Kurage Notes

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Q1 ​

python
def multiply(m, n):
    """Takes two positive integers and returns their product using recursion.
    >>> multiply(5, 3)
    15
    """
    "*** YOUR CODE HERE ***"
    if m == 1:
        return n
    else:
        return n + multiply(m - 1, n)

Q3 ​

python
def skip_mul(n): # Find the bug
    """Return the product of n * (n - 2) * (n - 4) * ...

    >>> skip_mul(5) # 5 * 3 * 1
    15
    >>> skip_mul(8) # 8 * 6 * 4 * 2
    384
    """
    if n == 1 or n == 2:
        return n
    else:
        return n * skip_mul(n - 2)

Q4 ​

python
def is_prime(n):
    """Returns True if n is a prime number and False otherwise.
    >>> is_prime(2)
    True
    >>> is_prime(16)
    False
    >>> is_prime(521)
    True
    """
    "*** YOUR CODE HERE ***"
    '''
    num = n + 1
    if n == 1:
        return True
    elif (num - 1) % n == 0:
        return False
    return is_prime(n - 1)
    ''' # My original intention is that "If a number N is not prime, then it can be divided into a prime number P and another number M"
    i = n - 1
    def prime_helper(n, i):
        if i == 1:
            return True
        elif n % i == 0:
            return False
        return prime_helper(n, i - 1)
    return prime_helper(n, i)

Solution ​

From bottom to top

python
def is_prime(n):
    """Returns True if n is a prime number and False otherwise.
    >>> is_prime(2)
    True
    >>> is_prime(16)
    False
    >>> is_prime(521)
    True
    """
    def helper(i):
        if i > (n ** 0.5): # Could replace with i == n
            return True
        elif n % i == 0:
            return False
        return helper(i + 1)
    return helper(2)

Q5 ​

python
def hailstone(n):
    """Print out the hailstone sequence starting at n, and return the number of elements in the sequence.
    >>> a = hailstone(10)
    10
    5
    16
    8
    4
    2
    1
    >>> a
    7
    >>> b = hailstone(1)
    1
    >>> b
    1
    """
    "*** YOUR CODE HERE ***"
    print(n)
    times = 0
    if n == 1:
        return times + 1
    elif n % 2 == 0:
        return hailstone(n // 2) + 1
    else:
        return hailstone(n * 3 + 1) + 1

Q6 ​

python
def merge(n1, n2):
    """Merges two numbers by digit in decreasing order.
    >>> merge(31, 42)
    4321
    >>> merge(21, 0)
    21
    >>> merge (21, 31) 
    3211
    """
    "*** YOUR CODE HERE ***"