Naming a Company

Problem Description

You are given an array of strings ideas that represents a list of names to be used in the process of naming a company. The process of naming a company involves choosing two distinct names, swapping their first letters, and checking if the resulting names are not in the original list. Your task is to return the number of distinct valid names for the company.

Key Insights

• You need to select pairs of distinct names from the list.
• After swapping the first letters of the selected names, both resulting names must not exist in the original list.
• The valid names are created by concatenating the two original names with a space in between.
• The problem requires efficient handling of string operations and checks against the original list.

Space and Time Complexity

Time Complexity: O(N^2) - for checking pairs of names and validating the new names, where N is the length of the ideas array.
Space Complexity: O(N) - for storing the original names in a set for quick lookup.

Solution

To solve this problem, we can use the following approach:

1. Create a set to store the original names for O(1) lookup times.
2. Use two nested loops to select pairs of distinct names from the ideas list.
3. For each pair, swap the first letters and generate the new names.
4. Check if both new names are not present in the original set.
5. Count the valid combinations and return the count.

Code Solutions