Number of Transactions per Visit

In many e-commerce or banking applications, understanding user behavior is crucial. One key metric is how many transactions a user performs within a single "visit" to the platform. This challenge asks you to calculate this metric, helping to analyze user engagement and potential friction points.

Problem Description

You are given a list of transactions, each associated with a user ID and a timestamp. A "visit" for a user is defined as a contiguous sequence of transactions where the time difference between consecutive transactions is less than or equal to a specified session_timeout duration. Your task is to count the number of transactions that occur within each distinct visit for every user.

Key Requirements:

• For each user, identify all their distinct visits.
• For each identified visit, count the total number of transactions within that visit.
• Handle cases where a user has no transactions.
• Handle cases where transactions for a user are not ordered by timestamp.

Expected Behavior:

The output should be a data structure that maps each user ID to a list of counts. Each count in the list represents the number of transactions in a single visit for that user.

Edge Cases to Consider:

• A user with only one transaction.
• Transactions for a single user occurring very close together (within session_timeout).
• Transactions for a single user occurring far apart (exceeding session_timeout).
• An empty input list of transactions.

Examples

Example 1:

Input:
transactions = [
    {"user_id": "user1", "timestamp": 1678886400}, # Visit 1 starts
    {"user_id": "user2", "timestamp": 1678886410}, # Visit 1 starts
    {"user_id": "user1", "timestamp": 1678886420}, # Still Visit 1 for user1
    {"user_id": "user1", "timestamp": 1678886500}, # Visit 1 ends (difference > 60s)
    {"user_id": "user1", "timestamp": 1678886530}, # Visit 2 starts
    {"user_id": "user2", "timestamp": 1678886550}, # Visit 1 ends (difference > 60s)
    {"user_id": "user2", "timestamp": 1678886580}, # Visit 2 starts
    {"user_id": "user1", "timestamp": 1678886600}, # Still Visit 2 for user1
    {"user_id": "user2", "timestamp": 1678886700}  # Visit 2 ends (difference > 60s)
]
session_timeout = 60 # seconds

Output:
{
    "user1": [2, 2],
    "user2": [1, 1]
}

Explanation:
- user1:
    - Transaction 1 (1678886400) and Transaction 3 (1678886420) are within 60s. Transaction 4 (1678886500) is > 60s from Transaction 3. So, Visit 1 has 2 transactions.
    - Transaction 5 (1678886530) and Transaction 8 (1678886600) are within 60s. So, Visit 2 has 2 transactions.
- user2:
    - Transaction 2 (1678886410) is within 60s of nothing before it. Transaction 6 (1678886550) is > 60s from Transaction 2. So, Visit 1 has 1 transaction.
    - Transaction 7 (1678886580) is within 60s of nothing before it. Transaction 9 (1678886700) is > 60s from Transaction 7. So, Visit 2 has 1 transaction.

Example 2:

Input:
transactions = [
    {"user_id": "userA", "timestamp": 100},
    {"user_id": "userA", "timestamp": 110},
    {"user_id": "userA", "timestamp": 120},
    {"user_id": "userB", "timestamp": 150},
    {"user_id": "userA", "timestamp": 200},
    {"user_id": "userB", "timestamp": 210}
]
session_timeout = 30

Output:
{
    "userA": [3, 1],
    "userB": [1, 1]
}

Explanation:
- userA: The first three transactions are within 30s of each other. The fourth transaction is more than 30s after the third. So, the visits are [3, 1].
- userB: The two transactions are more than 30s apart. So, the visits are [1, 1].

Example 3: (Edge Case: Single Transaction)

Input:
transactions = [
    {"user_id": "userX", "timestamp": 500}
]
session_timeout = 60

Output:
{
    "userX": [1]
}

Explanation:
- userX has only one transaction, which constitutes a single visit of 1 transaction.

Example 4: (Edge Case: Empty Transactions)

Input:
transactions = []
session_timeout = 60

Output:
{}

Explanation:
- With no transactions, the output is an empty dictionary.

Constraints

• The number of transactions can range from 0 to 100,000.
• user_id will be a string.
• timestamp will be an integer representing Unix time (seconds since epoch).
• session_timeout will be a positive integer.
• The solution should be efficient, aiming for a time complexity of O(N log N) or O(N) where N is the number of transactions.

Notes

• You will need to group transactions by user_id first.
• Within each user's transactions, ensure they are sorted by timestamp before processing visits.
• Consider how to handle the very first transaction for any user when determining if it starts a new visit.
• The session_timeout defines the maximum gap between consecutive transactions to be considered part of the same visit.