import numpy as np
 
def sigmoid(z):
    """Sigmoid activation function"""
    return 1 / (1 + np.exp(-z))
 
def logistic_cost_function(X, y, theta):
    """
    Compute the cost function for logistic regression
 
    Parameters:
    X : numpy array of shape (m, n) - feature matrix
    y : numpy array of shape (m,) - target labels (0 or 1)
    theta : numpy array of shape (n,) - parameters
 
    Returns:
    cost : float
    """
    m = len(y)
 
    # Calculate hypothesis using sigmoid
    h = sigmoid(X @ theta)
 
    # Avoid log(0) errors by using np.clip or np.where
    h = np.clip(h, 1e-15, 1 - 1e-15)  # Clip to prevent log(0)
 
    # Cost function with logs
    cost = (-1/m) * np.sum(y * np.log(h) + (1 - y) * np.log(1 - h))
 
    return cost

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