import numpy as np

def jaccard_similarity(x, y):
    """
    Calculate the Jaccard similarity between two vectors x and y

    Args:
    - x (np.array): The first vector
    - y (np.array): The second vector

    Returns:
    - the Jaccard similarity between two vectors x and y
    """
    # Q1
    # TODO

def euclidean_similarity(x, y):
    """
    Calculate the Euclidean similarity between two vectors x and y

    Args:
    - x (np.array): The first vector
    - y (np.array): The second vector

    Returns:
    - the Euclidean similarity between two vectors x and y
    """
    # Q2
    # TODO

def manhattan_similarity(x, y):
    """
    Calculate the Manhattan similarity between two vectors x and y

    Args:
    - x (np.array): The first vector
    - y (np.array): The second vector

    Returns:
    - the Manhattan similarity between two vectors x and y
    """
    # Q3
    # TODO

def cosine_similarity(x, y):
    """
    Calculates the Cosine similarity between two vectors x and y
    
    Args:
    - x (np.array): The first vector
    - y (np.array): The second vector

    Returns:
    - the Cosine similarity between two vectors x and y
    """
    # Q4
    # TODO

def compute_classification_accuracy(classification_matrix):
    """
    Computes classification accuracy from a classification matrix
    
    Args:
    - classification matrix (np.array): A classification matrix

    Returns:
    - The classification accuracy for a classification matrix.
    """
    # Q5
    # TODO