加拿大瑞尔森大学 Python习题 Lab 4
Lab 4 – CPS 106
This lab helps you practice recursion, string manipulation and numerical approximation.
1. Assume that L is a list with one element. The element might be a number or it might be a list of one element, where that element might be a number or a list of one element, and so on. Return the innermost number. You must use recursion. Your solution cannot use a loop.
Hint: type(52) == int is True.
Test your program with the following:
[5]
[[55]]
[[[123]]]
[[[[[[[[[[[[18]]]]]]]]]]]]
2. Assume that T is a tuple. Return a tuple which is the reverse of T. You must use recursion. Your solution cannot use a loop or a list or a built-in reverse function. Hint: Reverse the tuple starting at the second element, and concatenate to the end of that reversed tuple the first element.
Test your program with the following:
(1, 2, 3, 4, 5)
('red', 'green', 'blue', 'yellow')
3. Assume that sub and bigstring are strings. Return True if sub is part of bigstring, False otherwise. You must use recursion. Your solution cannot use a string funtion or the 'in operation'. Your solution cannot use a loop. Hint: check if sub is the beginning of bigstring, and if not, consider the string obtained by removing the first letter from bigstring.
4. Assume that phrase is a string. Return the number of words in phrase. Assume that words are separated by one or more blanks. You are not allowed to use the built-in function split() For example, countwords('The cat is black') would return 4. countwords('The cat is black') would also return 4. countwords('A whitecat and a black cow.') would also return 7.
Test your program with the following:
'A white cat and a black cow'
'a b c de f g h'
"Orange you glad I didn't say banana"
5. Return the first value of n such that the sum
Sum = 4/1 - 4/3 + 4/5 - 4/7 + ... + 4 * (-1)**(n+1)/(2n - 1)
is within epsilon of math.pi = 3.141592653589793. For example, if epsilon is 1, then return 1, since 4 is within 1 of pi. If epsilon is 0.5 then return 2, since 4 is not within 0.5 of pi but 4 - 4/3 = 2.67, and that is within 0.5 of pi
代码：
4-2 tuple
4-3 findsub
4-3-2 findsub
