Update app.py

app.py

@@ -29,17 +29,7 @@ def solve_matching(V, E):
     return matching
 
 
-def main():
-    V = st.number_input('Number of vertices', min_value=1, value=10)
-    density = st.slider('Density', min_value=0.0, max_value=1.0, value=0.5)
-    st.button('Generate')
-
-    V, E = generate_random_graph(V, density)
-
-    if len(E) > 40:
-        st.warning('Too many edges to display')
-        return
-
+def app_matching(V, E):
     M = set(solve_matching(V, E))
 
     if len(M) == V // 2:
@@ -57,5 +47,79 @@ def main():
     st.graphviz_chart(G)
 
 
+def solve_hamilton(V, E):
+    m = gp.Model()
+    x = m.addVars(range(V), range(V), vtype=GRB.BINARY)
+
+    m.addConstrs(x.sum(u, '*') == 1 for u in range(V))
+    m.addConstrs(x.sum('*', i) == 1 for i in range(V))
+    for u in range(V):
+        for v in range(V):
+            if (u, v) not in E and (v, u) not in E:
+                for i in range(V - 1):
+                    m.addConstr(x[u, i] + x[v, i + 1] <= 1)
+                m.addConstr(x[u, V - 1] + x[v, 0] <= 1)
+
+    m.optimize()
+
+    if m.status != GRB.OPTIMAL:
+        return None
+    
+    cycle = []
+    for i in range(V):
+        for u in range(V):
+            if x[u, i].x > 0.5:
+                cycle.append(u)
+                break
+    return cycle
+
+
+def app_hamilton(V, E):
+    cycle = solve_hamilton(V, E)
+
+    if cycle is None:
+        st.error('Hamilton cycle not found')
+    else:
+        st.success('Hamilton cycle found')
+
+    G = graphviz.Graph()
+    if cycle is not None:
+        for u in range(V):
+            G.node(str(cycle.index(u)))
+        for u, v in E:
+            if ((cycle.index(u) + 1) % len(cycle)) == cycle.index(v):
+                G.edge(str(cycle.index(u)), str(cycle.index(v)), dir='forward')
+            elif ((cycle.index(u) - 1) % len(cycle)) == cycle.index(v):
+                G.edge(str(cycle.index(u)), str(cycle.index(v)), dir='back')
+            else:
+                G.edge(str(cycle.index(u)), str(cycle.index(v)), style='dashed', color='gray')
+    else:
+        for u in range(V):
+            G.node(str(u))
+        for u, v in E:
+            G.edge(str(u), str(v))
+
+    st.graphviz_chart(G)
+
+
+def main():
+    V = st.number_input('Number of vertices', min_value=1, value=10)
+    density = st.slider('Density', min_value=0.0, max_value=1.0, value=0.5)
+    st.button('Generate')
+
+    V, E = generate_random_graph(V, density)
+
+    if len(E) > 40:
+        st.warning('Too many edges to display')
+        return
+
+    t1, t2 = st.tabs(['Matching', 'Hamilton'])
+
+    with t1:
+        app_matching(V, E)
+
+    with t2:
+        app_hamilton(V, E)
+
 if __name__ == '__main__':
     main()