added eulerian path and cycle check

src/classes/graph/graph.h

@@ -160,6 +160,14 @@ template <typename T> class graph {
    */
   bool connected();
 
+  /*
+   *eulerian function.
+   *Returns 0 if a graph is not eulerian.
+   *Returns 1 if a graph is semi-eulerian.
+   *Returns 2 if a graph is eulerian.
+   */
+  int eulerian();
+
   /*
    * visualize function.
    * Returns .dot file that can be previewed in vscode with graphviz.
@@ -435,6 +443,24 @@ template <typename T> bool graph<T>::connected() {
   return true;
 }
 
+template <typename T> int graph<T>::eulerian() {
+  if (this->connected() == false) {
+    return false;
+  }
+
+  int64_t odd = 0;
+  for (auto &el : adj) {
+    if (adj[el.first].size() & 1) {
+      odd++;
+    }
+  }
+
+  if (odd > 2) {
+    return false;
+  }
+  return (odd) ? 1 : 2;
+}
+
 template <typename T> void graph<T>::visualize() {
   std::string s;
   if (__type == "directed") {
@@ -643,6 +669,14 @@ template <typename T> class weighted_graph {
    */
   bool connected();
 
+  /*
+   *eulerian function.
+   *Returns 0 if a graph is not eulerian.
+   *Returns 1 if a graph is semi-eulerian.
+   *Returns 2 if a graph is eulerian.
+   */
+  int eulerian();
+
   /*
    * visualize function.
    * Returns .dot file that can be previewed in vscode with graphviz.
@@ -1009,6 +1043,25 @@ template <typename T> bool weighted_graph<T>::connected() {
   return true;
 }
 
+template <typename T> int weighted_graph<T>::eulerian() {
+  if (this->connected() == false) {
+    return false;
+  }
+
+  int odd = 0;
+  for (auto &el : adj) {
+    if (adj[el.first].size() & 1) {
+      odd++;
+    }
+  }
+
+  if (odd > 2) {
+    return 0;
+  }
+
+  return (odd) ? 1 : 2;
+}
+
 template <typename T> void weighted_graph<T>::visualize() {
   std::string s;
   if (__type == "directed") {

tests/graph/graph.cc

@@ -150,4 +150,33 @@ TEST_CASE("testing connectivity") {
   g2.add_edge(0, 1);
   g2.add_edge(5, 6);
   REQUIRE(g2.connected() == false);
+}
+
+TEST_CASE("testing eulerian check") {
+  graph<int> g("undirected");
+  g.add_edge(1, 3);
+  g.add_edge(1, 0);
+  g.add_edge(1, 2);
+  g.add_edge(2, 0);
+  g.add_edge(0, 3);
+  g.add_edge(3, 4);
+
+  REQUIRE(g.eulerian() == 0);
+
+  graph<int> g2("undirected");
+  g2.add_edge(1, 2);
+  g2.add_edge(2, 0);
+  g2.add_edge(1, 0);
+  g2.add_edge(0, 3);
+  g2.add_edge(3, 4);
+  REQUIRE(g2.eulerian() == 1);
+
+  graph<int> g3("undirected");
+  g3.add_edge(1, 0);
+  g3.add_edge(1, 2);
+  g3.add_edge(2, 0);
+  g3.add_edge(0, 3);
+  g3.add_edge(0, 4);
+  g3.add_edge(3, 4);
+  REQUIRE(g3.eulerian() == 2);
 }

tests/graph/weighted_graph.cc

@@ -152,4 +152,33 @@ TEST_CASE("testing connectivity") {
   g2.add_edge(0, 1, 100);
   g2.add_edge(5, 6, 9999);
   REQUIRE(g2.connected() == false);
+}
+
+TEST_CASE("testing eulerian check") {
+  weighted_graph<int> g("undirected");
+  g.add_edge(1, 3, 5);
+  g.add_edge(1, 0, 10);
+  g.add_edge(1, 2, 4);
+  g.add_edge(2, 0, 3);
+  g.add_edge(0, 3, 14);
+  g.add_edge(3, 4, 13);
+
+  REQUIRE(g.eulerian() == 0);
+
+  weighted_graph<int> g2("undirected");
+  g2.add_edge(1, 2, 11);
+  g2.add_edge(2, 0, 10);
+  g2.add_edge(1, 0, 8);
+  g2.add_edge(0, 3, 4);
+  g2.add_edge(3, 4, 3);
+  REQUIRE(g2.eulerian() == 1);
+
+  weighted_graph<int> g3("undirected");
+  g3.add_edge(1, 0, 10);
+  g3.add_edge(1, 2, 12);
+  g3.add_edge(2, 0, 13);
+  g3.add_edge(0, 3, 15);
+  g3.add_edge(0, 4, 13);
+  g3.add_edge(3, 4, 8);
+  REQUIRE(g3.eulerian() == 2);
 }