Understanding the Problem
We are given a list of accounts where each account belongs to a person and contains a list of emails. Some people may have multiple accounts, and emails may appear in more than one account. Our goal is to merge all the accounts that belong to the same person, meaning any accounts that share at least one common email should be merged into one.
For example, if "John" has one account with ["john@gmail.com", "john@yahoo.com"]
and another with ["john@yahoo.com", "john@outlook.com"]
, these two should be merged into a single account with all three emails, since "john@yahoo.com" is common to both.
We will solve this using Disjoint Set Union (DSU), which is great for managing groups of connected elements efficiently.
Step-by-Step Solution with Example
Step 1: Visualize the Problem as a Graph
Think of each email as a node in a graph. If two emails are part of the same account, draw an edge between them. This way, all emails that are connected form a cluster that belongs to the same user.
Step 2: Initialize DSU
We create a DSU (also known as Union-Find) structure to manage which emails are connected. Each email will be a node in this structure, and we'll use union and find operations to group them.
Step 3: Build Connections Using Union Operation
Iterate through each account. For every account, pick the first email and union it with all other emails in that account. This connects all emails in that account together.
Step 4: Map Emails to User Names
As we process each email, we also maintain a mapping from email to user name so that we can retrieve the correct name when building the final result.
Step 5: Group Emails by Root
After all unions are done, go through every email and use the find operation to determine its representative (root parent). Group all emails with the same root together. These are emails that belong to the same person.
Step 6: Sort and Format the Result
For each group of emails, sort them alphabetically and prepend the user name (using our earlier mapping). This gives us the merged account in the correct format.
Example:
Input:
[
["John", "john@gmail.com", "john@yahoo.com"],
["John", "john@yahoo.com", "john@outlook.com"],
["Mary", "mary@gmail.com"]
]
Process:
- Union "john@gmail.com" with "john@yahoo.com"
- Union "john@yahoo.com" with "john@outlook.com"
- Map all emails to "John"
- Map "mary@gmail.com" to "Mary"
Result:
[
["John", "john@gmail.com", "john@outlook.com", "john@yahoo.com"],
["Mary", "mary@gmail.com"]
]
Edge Cases
- Multiple accounts with no overlapping emails: Each account will remain separate.
- One email used by multiple accounts of the same name: All such accounts should be merged using that common email as the connector.
- Emails that belong to different users but look similar: Be careful; merge only if the actual email strings match exactly.
- Empty account list: Simply return an empty result.
Finally
This problem is a great example of applying DSU to a real-world scenario involving connected data. By modeling emails as a graph and using DSU to manage the components, we can efficiently merge related accounts. Always remember to handle mapping and sorting properly when preparing the final answer.
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