Add Karger's Algorithm for partitioning a graph

Issue: ZigRazor#240

Author: Saj18

include/CXXGraph/Graph/Algorithm/Krager_impl.hpp

@@ -0,0 +1,64 @@
+#include <iostream>
+#include <unordered_map>
+#include <unordered_set>
+#include <vector>
+#include <random>
+#include "Node_impl.h"
+
+namespace CXXGraph {
+
+template <typename T>
+class Graph {
+private:
+    std::unordered_map<CXXGraph::id_t, Node<T>> nodes;
+    std::unordered_map<CXXGraph::id_t, std::unordered_set<CXXGraph::id_t>> adjacency_list;
+
+public:
+    // Other graph methods...
+
+    // Function to add an edge between two nodes
+    void addEdge(const std::string& from_id, const std::string& to_id) {
+        adjacency_list[from_id].insert(to_id);
+        adjacency_list[to_id].insert(from_id);
+        // Assuming nodes are already added to the graph
+    }
+
+    // Krager's algorithm for graph partitioning
+    std::pair<std::unordered_set<CXXGraph::id_t>, std::unordered_set<CXXGraph::id_t>> kragersAlgorithm() {
+        // Initialize clusters
+        std::unordered_set<CXXGraph::id_t> cluster1;
+        std::unordered_set<CXXGraph::id_t> cluster2;
+        for (const auto& node_pair : nodes) {
+            cluster1.insert(node_pair.first);
+        }
+
+        // Perform Krager's algorithm
+        std::random_device rd;
+        std::mt19937 gen(rd());
+        while (cluster1.size() > 2) {
+            // Select a random edge
+            std::uniform_int_distribution<size_t> dist(0, adjacency_list.size() - 1);
+            size_t rand_index = dist(gen);
+            auto it = std::next(std::begin(adjacency_list), rand_index);
+            CXXGraph::id_t u = it->first;
+            auto& neighbors = it->second;
+            std::uniform_int_distribution<size_t> dist_neighbor(0, neighbors.size() - 1);
+            size_t rand_neighbor_index = dist_neighbor(gen);
+            auto neighbor_it = std::next(std::begin(neighbors), rand_neighbor_index);
+            CXXGraph::id_t v = *neighbor_it;
+
+            // Merge clusters if the vertices belong to different clusters
+            if (cluster1.count(u) && cluster1.count(v)) {
+                cluster1.erase(v);
+                cluster2.insert(v);
+            } else if (cluster2.count(u) && cluster1.count(v)) {
+                cluster1.erase(v);
+                cluster2.insert(v);
+            }
+        }
+
+        return {cluster1, cluster2};
+    }
+};
+
+} // namespace CXXGraph