add euler path/cycle validation

src/graph.rs

@@ -139,11 +139,45 @@ where
     /// this assumes a path only containing the start/end vertex once,
     /// so a valid 2-vertex-loop would be represented as `[v, w]` and not `[v, w, v]`.
     ///
-    /// empty paths are never considered a cycle.
+    /// empty paths are considered a hamilton cycle for graphs with no vertices.
     pub fn is_hamilton_cycle(&self, path: &[V]) -> bool {
-        !path.is_empty()
-            && self.is_hamilton_path(path)
-            && self.has_edge((path.last().unwrap(), path.first().unwrap()))
+        (path.is_empty() && self.vertex_count() == 0)
+            || (!path.is_empty()
+                && self.is_hamilton_path(path)
+                && self.has_edge((path.last().unwrap(), path.first().unwrap())))
+    }
+
+    /// check if a provided path is an euler path within the graph,
+    /// meaning it contains all of the graphs edges exactly once.
+    ///
+    /// an empty path is considered an euler path for graphs with no edges.
+    pub fn is_euler_path(&self, path: &[(V, V)]) -> bool {
+        match self.edge_count() {
+            0 => path.is_empty(),
+            n => {
+                let edges_connected = path.windows(2).all(|w| w[0].1 == w[1].0);
+
+                let path_edges = path.iter().collect::<HashSet<_>>();
+                let has_all_edges_once = path.len() == n
+                    && self.edges.iter().all(|(v, ws)| {
+                        ws.iter()
+                            .all(|w| path_edges.contains(&(v.clone(), w.clone())))
+                    });
+
+                edges_connected && has_all_edges_once
+            }
+        }
+    }
+
+    /// check if a provided path is an euler cycle within the graph,
+    /// meaning it is a cycle and contains all of the graphs edges exactly once.
+    ///
+    /// an empty path are considered an euler cycle for graphs with no edges.
+    pub fn is_euler_cycle(&self, path: &[(V, V)]) -> bool {
+        (path.is_empty() && self.edge_count() == 0)
+            || (!path.is_empty()
+                && self.is_euler_path(path)
+                && path.first().unwrap().0 == path.last().unwrap().1)
     }
 
     pub fn iter(&self) -> impl Iterator<Item = &V> {
@@ -404,6 +438,39 @@ where
             && self.has_edge((path.last().unwrap(), path.first().unwrap()))
     }
 
+    /// check if a provided path is an euler path within the graph,
+    /// meaning it contains all of the graphs edges exactly once.
+    ///
+    /// an empty path is considered an euler path for graphs with no edges.
+    pub fn is_euler_path(&self, path: &[(V, V)]) -> bool {
+        match self.edge_count() {
+            0 => path.is_empty(),
+            n => {
+                let edges_connected = path.windows(2).all(|w| w[0].1 == w[1].0);
+
+                let path_edges = path.iter().collect::<HashSet<_>>();
+                let has_all_edges_once = path.len() == n
+                    && self.edges.iter().all(|(v, ws)| {
+                        ws.iter()
+                            .all(|(_, w)| path_edges.contains(&(v.clone(), w.clone())))
+                    });
+
+                edges_connected && has_all_edges_once
+            }
+        }
+    }
+
+    /// check if a provided path is an euler cycle within the graph,
+    /// meaning it is a cycle and contains all of the graphs edges exactly once.
+    ///
+    /// an empty path are considered an euler cycle for graphs with no edges.
+    pub fn is_euler_cycle(&self, path: &[(V, V)]) -> bool {
+        (path.is_empty() && self.edge_count() == 0)
+            || (!path.is_empty()
+                && self.is_euler_path(path)
+                && path.first().unwrap().0 == path.last().unwrap().1)
+    }
+
     pub fn iter(&self) -> impl Iterator<Item = &V> {
         self.vertices.iter()
     }
@@ -427,6 +494,6 @@ macro_rules! graph {
             $( vertices.insert($e); )*
         )*
 
-        Graph { vertices, edges }
+            Graph { vertices, edges }
     }};
 }

src/main.rs

@@ -5,9 +5,9 @@ pub use graph::{Graph, WeightedGraph};
 
 fn main() {
     // test graph:
-    //      ┏━━━━━1━━━━━┓
-    //   -> 0     ┃     3
-    //      ┗━━━━━2━━━━━┛
+    //      ┏━━━1━━━┓
+    //   -> 0   ┃   3
+    //      ┗━━━2━━━┛
 
     // adjacency list
     let g = graph! {
@@ -129,9 +129,9 @@ fn main() {
     );
 
     // test graph:
-    //      ┏━━━━━1━━━━━┓
-    //   -> 0     ┃     3
-    //      ┗━━━━━2━━━━━┛
+    //      ┏━━━1━━━┓
+    //   -> 0   ┃   3
+    //      ┗━━━2━━━┛
 
     let g = graph! {
         0: 1, 2;
@@ -164,6 +164,66 @@ fn main() {
         "Cycle that does not contain all vertices is not a hamilton cycle"
     );
 
+    // test graph:
+    //      ┏━━━1━━━┓
+    //   -> 0       3
+    //      ┗━━━2━━━┛
+
+    let g = graph! {
+        0: 1;
+        1: 3;
+        2: 0;
+        3: 2;
+    };
+
+    let path = [(0, 1), (1, 3), (3, 2), (2, 0)];
+    assert!(
+        g.is_euler_path(&path),
+        "Valid euler path in graph should be recognized as such"
+    );
+
+    let path = [(0, 1), (1, 2), (2, 3), (3, 0)];
+    assert!(
+        !g.is_euler_path(&path),
+        "A path with a non-existent edge is not a euler path"
+    );
+
+    // test graph:
+    //      ┏━━━1━━━┓
+    //   -> 0   ┃   3
+    //      ┗━━━2━━━┛
+
+    let g = graph! {
+        0: 1;
+        1: 2, 3;
+        2: 0;
+        3: 2;
+    };
+
+    let path = [(0, 1), (1, 3), (3, 2), (2, 0)];
+    assert!(
+        !g.is_euler_path(&path),
+        "A path with missing edges is not an euler path"
+    );
+
+    // test graph:
+    //      ┏━>━1━>━┓
+    //   -> 0       3
+    //      ┗━<━2━━━┛
+
+    let g = graph! {
+        0: 1;
+        1: 3;
+        2: 0, 3;
+        3: 2;
+    };
+
+    let path = [(0, 1), (1, 3), (3, 2), (2, 3), (3, 2), (2, 0)];
+    assert!(
+        !g.is_euler_path(&path),
+        "A path with duplicate edges is not an euler path"
+    );
+
     // yay
     println!("All tests passed.");
 }