Fewest Subsequences of a Source String That Concatenate to a Target String

You are given two strings, `source` and `target`. A subsequence of `source` is any string obtained by deleting zero or more characters of `source` without changing the order of the characters that remain. Return the minimum number of subsequences of `source` that, concatenated in order, form exactly `target`. If `target` cannot be formed this way, return `-1`. In the reported screen this came in two stages: first decide only whether `target` can be formed at all, then compute the minimum number of subsequences. The function below answers both, with `-1` meaning that it cannot be formed. ### Function Signature ```python def min_subsequences_to_form(source: str, target: str) -> int: ``` ### Rules - The same subsequence of `source` may be used any number of times, and each use counts separately. - Every subsequence used must be non-empty. - Characters are matched exactly. ### Constraints - `1 <= len(source) <= 1000` - `1 <= len(target) <= 1000` - `source` and `target` contain only lowercase English letters `a` to `z`. - The result is either `-1` or an integer from `1` to `len(target)` inclusive, and it is uniquely determined by the input. ### Examples **Example 1** - Input: `source = "cab"`, `target = "abcab"` - Output: `2` - Explanation: `"ab"` and `"cab"` are both subsequences of `"cab"`, and `"ab" + "cab" = "abcab"`. One subsequence is not enough, because `target` is longer than `source`. **Example 2** - Input: `source = "abc"`, `target = "abd"` - Output: `-1` - Explanation: `d` does not occur in `source`, so no concatenation of its subsequences can contain it. **Example 3** - Input: `source = "xyz"`, `target = "zyxz"` - Output: `3` - Explanation: One optimal split is `"z" + "y" + "xz"`. Two pieces are impossible: in `source`, `z` comes after `y` and `y` comes after `x`, so no subsequence contains `"zy"` or `"yx"`, and each of `z`, `y` and the following `x` must therefore start a new piece.