# Complete PYOMO implementation - Retry Attempt 4

import pyomo.environ as pyo
from pyomo.opt import SolverFactory

def music_festival_optimization():
    # 1. MODEL CREATION
    model = pyo.ConcreteModel()
    
    # 2. DATA SETUP
    # Example data for demonstration
    songs = ['S1', 'S2', 'S3', 'S4', 'S5']
    artists = ['A1', 'A2', 'A3', 'A4', 'A5', 'A6', 'A7', 'A8', 'A9', 'A10', 'A11']
    weeks_on_top = {'S1': 5, 'S2': 10, 'S3': 15, 'S4': 3, 'S5': 8}
    artist_songs = {
        'A1': ['S1', 'S2'],
        'A2': ['S3'],
        'A3': ['S4'],
        'A4': ['S5'],
        'A5': [],
        'A6': [],
        'A7': [],
        'A8': [],
        'A9': [],
        'A10': [],
        'A11': []
    }
    
    # 3. SETS
    model.SONGS = pyo.Set(initialize=songs)
    model.ARTISTS = pyo.Set(initialize=artists)
    
    # 4. PARAMETERS
    model.weeks_on_top = pyo.Param(model.SONGS, initialize=weeks_on_top)
    
    # 5. VARIABLES
    model.x = pyo.Var(model.SONGS, within=pyo.Binary)
    model.y = pyo.Var(model.ARTISTS, within=pyo.Binary)
    
    # 6. OBJECTIVE FUNCTION
    def obj_rule(model):
        return sum(model.weeks_on_top[s] * model.x[s] for s in model.SONGS)
    model.objective = pyo.Objective(rule=obj_rule, sense=pyo.maximize)
    
    # 7. CONSTRAINTS
    # Total Song Capacity
    def total_song_capacity_rule(model):
        return sum(model.x[s] for s in model.SONGS) <= 50
    model.total_song_capacity = pyo.Constraint(rule=total_song_capacity_rule)
    
    # Maximum Songs Per Artist
    def max_songs_per_artist_rule(model, a):
        return sum(model.x[s] for s in artist_songs[a]) <= 3
    model.max_songs_per_artist = pyo.Constraint(model.ARTISTS, rule=max_songs_per_artist_rule)
    
    # Minimum Number of Artists
    def min_artists_rule(model):
        return sum(model.y[a] for a in model.ARTISTS) >= 10
    model.min_artists = pyo.Constraint(rule=min_artists_rule)
    
    # Linking constraints for y_j
    def linking_rule_1(model, a):
        return model.y[a] <= sum(model.x[s] for s in artist_songs[a])
    model.linking_constraint_1 = pyo.Constraint(model.ARTISTS, rule=linking_rule_1)
    
    def linking_rule_2(model, a):
        return model.y[a] >= sum(model.x[s] for s in artist_songs[a]) / len(artist_songs[a]) if len(artist_songs[a]) > 0 else pyo.Constraint.Skip
    model.linking_constraint_2 = pyo.Constraint(model.ARTISTS, rule=linking_rule_2)
    
    # 8. SOLVING WITH GUROBI
    solver = SolverFactory('gurobi')
    
    # Optional: Set solver options
    solver.options['TimeLimit'] = 300  # 5 minutes
    solver.options['MIPGap'] = 0.01    # 1% gap
    
    # Solve the model
    results = solver.solve(model, tee=True)  # tee=True shows solver output
    
    # 9. RESULT PROCESSING
    # Check solver status
    if results.solver.termination_condition == pyo.TerminationCondition.optimal:
        print("Optimal solution found!")
        print(f"Optimal value: {pyo.value(model.objective)}")
        
        # Extract variable values
        print("\nSelected songs:")
        for s in model.SONGS:
            if pyo.value(model.x[s]) > 0.5:
                print(f"Song {s} selected")
        
        print("\nSelected artists:")
        for a in model.ARTISTS:
            if pyo.value(model.y[a]) > 0.5:
                print(f"Artist {a} selected")
        
    elif results.solver.termination_condition == pyo.TerminationCondition.infeasible:
        print("Problem is infeasible")
    elif results.solver.termination_condition == pyo.TerminationCondition.unbounded:
        print("Problem is unbounded")
    else:
        print(f"Solver terminated with condition: {results.solver.termination_condition}")
    
    return model

# Execute the optimization
if __name__ == "__main__":
    music_festival_optimization()