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

HYPERGRAPH = {	 1, (['Butadien'], ['Butadien']),
	 4, (['Butadien', 'Butadien'], ['p_{0,0}', 'p_{0,1}']),
	 5, (['Butadien', 'Butadien'], ['Butadien', 'Butadien']),
	 7, (['Butadien', 'Butadien'], ['p_{0,2}']),
	 9, (['p_{0,0}', 'p_{0,0}'], ['p_{0,0}', 'p_{0,0}']),
	 10, (['p_{0,0}', 'p_{0,1}'], ['Butadien', 'Butadien']),
	 11, (['p_{0,0}', 'p_{0,1}'], ['p_{0,0}', 'p_{0,1}']),
	 13, (['p_{0,0}', 'p_{0,2}'], ['p_{0,3}']),
	 14, (['p_{0,0}', 'p_{0,2}'], ['p_{0,0}', 'p_{0,2}']),
	 15, (['Butadien', 'p_{0,0}'], ['Butadien', 'p_{0,0}']),
	 16, (['p_{0,1}', 'p_{0,1}'], ['p_{0,1}', 'p_{0,1}']),
	 18, (['p_{0,1}', 'p_{0,1}'], ['Butadien', 'p_{0,4}']),
	 20, (['p_{0,1}', 'p_{0,2}'], ['Butadien', 'p_{0,5}']),
	 21, (['Butadien', 'p_{0,1}'], ['Butadien', 'p_{0,1}']),
	 22, (['p_{0,1}', 'p_{0,2}'], ['p_{0,1}', 'p_{0,2}']),
	 23, (['Butadien', 'p_{0,1}'], ['p_{0,0}', 'p_{0,4}']),
	 24, (['p_{0,2}', 'p_{0,2}'], ['p_{0,2}', 'p_{0,2}']),
	 25, (['Butadien', 'p_{0,2}'], ['Butadien', 'p_{0,2}']),
	 26, (['Butadien', 'p_{0,2}'], ['p_{0,0}', 'p_{0,5}']),
	 28, (['p_{0,0}', 'p_{0,1}'], ['p_{0,6}']),
	 30, (['Butadien', 'p_{0,0}'], ['p_{0,7}']),
	 32, (['Butadien', 'p_{0,1}'], ['p_{0,8}']),
	 33, (['Butadien', 'p_{0,1}'], ['p_{0,5}']),
	 35, (['Butadien', 'p_{0,1}'], ['p_{0,9}']),
	 37, (['Butadien', 'p_{0,1}'], ['p_{0,10}']),
	 38, (['p_{0,3}'], ['p_{0,0}', 'p_{0,2}']),
	 42, (['p_{0,4}'], ['p_{0,0}', 'p_{0,11}']),
	 50, (['p_{0,3}', 'p_{0,3}'], ['p_{0,3}', 'p_{0,3}']),
	 51, (['p_{0,3}', 'p_{0,4}'], ['p_{0,3}', 'p_{0,4}']),
	 52, (['p_{0,3}', 'p_{0,5}'], ['p_{0,3}', 'p_{0,5}']),
	 53, (['p_{0,3}', 'p_{0,6}'], ['p_{0,3}', 'p_{0,6}']),
	 54, (['p_{0,3}', 'p_{0,8}'], ['p_{0,3}', 'p_{0,8}']),
	 55, (['p_{0,3}', 'p_{0,9}'], ['p_{0,3}', 'p_{0,9}']),
	 56, (['p_{0,3}', 'p_{0,10}'], ['p_{0,3}', 'p_{0,10}']),
	 57, (['p_{0,2}', 'p_{0,3}'], ['p_{0,2}', 'p_{0,3}']),
	 58, (['p_{0,0}', 'p_{0,3}'], ['p_{0,0}', 'p_{0,3}']),
	 59, (['Butadien', 'p_{0,3}'], ['Butadien', 'p_{0,3}']),
	 60, (['p_{0,1}', 'p_{0,3}'], ['p_{0,1}', 'p_{0,3}']),
	 61, (['p_{0,4}', 'p_{0,4}'], ['p_{0,4}', 'p_{0,4}']),
	 62, (['p_{0,4}', 'p_{0,5}'], ['p_{0,4}', 'p_{0,5}']),
	 64, (['p_{0,4}', 'p_{0,6}'], ['p_{0,1}', 'p_{0,13}']),
	 65, (['p_{0,2}', 'p_{0,4}'], ['p_{0,1}', 'p_{0,5}']),
	 66, (['p_{0,0}', 'p_{0,4}'], ['Butadien', 'p_{0,1}']),
	 67, (['Butadien', 'p_{0,4}'], ['p_{0,1}', 'p_{0,1}']),
	 68, (['Butadien', 'p_{0,4}'], ['Butadien', 'p_{0,4}']),
	 69, (['p_{0,1}', 'p_{0,4}'], ['p_{0,1}', 'p_{0,4}']),
	 70, (['p_{0,4}', 'p_{0,6}'], ['p_{0,4}', 'p_{0,6}']),
	 71, (['p_{0,4}', 'p_{0,8}'], ['p_{0,4}', 'p_{0,8}']),
	 72, (['p_{0,4}', 'p_{0,9}'], ['p_{0,4}', 'p_{0,9}']),
	 73, (['p_{0,4}', 'p_{0,10}'], ['p_{0,4}', 'p_{0,10}']),
	 74, (['p_{0,2}', 'p_{0,4}'], ['p_{0,2}', 'p_{0,4}']),
	 75, (['p_{0,0}', 'p_{0,4}'], ['p_{0,0}', 'p_{0,4}']),
	 76, (['p_{0,5}', 'p_{0,5}'], ['p_{0,5}', 'p_{0,5}']),
	 77, (['p_{0,5}', 'p_{0,6}'], ['p_{0,2}', 'p_{0,13}']),
	 78, (['p_{0,2}', 'p_{0,5}'], ['p_{0,2}', 'p_{0,5}']),
	 79, (['p_{0,0}', 'p_{0,5}'], ['Butadien', 'p_{0,2}']),
	 80, (['Butadien', 'p_{0,5}'], ['p_{0,1}', 'p_{0,2}']),
	 81, (['Butadien', 'p_{0,5}'], ['Butadien', 'p_{0,5}']),
	 82, (['p_{0,1}', 'p_{0,5}'], ['p_{0,1}', 'p_{0,5}']),
	 83, (['p_{0,1}', 'p_{0,5}'], ['p_{0,2}', 'p_{0,4}']),
	 84, (['p_{0,5}', 'p_{0,6}'], ['p_{0,5}', 'p_{0,6}']),
	 85, (['p_{0,5}', 'p_{0,8}'], ['p_{0,5}', 'p_{0,8}']),
	 86, (['p_{0,5}', 'p_{0,9}'], ['p_{0,5}', 'p_{0,9}']),
	 87, (['p_{0,5}', 'p_{0,10}'], ['p_{0,5}', 'p_{0,10}']),
	 88, (['p_{0,0}', 'p_{0,5}'], ['p_{0,0}', 'p_{0,5}']),
	 89, (['p_{0,6}', 'p_{0,6}'], ['p_{0,6}', 'p_{0,6}']),
	 90, (['p_{0,6}', 'p_{0,8}'], ['p_{0,6}', 'p_{0,8}']),
	 91, (['p_{0,6}', 'p_{0,9}'], ['p_{0,6}', 'p_{0,9}']),
	 92, (['p_{0,6}', 'p_{0,10}'], ['p_{0,6}', 'p_{0,10}']),
	 93, (['p_{0,2}', 'p_{0,6}'], ['p_{0,2}', 'p_{0,6}']),
	 94, (['p_{0,0}', 'p_{0,6}'], ['p_{0,0}', 'p_{0,6}']),
	 95, (['Butadien', 'p_{0,6}'], ['Butadien', 'p_{0,6}']),
	 96, (['Butadien', 'p_{0,6}'], ['p_{0,0}', 'p_{0,13}']),
	 97, (['p_{0,1}', 'p_{0,6}'], ['Butadien', 'p_{0,13}']),
	 98, (['p_{0,1}', 'p_{0,6}'], ['p_{0,1}', 'p_{0,6}']),
	 100, (['p_{0,0}', 'p_{0,6}'], ['p_{0,14}']),
	 102, (['p_{0,0}', 'p_{0,7}'], ['p_{0,15}']),
	 103, (['p_{0,8}', 'p_{0,8}'], ['p_{0,8}', 'p_{0,8}']),
	 104, (['p_{0,8}', 'p_{0,9}'], ['p_{0,8}', 'p_{0,9}']),
	 105, (['p_{0,8}', 'p_{0,10}'], ['p_{0,8}', 'p_{0,10}']),
	 106, (['p_{0,2}', 'p_{0,8}'], ['p_{0,2}', 'p_{0,8}']),
	 107, (['p_{0,0}', 'p_{0,8}'], ['p_{0,0}', 'p_{0,8}']),
	 108, (['Butadien', 'p_{0,8}'], ['Butadien', 'p_{0,8}']),
	 109, (['p_{0,1}', 'p_{0,8}'], ['p_{0,1}', 'p_{0,8}']),
	 110, (['p_{0,9}', 'p_{0,9}'], ['p_{0,9}', 'p_{0,9}']),
	 111, (['p_{0,9}', 'p_{0,10}'], ['p_{0,9}', 'p_{0,10}']),
	 112, (['p_{0,2}', 'p_{0,9}'], ['p_{0,2}', 'p_{0,9}']),
	 113, (['p_{0,0}', 'p_{0,9}'], ['p_{0,0}', 'p_{0,9}']),
	 114, (['Butadien', 'p_{0,9}'], ['Butadien', 'p_{0,9}']),
	 115, (['p_{0,1}', 'p_{0,9}'], ['p_{0,1}', 'p_{0,9}']),
	 116, (['p_{0,10}', 'p_{0,10}'], ['p_{0,10}', 'p_{0,10}']),
	 117, (['p_{0,2}', 'p_{0,10}'], ['p_{0,2}', 'p_{0,10}']),
	 118, (['p_{0,0}', 'p_{0,10}'], ['p_{0,0}', 'p_{0,10}']),
	 119, (['Butadien', 'p_{0,10}'], ['Butadien', 'p_{0,10}']),
	 120, (['p_{0,1}', 'p_{0,10}'], ['p_{0,1}', 'p_{0,10}']),
	 121, (['p_{0,0}', 'p_{0,4}'], ['p_{0,13}']),
	 123, (['p_{0,0}', 'p_{0,4}'], ['p_{0,16}']),
	 125, (['Butadien', 'p_{0,7}'], ['p_{0,17}']),
	 130, (['p_{0,14}'], ['p_{0,0}', 'p_{0,6}']),
	 132, (['p_{0,15}'], ['p_{0,0}', 'p_{0,7}']),
	 135, (['p_{0,0}', 'p_{0,11}'], ['p_{0,4}']),
	 136, (['p_{0,12}', 'p_{0,12}'], ['p_{0,12}', 'p_{0,12}']),
	 137, (['p_{0,12}', 'p_{0,13}'], ['p_{0,12}', 'p_{0,13}']),
	 138, (['p_{0,12}', 'p_{0,14}'], ['p_{0,12}', 'p_{0,14}']),
	 139, (['p_{0,12}', 'p_{0,15}'], ['p_{0,12}', 'p_{0,15}']),
	 140, (['p_{0,12}', 'p_{0,16}'], ['p_{0,12}', 'p_{0,16}']),
	 141, (['p_{0,8}', 'p_{0,12}'], ['p_{0,8}', 'p_{0,12}']),
	 142, (['p_{0,9}', 'p_{0,12}'], ['p_{0,9}', 'p_{0,12}']),
	 143, (['Butadien', 'p_{0,12}'], ['Butadien', 'p_{0,12}']),
	 144, (['p_{0,10}', 'p_{0,12}'], ['p_{0,10}', 'p_{0,12}']),
	 145, (['p_{0,0}', 'p_{0,12}'], ['p_{0,0}', 'p_{0,12}']),
	 146, (['p_{0,1}', 'p_{0,12}'], ['p_{0,1}', 'p_{0,12}']),
	 147, (['p_{0,2}', 'p_{0,12}'], ['p_{0,2}', 'p_{0,12}']),
	 148, (['p_{0,3}', 'p_{0,12}'], ['p_{0,3}', 'p_{0,12}']),
	 149, (['p_{0,4}', 'p_{0,12}'], ['p_{0,4}', 'p_{0,12}']),
	 150, (['p_{0,5}', 'p_{0,12}'], ['p_{0,5}', 'p_{0,12}']),
	 151, (['p_{0,6}', 'p_{0,12}'], ['p_{0,6}', 'p_{0,12}']),
	 152, (['p_{0,13}', 'p_{0,13}'], ['p_{0,13}', 'p_{0,13}']),
	 153, (['Butadien', 'p_{0,13}'], ['p_{0,1}', 'p_{0,6}']),
	 154, (['Butadien', 'p_{0,13}'], ['Butadien', 'p_{0,13}']),
	 155, (['p_{0,0}', 'p_{0,13}'], ['Butadien', 'p_{0,6}']),
	 156, (['p_{0,1}', 'p_{0,13}'], ['p_{0,1}', 'p_{0,13}']),
	 157, (['p_{0,1}', 'p_{0,13}'], ['p_{0,4}', 'p_{0,6}']),
	 158, (['p_{0,2}', 'p_{0,13}'], ['p_{0,5}', 'p_{0,6}']),
	 159, (['p_{0,4}', 'p_{0,13}'], ['p_{0,4}', 'p_{0,13}']),
	 160, (['p_{0,5}', 'p_{0,13}'], ['p_{0,5}', 'p_{0,13}']),
	 161, (['p_{0,6}', 'p_{0,13}'], ['p_{0,6}', 'p_{0,13}']),
	 162, (['p_{0,13}', 'p_{0,14}'], ['p_{0,13}', 'p_{0,14}']),
	 163, (['p_{0,13}', 'p_{0,15}'], ['p_{0,13}', 'p_{0,15}']),
	 164, (['p_{0,13}', 'p_{0,16}'], ['p_{0,13}', 'p_{0,16}']),
	 165, (['p_{0,8}', 'p_{0,13}'], ['p_{0,8}', 'p_{0,13}']),
	 166, (['p_{0,9}', 'p_{0,13}'], ['p_{0,9}', 'p_{0,13}']),
	 167, (['p_{0,10}', 'p_{0,13}'], ['p_{0,10}', 'p_{0,13}']),
	 168, (['p_{0,0}', 'p_{0,13}'], ['p_{0,0}', 'p_{0,13}']),
	 169, (['p_{0,2}', 'p_{0,13}'], ['p_{0,2}', 'p_{0,13}']),
	 170, (['p_{0,3}', 'p_{0,13}'], ['p_{0,3}', 'p_{0,13}']),
	 171, (['p_{0,14}', 'p_{0,14}'], ['p_{0,14}', 'p_{0,14}']),
	 172, (['p_{0,14}', 'p_{0,15}'], ['p_{0,14}', 'p_{0,15}']),
	 173, (['p_{0,14}', 'p_{0,16}'], ['p_{0,14}', 'p_{0,16}']),
	 174, (['p_{0,8}', 'p_{0,14}'], ['p_{0,8}', 'p_{0,14}']),
	 175, (['p_{0,9}', 'p_{0,14}'], ['p_{0,9}', 'p_{0,14}']),
	 176, (['Butadien', 'p_{0,14}'], ['Butadien', 'p_{0,14}']),
	 177, (['p_{0,10}', 'p_{0,14}'], ['p_{0,10}', 'p_{0,14}']),
	 178, (['p_{0,0}', 'p_{0,14}'], ['p_{0,0}', 'p_{0,14}']),
	 179, (['p_{0,1}', 'p_{0,14}'], ['p_{0,1}', 'p_{0,14}']),
	 180, (['p_{0,2}', 'p_{0,14}'], ['p_{0,2}', 'p_{0,14}']),
	 181, (['p_{0,3}', 'p_{0,14}'], ['p_{0,3}', 'p_{0,14}']),
	 182, (['p_{0,4}', 'p_{0,14}'], ['p_{0,4}', 'p_{0,14}']),
	 183, (['p_{0,5}', 'p_{0,14}'], ['p_{0,5}', 'p_{0,14}']),
	 184, (['p_{0,6}', 'p_{0,14}'], ['p_{0,6}', 'p_{0,14}']),
	 185, (['p_{0,15}', 'p_{0,15}'], ['p_{0,15}', 'p_{0,15}']),
	 186, (['p_{0,15}', 'p_{0,16}'], ['p_{0,15}', 'p_{0,16}']),
	 187, (['p_{0,8}', 'p_{0,15}'], ['p_{0,8}', 'p_{0,15}']),
	 188, (['p_{0,9}', 'p_{0,15}'], ['p_{0,9}', 'p_{0,15}']),
	 189, (['Butadien', 'p_{0,15}'], ['Butadien', 'p_{0,15}']),
	 190, (['p_{0,10}', 'p_{0,15}'], ['p_{0,10}', 'p_{0,15}']),
	 191, (['p_{0,0}', 'p_{0,15}'], ['p_{0,0}', 'p_{0,15}']),
	 192, (['p_{0,1}', 'p_{0,15}'], ['p_{0,1}', 'p_{0,15}']),
	 193, (['p_{0,2}', 'p_{0,15}'], ['p_{0,2}', 'p_{0,15}']),
	 194, (['p_{0,3}', 'p_{0,15}'], ['p_{0,3}', 'p_{0,15}']),
	 195, (['p_{0,4}', 'p_{0,15}'], ['p_{0,4}', 'p_{0,15}']),
	 196, (['p_{0,5}', 'p_{0,15}'], ['p_{0,5}', 'p_{0,15}']),
	 197, (['p_{0,6}', 'p_{0,15}'], ['p_{0,6}', 'p_{0,15}']),
	 198, (['p_{0,16}', 'p_{0,16}'], ['p_{0,16}', 'p_{0,16}']),
	 199, (['p_{0,8}', 'p_{0,16}'], ['p_{0,8}', 'p_{0,16}']),
	 200, (['p_{0,9}', 'p_{0,16}'], ['p_{0,9}', 'p_{0,16}']),
	 201, (['Butadien', 'p_{0,16}'], ['Butadien', 'p_{0,16}']),
	 202, (['p_{0,10}', 'p_{0,16}'], ['p_{0,10}', 'p_{0,16}']),
	 203, (['p_{0,0}', 'p_{0,16}'], ['p_{0,0}', 'p_{0,16}']),
	 204, (['p_{0,1}', 'p_{0,16}'], ['p_{0,1}', 'p_{0,16}']),
	 205, (['p_{0,2}', 'p_{0,16}'], ['p_{0,2}', 'p_{0,16}']),
	 206, (['p_{0,3}', 'p_{0,16}'], ['p_{0,3}', 'p_{0,16}']),
	 207, (['p_{0,4}', 'p_{0,16}'], ['p_{0,4}', 'p_{0,16}']),
	 208, (['p_{0,5}', 'p_{0,16}'], ['p_{0,5}', 'p_{0,16}']),
	 209, (['p_{0,6}', 'p_{0,16}'], ['p_{0,6}', 'p_{0,16}']),
	 211, (['Butadien', 'p_{0,11}'], ['p_{0,18}']),
	 8, (['p_{0,1}'], ['p_{0,1}']),
	 39, (['p_{0,3}'], ['p_{0,3}']),
	 40, (['p_{0,4}'], ['p_{0,4}']),
	 44, (['p_{0,5}'], ['p_{0,12}']),
	 45, (['p_{0,5}'], ['p_{0,5}']),
	 46, (['p_{0,6}'], ['p_{0,6}']),
	 47, (['p_{0,8}'], ['p_{0,8}']),
	 48, (['p_{0,9}'], ['p_{0,9}']),
	 49, (['p_{0,10}'], ['p_{0,10}']),
	 126, (['p_{0,11}'], ['p_{0,11}']),
	 127, (['p_{0,12}'], ['p_{0,5}']),
	 128, (['p_{0,12}'], ['p_{0,12}']),
	 129, (['p_{0,13}'], ['p_{0,13}']),
	 131, (['p_{0,14}'], ['p_{0,14}']),
	 133, (['p_{0,15}'], ['p_{0,15}']),
	 134, (['p_{0,16}'], ['p_{0,16}']),
	 212, (['p_{0,18}'], ['p_{0,18}']),
}

VERTICES = ['Butadien', 'p_{0,0}', 'p_{0,1}', 'p_{0,2}', 'p_{0,3}', 'p_{0,4}', 'p_{0,5}', 'p_{0,6}', 'p_{0,7}', 'p_{0,8}', 'p_{0,9}', 'p_{0,10}', 'p_{0,11}', 'p_{0,12}', 'p_{0,13}', 'p_{0,14}', 'p_{0,15}', 'p_{0,16}', 'p_{0,17}', 'p_{0,18}']
#Vergleich mit dem NMR von Ethylen und Hexatrien
NMR1 = [0.32, 0.5, 0.87, 0.0, 0.11, 0.58, 0.06, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09, 0.0, 0.0, 0.17, 0.0, 0.09]
#Vergleich mit dem NMR von Ethylen und Octrien
NMR2 = [0.33, 0.43, 0.6, 0.0, 0.13, 0.9, 0.07, 0.01, 0.0, 0.0, 0.01, 0.0, 0.0, 0.01, 0.1, 0.0, 0.0, 0.22, 0.0, 0.13]
#Vergleich mit dem NMR von Ethylen und Benzol
NMR3 = [0.0, 0.32, 0.0, 0.0, 0.0, 0.0, 0.05, 0.0, 0.0, 0.02, 0.0, 0.29, 0.95, 0.17, 0.0, 0.0, 0.0, 0.0, 0.0, 0.05]
VERTICESSMILES = ['C=CC=C', 'C=C', 'C=CC=CC=C', 'C1CCC(C=C)CC=1', 'C(CCC(C=C)CC=C)=C', 'C=CC=CC=CC=C', 'C1CCC(C=CC=C)CC=1', 'C=CC1C=CCCC1', 'C1CCCCC=1', 'C=CC1CC=CCC1C=C', 'C1CCC(C=C)C(C=C)C=1', 'C(C1CC(C=C)C=CC1)=C', 'C1C=CC=CC=1', 'C(CCC1C=CC=CC1)=C', 'C1C(C=CC=C)CCCC=1', 'C=CC(C=C)CCCC=C', 'C=CCCCCC=C', 'C=CC1C=CC(C=C)CC1', 'C1CC2CCCCC2CC=1', 'C1CC2C=CC=CC2CC=1']

FIXED_FLOWS = {
    #1: 1,
}

def build_model(name, hyperedges, vertices, nmrlikelihoods1, nmrlikelihoods2, nmrlikelihoods3, 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}
    n1 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "nmr1")
    n2 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "nmr2")
    n3 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "nmr3")
    en1 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 2.0, name = "edgenmr1")
    en2 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 2.0, name = "edgenmr2")
    en3 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 2.0, name = "edgenmr3")

    #Assigns every Molecule the likelihood compared to the three different reference spectra
    for v, nmr1, nmr2, nmr3 in zip(vertices, nmrlikelihoods1, nmrlikelihoods2, nmrlikelihoods3):
        n1[v] = nmr1
        n2[v] = nmr2
        n3[v] = nmr3

    #Assigns the edges a likelihood based on the products
    for e, (_, heads) in hyperedges.items():
        en1[e] = quicksum(n1[head] for head in heads)
        en2[e] = quicksum(n2[head] for head in heads)
        en3[e] = quicksum(n3[head] for head in heads)

    print(en1[7])

    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}")

    reaction_path = {}


    if excluded_support:
        model.addConstr(quicksum(b[e_id] for e_id in excluded_support) <= len(excluded_support) - 1, name = "different_hyperedges",)
    
    #Multiplizier den node Wert mit infow + outflow
    model.ModelSense = GRB.MAXIMIZE


    #Multiply node value with infow or outflow
    model.setObjectiveN(
        quicksum(n[t_id[0]] * x[e_id] for e_id, (_, t_id) in hyperedges.items() if t_id != []),
        index = 0,
        priority = 2,
        name = "maximize_nmr_similarity",
    )    

    model.setObjectiveN(
        quicksum(-1 * x[e_id] for e_id in hyperedges),
        index=1,
        priority=1,
        name="minimize_used_hyperedges",
    )

    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, VERTICES, NMR1, NMR2, NMR3)
    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()