Implement transaction network queries

## Problem You are building a small in-memory library to track **pairwise customer transactions** and answer connectivity questions about who has transacted with whom. Model each transaction as an interaction between **exactly two** customers (e.g., `"Jim pays Pam"`). Once two customers transact, they are considered directly connected. Treat the relationship as **undirected** (if A transacts with B, then B has transacted with A). Design a class (e.g., `Transactions`) that supports the following capabilities. --- ## Part 1 — Direct/indirect existence query ("ever transacted together") Implement an operation to record a transaction between two customers, and a query: - `haveEverTransactedTogether(x, y) -> bool` Return `true` if and only if customers `x` and `y` have **ever** been part of the **same connected component** in the transaction graph **at the time of the query** (i.e., based on all transactions recorded so far). ### Example 1. `haveEverTransactedTogether(Jim, Pam) -> false` 2. Record: `Jim` transacts with `Pam` 3. `haveEverTransactedTogether(Jim, Pam) -> true` 4. Record: `Pam` transacts with `Michael` 5. `haveEverTransactedTogether(Michael, Jim) -> true` (because Michael—Pam—Jim forms a connected component) --- ## Part 2 — Full network query Implement: - `findNetwork(person) -> list/set` A person’s **network** is everyone who is reachable from that person via one or more transactions (i.e., all nodes in the same connected component), **excluding the person themself**. ### Example 1 (two disconnected components) Transactions: `(a,b), (b,c), (a,d), (d,e), (g,f)` - `findNetwork(a) -> {b,c,d,e}` - `findNetwork(g) -> {f}` ### Example 2 (loop) Transactions: `(a,b), (b,d), (d,c), (c,a)` - `findNetwork(a) -> {b,c,d}` --- ## Part 3 — Network query with degree limit Extend the previous method to accept a second parameter `n`: - `findNetwork(person, n) -> list/set` Return all customers within **at most `n` degrees of separation** from `person`, excluding `person`. - Degree 1: direct transaction partners - Degree 2: partners of partners, etc. ### Example 1 Transactions: `(a,b), (b,c), (a,d), (d,e), (g,f)` - `findNetwork(a, 1) -> {b,d}` - `findNetwork(g, 1) -> {f}` ### Example 2 (loop) Transactions: `(a,b), (b,d), (d,c), (c,a)` - `findNetwork(a, 1) -> {b,c}` ### Example 3 Transactions: `(a,b), (b,c), (c,d), (b,e), (c,f), (d,g), (f,g), (g,h)` - `findNetwork(d, 2) -> {c,g,b,f,h}` - `findNetwork(h, 3) -> {g,d,f,c}` - `findNetwork(a, 1) -> {b}` --- ## Notes / expectations - You may assume customer identifiers are strings. - The class should support adding transactions over time and answering queries at any point. - Clearly define any helper methods and choose appropriate data structures. - Be careful about cycles and repeated visits when exploring the network.