def min_max_norm(scores):
    if not scores: return []
    mn, mx = min(scores), max(scores)
    return [(s - mn) / (mx - mn) if mx > mn else 0.0 for s in scores]

def fuse_results(sparse_res, dense_res, alpha):
    s_dict = dict(zip([r[0] for r in sparse_res], min_max_norm([r[1] for r in sparse_res])))
    d_dict = dict(zip([r[0] for r in dense_res], min_max_norm([r[1] for r in dense_res])))
    
    fused = {doc_i: alpha * s_dict.get(doc_i, 0.0) + (1 - alpha) * d_dict.get(doc_i, 0.0) 
             for doc_i in set(s_dict.keys()) | set(d_dict.keys())}
    return sorted(fused.items(), key=lambda x: x[1], reverse=True)