[NEW] Add solution for Round Trip Problem

[ayyush08]

🎯 Problem Information

• Problem Name: Round Trip
• CSES Link: https://cses.fi/problemset/task/1669/
• Category: Graph Algorithms
• Estimated Difficulty: Medium

📋 Problem Description

Byteland has n cities and m roads. The task is to find any cycle (round trip) in the undirected graph — a path that starts and ends at the same city, passing through at least two other distinct cities.
If no cycle exists, print IMPOSSIBLE.

💡 Proposed Approach

• Use DFS to detect a cycle in the undirected graph.
• Track parent nodes to reconstruct the cycle path when found.
• If a visited node (other than the parent) is encountered, we found a cycle.
• Once detected, backtrack using the parent array to print the cycle.

Time Complexity: O(n + m)
Space Complexity: O(n + m)

📝 Implementation Notes

Any special considerations or optimizations needed:

• Requires fast I/O
• Needs modular arithmetic
• Large input constraints
• Edge cases to consider

🏷️ Labels

Please add appropriate labels:

• hacktoberfest (if contributing during Hacktoberfest)
• good first issue (if suitable for beginners)
• help wanted (if you need assistance)

👤 Assignee

• I would like to work on this issue
• I'm available for guidance/review

📎 Additional Context

Tested on the sample input and several custom cases — works for both connected and disconnected graphs.

[ayyush08]

@ks-iitjmu please assign

[ks-iitjmu]

@ayyush08 Assigned