l)\n            return tbl\n\n        match_tbl_list = []\n        for word in words:\n            kmp_tbl = build_kmp_table(word)\n            match_tbl = build_match_table(word, kmp_tbl)\n            match_tbl_list.append(match_tbl)\n            if DEBUG_VIZ:\n                print(f"===== {word}")\n                for i, l in enumerate(match_tbl):\n                    print(f"-- idx = {i}, prefix_len = {l}: {word} vs {target}")\n                    print(f" : {word[:l]}")\n                    matching = "." * (i - l + 1) + target[(i - l + 1) : (i + 1)]\n                    print(f" : {matching}")\n\n        tbl_min_ops = [0]\n        for i, ch in enumerate(target):\n            min_ops = None\n            for match_tbl in match_tbl_list:\n                l = match_tbl[i]\n                if l == 0:\n                    continue\n                curr = tbl_min_ops[i + 1 - l] + 1\n                if min_ops is None:\n                    min_ops = curr\n                else:\n                    min_ops = min(curr, min_ops)\n            if min_ops is None:\n                return -1\n            tbl_min_ops.append(min_ops)\n            \n        return tbl_min_ops[-1]\n```\n\n
['Python3']