Find linked merchants by shared fields

Problem Statement

You are given a list of Merchant objects. Two merchants are considered 'linked' if they share at least one non-null value in the same field (e.g., they share the same tax_id or email). A linkage is transitive: if Merchant A is linked to Merchant B, and B is linked to C, then A, B, and C are all part of the same entity group.

Your task is to write a function that takes a list of merchants and returns a list of sets, where each set contains the ids of all merchants belonging to the same entity group.

Class Definition

class Merchant:
    def __init__(self, id, tax_id, email, phone):
        self.id = id
        self.tax_id = tax_id # Can be None
        self.email = email   # Can be None
        self.phone = phone   # Can be None

Example

Input:

• M1: {id: 1, tax_id: 'T1', email: '[email protected]', phone: None}
• M2: {id: 2, tax_id: 'T1', email: None, phone: '123'}
• M3: {id: 3, tax_id: None, email: None, phone: '456'}

Output: [{1, 2}, {3}] Explanation: M1 and M2 share tax_id 'T1', linking them. M3 shares no fields with anyone else.

Constraints

• n (number of merchants) <= 10,000.
• Fields may be None. Ignore None values when determining links.
• An empty list returns an empty list.

Edge Cases

• All fields are None for a merchant (should appear as a singleton group).
• Chains of links (A-B, B-C, C-D).
• Multiple merchants sharing the same email but different tax_ids.