Aufgabe 2

agt_übung2.py

@@ -0,0 +1,32 @@
+from pulp import *
+
+def min_vertexcover(nodes, edges):
+    #Problemdefinition
+    prob = LpProblem("Kleinste Knotenüberdeckung", LpMinimize)
+
+    #Binäre Variablen
+    x = {v: LpVariable(f"x_{v}", cat=LpBinary) for v in nodes}
+
+    #Zielfunktion
+    prob += lpSum(x[v] for v in nodes)
+
+    #Nebenbedingung
+    for u,v in edges:
+        prob += x[u] + x[v] >=1, f"Kante_{u}_{v}"
+    
+    #Lösen mit gurobi
+    prob.solve(GUROBI())
+
+    #Ergebnis
+    status = LpStatus[prob.status]
+    vertex_cover = [v for v in nodes if value(x[v]) == 1]
+
+    return status, vertex_cover, value(prob.objective)
+
+nodes_test = ['A', 'B', 'C', 'D', 'E']
+edges_test = [('A', 'B'), ('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'D'), ('D', 'E')]
+
+status, cover, size = min_vertexcover(nodes_test, edges_test)
+print(f"Status: {status}")
+print(f"Minimale Knotenüberdeckung: {cover}")
+print(f"Größe der Überdeckung: {size}")