feat: graph utils

utils/graph.h

@@ -0,0 +1,37 @@
+#include <tuple>
+#include <vector>
+
+template <typename T>
+class Graph {
+  private:
+    // Indexes of the first edge of each vertex.
+    std::vector<std::size_t> head;
+
+    // Edges of the graph.
+    // Elements in a std::tuple are <to, weight, next>
+    std::vector<std::tuple<std::size_t, T, std::size_t>> edge;
+
+  public:
+    Graph() = default;
+
+    Graph(const int &_n)
+        : head(n, -1) {}
+
+    // Add an edge from u to v with weight w.
+    void add(const std::size_t &_u, const std::size_t &_v, const T &_w) {
+        edge.emplace_back(_v, _w, head[_u]);
+        head[_u] = edge.size() - 1;
+    }
+
+    // Add an undirected edge from u to v with weight `w`.
+    void add_undirected(const std::size_t &_u, const std::size_t &_v, const T &_w) {
+        add(_u, _v, _w);
+        add(_v, _u, _w);
+    }
+
+    // Add an undirected edge from u to v with weight `w`, specifies the weight `rw` of reverse edge.
+    void add_undirected(const std::size_t &_u, const std::size_t &_v, const T &_w, const T &_rw) {
+        add(_u, _v, _w);
+        add(_v, _u, _rw);
+    }
+};