Naming a Company Python Solution with Tests

lcpy gen -n 2306   # by problem number
lcpy gen -s naming_a_company   # by problem name

Input: ideas = ["coffee","donuts","time","toffee"]
Output: 6
Explanation: The following selections are valid:
- ("coffee", "donuts"): The company name created is "doffee conuts".
- ("donuts", "coffee"): The company name created is "conuts doffee".
- ("donuts", "time"): The company name created is "tonuts dime".
- ("donuts", "toffee"): The company name created is "tonuts doffee".
- ("time", "donuts"): The company name created is "dime tonuts".
- ("toffee", "donuts"): The company name created is "doffee tonuts".
Therefore, there are a total of 6 distinct company names.

The following are some examples of invalid selections:
- ("coffee", "time"): The name "toffee" formed after swapping already exists in the original array.
- ("time", "toffee"): Both names are still the same after swapping and exist in the original array.
- ("coffee", "toffee"): Both names formed after swapping already exist in the original array.

Input: ideas = ["lack","back"]
Output: 0
Explanation: There are no valid selections. Therefore, 0 is returned.

class Solution:
    # Time: O(n * L + 26^2 * S) where S is the largest group size
    # Space: O(n * L)
    def distinct_names(self, ideas: list[str]) -> int:
        groups: list[set[str]] = [set() for _ in range(26)]
        for idea in ideas:
            groups[ord(idea[0]) - ord("a")].add(idea[1:])

        total = 0
        for a in range(26):
            for b in range(a + 1, 26):
                common = len(groups[a] & groups[b])
                total += 2 * (len(groups[a]) - common) * (len(groups[b]) - common)
        return total