Python 断言语句的最佳放置以确保使用不变量的正确性

我正在try 通过用Python语言编写的真实示例来理解编程中的不变量.我对在哪里放置assert条语句来判断不变量感到困惑.

我的研究显示了在哪里判断不变量的不同模式.例如:

before the loop starts
before each iteration of the loop
after the loop terminates

VS

... // the Loop Invariant must be true here
while ( TEST CONDITION ) {
// top of the loop
...
// bottom of the loop
// the Loop Invariant must be true here
}
// Termination + Loop Invariant = Goal

下面我给出了一本数学书中一个不变例子的代码.有两个版本，一个使用函数，另一个不使用函数.我希望这不会有什么不同，但我想要彻底.

我的问题是:

• 为了与不变量保持一致，我至少需要多少个断言状态来确保程序的正确性？
• 在我的示例中，哪些断言语句是多余的？
• 如果上述问题有多个答案，哪一个将被认为是最佳实践？

理想情况下，我希望看到重写我的代码，包括最好的实践和对我在工作中迄今可能忽略的任何问题的关注.

非常感谢您提供的任何意见.

下面是练习:

E2. Suppose the positive integer n is odd. First Al writes the numbers 1, 2,..., 2n on the blackboard. Then he picks any two numbers a, b, erases them, and writes, instead, |a − b|. Prove that an odd number will remain at the end.个

Solution. Suppose S is the sum of all the numbers still on the blackboard. Initially this sum is S = 1+2+···+2n = n(2n+1), an odd number. Each step reduces S by 2 min(a, b), which is an even number. So the parity of S is an invariant. During the whole reduction process we have S ≡ 1 mod 2. Initially the parity is odd. So, it will also be odd at the end.个

import random

def invariant_example(n):
    xs = [x for x in range(1, 2*n+1)]
    print(xs)
    assert sum(xs) % 2 == 1
    while len(xs) >= 2:
        assert sum(xs) % 2 == 1
        a, b = random.sample(xs, 2)
        print(f"a: {a}, b: {b}, xs: {xs}")
        xs.remove(a)
        xs.remove(b)
        xs.append(abs(a - b))
        assert sum(xs) % 2 == 1
    assert sum(xs) % 2 == 1
    return xs
    
print(invariant_example(5))

n = 5
xs = [x for x in range(1, 2*n+1)]
print(xs)
assert sum(xs) % 2 == 1
while len(xs) >= 2:
    assert sum(xs) % 2 == 1
    a, b = random.sample(xs, 2)
    print(f"a: {a}, b: {b}, xs: {xs}")
    xs.remove(a)
    xs.remove(b)
    xs.append(abs(a - b))
    assert sum(xs) % 2 == 1
assert sum(xs) % 2 == 1
print(xs)