input: from typing import List
  
  def classify_string(input_strings: List[str]) -> List[int]:
      """
      Classifies a list of input strings using a machine learning classifier based on the sklearn.naive_bayes.MultinomialNB model. 
      The function preprocesses the input strings by extracting and transforming features into numerical values, which are then used to train and predict the category of the input strings. 
      Example:
      classify_string(['Hello world', 'Machine learning']) == [1, 2]
      """
      from sklearn.naive_bayes import MultinomialNB
      # Example features extraction
      features = [some_feature_extraction(s) for s in input_strings]
      # Example training with dummy data and targets
      data, target = some_training_data, some_target_data
      model = MultinomialNB()
      model.fit(data, target)
      predictions = model.predict(features)
      return predictions
output:     from sklearn.feature_extraction.text import CountVectorizer
      from sklearn.model_selection import train_test_split
      from sklearn.naive_bayes import MultinomialNB
      import numpy as np
  
      # Example feature extraction using CountVectorizer
      vectorizer = CountVectorizer()
      features = vectorizer.fit_transform(input_strings)
  
      # Example training data and targets
      some_training_data = vectorizer.transform(['Hello world', 'Machine learning'])
      some_target_data = np.array([1, 2])
  
      # Train the model
      model = MultinomialNB()
      model.fit(some_training_data, some_target_data)
  
      # Predict the categories of the input strings
      predictions = model.predict(features)
      return predictions.tolist()