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

HYPERGRAPH = {
	 0: (['Butadien'], []),
	 1: (['Butadien'], ['Butadien']),
	 2: (['p_{0,0}'], []),
	 3: (['p_{0,1}'], []),
	 4: (['Butadien', 'Butadien'], ['p_{0,0}', 'p_{0,1}']),
	 5: (['Butadien', 'Butadien'], ['Butadien', 'Butadien']),
	 6: (['p_{0,2}'], []),
	 7: (['Butadien', 'Butadien'], ['p_{0,2}']),
	 8: (['p_{0,1}'], ['p_{0,1}']),
	 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}']),
	 12: (['p_{0,3}'], []),
	 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}']),
	 17: (['p_{0,4}'], []),
	 18: (['p_{0,1}', 'p_{0,1}'], ['Butadien', 'p_{0,4}']),
	 19: (['p_{0,5}'], []),
	 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}']),
	 27: (['p_{0,6}'], []),
	 28: (['p_{0,0}', 'p_{0,1}'], ['p_{0,6}']),
	 29: (['p_{0,7}'], []),
	 30: (['Butadien', 'p_{0,0}'], ['p_{0,7}']),
	 31: (['p_{0,8}'], []),
	 32: (['Butadien', 'p_{0,1}'], ['p_{0,8}']),
	 33: (['Butadien', 'p_{0,1}'], ['p_{0,5}']),
	 34: (['p_{0,9}'], []),
	 35: (['Butadien', 'p_{0,1}'], ['p_{0,9}']),
	 36: (['p_{0,10}'], []),
	 37: (['Butadien', 'p_{0,1}'], ['p_{0,10}']),
	 38: (['p_{0,3}'], ['p_{0,0}', 'p_{0,2}']),
	 39: (['p_{0,3}'], ['p_{0,3}']),
	 40: (['p_{0,4}'], ['p_{0,4}']),
	 41: (['p_{0,11}'], []),
	 42: (['p_{0,4}'], ['p_{0,0}', 'p_{0,11}']),
	 43: (['p_{0,12}'], []),
	 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}']),
	 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}']),
	 63: (['p_{0,13}'], []),
	 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}']),
	 99: (['p_{0,14}'], []),
	 100: (['p_{0,0}', 'p_{0,6}'], ['p_{0,14}']),
	 101: (['p_{0,15}'], []),
	 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}']),
	 122: (['p_{0,16}'], []),
	 123: (['p_{0,0}', 'p_{0,4}'], ['p_{0,16}']),
	 124: (['p_{0,17}'], []),
	 125: (['Butadien', 'p_{0,7}'], ['p_{0,17}']),
	 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}']),
	 130: (['p_{0,14}'], ['p_{0,0}', 'p_{0,6}']),
	 131: (['p_{0,14}'], ['p_{0,14}']),
	 132: (['p_{0,15}'], ['p_{0,0}', 'p_{0,7}']),
	 133: (['p_{0,15}'], ['p_{0,15}']),
	 134: (['p_{0,16}'], ['p_{0,16}']),
	 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}']),
	 210: (['p_{0,18}'], []),
	 211: (['Butadien', 'p_{0,11}'], ['p_{0,18}']),
	 212: (['p_{0,18}'], ['p_{0,18}']),
	 213: ([], ['Butadien']),
}

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 = {
    213: 3,
    41: 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[203])

    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((en1[e_id] + en2[e_id] + en3[e_id]) * x[e_id] for e_id, (_, _) in hyperedges.items()),
        index = 0,
        priority = 2,
        name = "maximize_nmr_similarity",
    )  

    model.setObjectiveN(
        quicksum(-1 * x[e_id] for e_id in hyperedges),
        index=3,
        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", HYPERGRAPH, 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, HYPERGRAPH)

    """ 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()