From f869a20cf7a814a6e5bf48f43d4bd94f7574239f Mon Sep 17 00:00:00 2001
From: AYUSH KUMAR GUPTA <ayushkumargupta2908@gmail.com>
Date: Wed, 22 Oct 2025 15:58:18 +0530
Subject: [PATCH]  solution for the Round Trip problem in graph algorithms

---
 4_graph_algorithms/Round-Trip.cpp | 81 +++++++++++++++++++++++++++++++
 1 file changed, 81 insertions(+)
 create mode 100644 4_graph_algorithms/Round-Trip.cpp

diff --git a/4_graph_algorithms/Round-Trip.cpp b/4_graph_algorithms/Round-Trip.cpp
new file mode 100644
index 0000000..2daffe5
--- /dev/null
+++ b/4_graph_algorithms/Round-Trip.cpp
@@ -0,0 +1,81 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int n, m;
+vector<vector<int>> adj;
+vector<bool> visited;
+vector<int> parent;
+int cycle_start, cycle_end;
+
+bool isCycle(int v, int p)
+{
+    visited[v] = true;
+    for (int child : adj[v])
+    {
+        if (child == p)
+            continue; // Skip the parent node
+        if (visited[child])
+        {
+            cycle_end = v;
+            cycle_start = child;
+            return true;
+        }
+        parent[child] = v;
+        if (isCycle(child, v))
+        {
+            return true;
+        }
+    }
+    return false;
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+    cin >> n >> m;
+    adj.resize(n);
+    for (int i = 0; i < m; i++)
+    {
+        int u, v;
+        cin >> u >> v;
+        u--;
+        v--;
+        adj[u].push_back(v);
+        adj[v].push_back(u);
+    }
+    visited.assign(n, false);
+    parent.assign(n, -1);
+    cycle_start = -1;
+    for (int v = 0; v < n; v++)
+    {
+        if (!visited[v] && isCycle(v, parent[v]))
+            break;
+    }
+
+    if (cycle_start == -1)
+    {
+        cout << "IMPOSSIBLE" << '\n';
+    }
+    else
+    {
+        vector<int> cycle;
+        cycle.push_back(cycle_start);
+        for (int v = cycle_end; v != cycle_start; v = parent[v])
+        {
+            cycle.push_back(v);
+        }
+        cycle.push_back(cycle_start);
+        cout << cycle.size() << '\n';
+        for (int v : cycle)
+        {
+            cout << v + 1 << ' ';
+        }
+    }
+    return 0;
+}
+
+//Time Complexity: O(n + m) where n is number of nodes and m is number of edges
+//Space Complexity: O(n + m) for adjacency list and O(n) for visited and parent arrays
+
+//Problem link: https://cses.fi/problemset/task/1669/
\ No newline at end of file