import gurobipy as gp
from gurobipy import GRB, Model, quicksum

HYPEREDGES = {
    1: ([], ["Xanthine"])
    2: (["Xanthine"], ["p_{0,0}"])
    3: (["Xanthine"], ["p_{0,1}"])
    4: (["Xanthine"], ["p_{0,2}"])
    5: (["p_{0,0}"], ["p_{0,3}"])
    6: (["p_{0,0}"], ["p_{0,4}"])
    7: (["p_{0,1}"], ["p_{0,3}"])
    8: (["p_{0,1}"], ["p_{0,5}"])
    9: (["p_{0,2}"], ["p_{0,4}"])
    10: (["p_{0,2}"], ["p_{0,5}"])
    11: (["p_{0,3}"], ["Caffeine"])
    12: (["p_{0,4}"], ["Caffeine"])
    13: (["p_{0,5}"], ["Caffeine"])
    14: (["Caffeine"], [])
}
#Similyrity of Nodes NMR to Measured NMR
VERTICES = {
    1: ([0, 0], ["Xanthine"])
    2: ([0, 0], ["p_{0,0}"])
    3: ([0, 0], ["p_{0,1}"])
    4: ([1, 0], ["p_{0,2}"])
    5: ([0, 0], ["p_{0,3}"])
    6: ([0, 0], ["p_{0,4}"])
    7: ([0, 1], ["p_{0,5}"])
    8: ([0, 0], ["Caffeine"])
}
FIXED_FLOWS = {
    1: 1,
    14: 1,
}

def build_model(name, hyperedges, vertices,  excluded_support=None):
    model = Model(name)

    x = {e_id: model.addVar(vtype=GRB.INTEGER, lb=0, name=f"x_{e_id}") for e_id in hyperedges}
    b = {e_id: model.addVar(vtype=GRB.BINARY, name=f"b_{e_id}") for e_id in hyperedges}

    vertices = set(v for tails, heads in hyperedges.values() for v in tails + heads)

    for v in vertices:
        inflow = quicksum(x[e_id] for e_id, (_, heads) in hyperedges.items() if v in heads)
        outflow = quicksum(x[e_id] for e_id, (tails, _) in hyperedges.items() if v in tails)
        model.addConstr(inflow == outflow, name=f"flow_conservation_{v}")

    for e_id, value in FIXED_FLOWS.items():
        model.addConstr(x[e_id] == value, name=f"fixed_flow_{e_id}")

    for e_id in hyperedges:

    model.addGenConstrIndicator(b[e_id], 0, x[e_id] == 0, name=f"unused_implies_zero_{e_id}")
    model.addConstr(x[e_id] >= b[e_id], name=f"used_implies_positive_flow_{e_id}")

    if excluded_support:
        model.addConstr(quicksum(b[e_id] for e_id in excluded_support) <= len(excluded_support) - 1, name="different_hyperedges",)

    model.setObjective(quicksum(quicksum(x[v_id]) for v_id in vertices), GRB.MAXIMIZE) #Maximize Similarity of Nodes
    return model, x, b

def positive_entries(variable_dict, threshold=0.5):
    return {e_id: var.X for e_id, var in variable_dict.items() if var.X > threshold}

def print_solution(title, flow_solution, binary_solution, hyperedges):
    print(f"\n{title}:")
    for e_id in sorted(flow_solution):
        flow = flow_solution[e_id]
        tails, heads = hyperedges[e_id]
        print(f"Hyperedge {e_id}: Flow = {flow}, Tails = {tails}, Heads = {heads}")
    print("\nBinary Variables:")
    for e_id in sorted(binary_solution):
        print(f"Binary Variable b_{e_id} = {binary_solution[e_id]}")

    print(f"\nTotal flow: {sum(flow_solution.values())}")
    print(f"Number of used hyperedges: {len(binary_solution)}")

def main():
    model, x, b = build_model("HypergraphFlow", HYPEREDGES, NODES)
    model.optimize()
    if model.status != GRB.Status.OPTIMAL:
        print("No optimal solution found for the first model.")
        return
    optimal_solution = positive_entries(x)
    optimal_binary_solution = positive_entries(b)
    print_solution("Optimal Solution", optimal_solution, optimal_binary_solution, HYPEREDGES)

    excluded_support = list(optimal_binary_solution.keys())
    second_model, x2, b2 = build_model("SecondBestHypergraphFlow", HYPEREDGES, excluded_support=excluded_support,)

    second_model.optimize()
    if second_model.status == GRB.Status.OPTIMAL:
        second_solution = positive_entries(x2)
        second_binary_solution = positive_entries(b2)
        print_solution("Second Best Solution", second_solution, second_binary_solution, HYPEREDGES, VERTICES)
    else:
        print("No optimal solution found for the second best model.")

if __name__ == "__main__":
    main()