CS61A:HW2

from operator import add, mul

square = lambda x: x * x

identity = lambda x: x

triple = lambda x: 3 * x

increment = lambda x: x + 1

LAMBDA函数，适用于表达式，（不可用与循环语句等复杂的语句，只有简短一句），可以使用多个参数，对于参数只是用一次或者临时使用的情况

from operator import add, mul

square = lambda x: x * x

identity = lambda x: x

triple = lambda x: 3 * x

increment = lambda x: x + 1


HW_SOURCE_FILE=__file__


def product(n, term):
    """Return the product of the first n terms in a sequence.

    n: a positive integer
    term:  a function that takes one argument to produce the term

    >>> product(3, identity)  # 1 * 2 * 3
    6
    >>> product(5, identity)  # 1 * 2 * 3 * 4 * 5
    120
    >>> product(3, square)    # 1^2 * 2^2 * 3^2
    36
    >>> product(5, square)    # 1^2 * 2^2 * 3^2 * 4^2 * 5^2
    14400
    >>> product(3, increment) # (1+1) * (2+1) * (3+1)
    24
    >>> product(3, triple)    # 1*3 * 2*3 * 3*3
    162
    """
    "*** YOUR CODE HERE ***"
    ret = 1
    for i in range(1,n + 1):
        ret *= term(i)
    return ret



def accumulate(fuse, start, n, term):
    """Return the result of fusing together the first n terms in a sequence 
    and start.  The terms to be fused are term(1), term(2), ..., term(n). 
    The function fuse is a two-argument commutative & associative function.

    >>> accumulate(add, 0, 5, identity)  # 0 + 1 + 2 + 3 + 4 + 5
    15
    >>> accumulate(add, 11, 5, identity) # 11 + 1 + 2 + 3 + 4 + 5
    26
    >>> accumulate(add, 11, 0, identity) # 11 (fuse is never used)
    11
    >>> accumulate(add, 11, 3, square)   # 11 + 1^2 + 2^2 + 3^2
    25
    >>> accumulate(mul, 2, 3, square)    # 2 * 1^2 * 2^2 * 3^2
    72
    >>> # 2 + (1^2 + 1) + (2^2 + 1) + (3^2 + 1)
    >>> accumulate(lambda x, y: x + y + 1, 2, 3, square)
    19
    """
    "*** YOUR CODE HERE ***"
    
    count = start
    for i in range(1,n + 1):
        count = fuse(count,term(i))
        
    return count

def summation_using_accumulate(n, term):
    """Returns the sum: term(1) + ... + term(n), using accumulate.

    >>> summation_using_accumulate(5, square) # square(1) + square(2) + ... + square(4) + square(5)
    55
    >>> summation_using_accumulate(5, triple) # triple(1) + triple(2) + ... + triple(4) + triple(5)
    45
    >>> # This test checks that the body of the function is just a return statement.
    >>> import inspect, ast
    >>> [type(x).__name__ for x in ast.parse(inspect.getsource(summation_using_accumulate)).body[0].body]
    ['Expr', 'Return']
    """
    return accumulate(add,0,n,term)


def product_using_accumulate(n, term):
    """Returns the product: term(1) * ... * term(n), using accumulate.

    >>> product_using_accumulate(4, square) # square(1) * square(2) * square(3) * square()
    576
    >>> product_using_accumulate(6, triple) # triple(1) * triple(2) * ... * triple(5) * triple(6)
    524880
    >>> # This test checks that the body of the function is just a return statement.
    >>> import inspect, ast
    >>> [type(x).__name__ for x in ast.parse(inspect.getsource(product_using_accumulate)).body[0].body]
    ['Expr', 'Return']
    """
    return accumulate(mul,1,n,term)


def make_repeater(f, n):
    """Returns the function that computes the nth application of f.

    >>> add_three = make_repeater(increment, 3)
    >>> add_three(5)
    8
    >>> make_repeater(triple, 5)(1) # 3 * (3 * (3 * (3 * (3 * 1))))
    243
    >>> make_repeater(square, 2)(5) # square(square(5))
    625
    >>> make_repeater(square, 3)(5) # square(square(square(5)))
    390625
    """
    "*** YOUR CODE HERE ***"
    def repeater(x):
        if n == 0:
            return x
        else:
            return f(make_repeater(f, n - 1)(x))
    return repeater

# 测试 product 函数
assert product(3, identity) == 6
assert product(5, identity) == 120
assert product(3, square) == 36
assert product(5, square) == 14400
assert product(3, increment) == 24
assert product(3, triple) == 162

# 测试 accumulate 函数
assert accumulate(add, 0, 5, identity) == 15
assert accumulate(add, 11, 5, identity) == 26
assert accumulate(add, 11, 0, identity) == 11
assert accumulate(add, 11, 3, square) == 25
assert accumulate(mul, 2, 3, square) == 72
assert accumulate(lambda x, y: x + y + 1, 2, 3, square) == 19

# 测试 summation_using_accumulate 函数
assert summation_using_accumulate(5, square) == 55
assert summation_using_accumulate(5, triple) == 45

# 测试 product_using_accumulate 函数
assert product_using_accumulate(4, square) == 576
assert product_using_accumulate(6, triple) == 524880

# 测试 make_repeater 函数
add_three = make_repeater(increment, 3)
assert add_three(5) == 8
assert make_repeater(triple, 5)(1) == 243
assert make_repeater(square, 2)(5) == 625
assert make_repeater(square, 3)(5) == 390625

print("所有测试通过！")