Práctica 7: Listas

Activity Description

Solve the following set of problems using Python 3. Run and test each of your programs to make sure they work as expected.

1. Write a program called positives.py. Define in this program a function called positives(x) that takes a list of numbers x as its argument, and returns a new list that only contains the positive numbers of x.

   Test your program with the following main() function:

   def main():
       print(positives([-21, -31]))
       print(positives([-48, -2, 0, -47, 45]))
       print(positives([-9, -38, 49, -49, 32, 6, 4, 26, -8, 45]))
       print(positives([-27, 48, 13, 5, 27, 5, -48, -42, -35, 49,
                        -41, -24, 11, 29, 33, -8, 45, -44, 12, 46]))
       print(positives([-2, 0, 27, 47, -13, -23, 8, -28, 23, 7,
                        -29, -24, -30, -6, -21, -17, -35, -8, -30,
                        -7, -48, -18, -2, 1, -1, 18, 35, -32, -42,
                        -5, 46, 8, 0, -31, -23, -47, -4, 37, -5,
                        -45, -17, -5, -29, -35, -2, 40, 9, 25, -11,
                        -32]))

   The expected program output should be:

   []
   [0, 45]
   [49, 32, 6, 4, 26, 45]
   [48, 13, 5, 27, 5, 49, 11, 29, 33, 45, 12, 46]
   [0, 27, 47, 8, 23, 7, 1, 18, 35, 46, 8, 0, 37, 40, 9, 25]

2. Write a program called dotproduct.py. Define in this program a function called dotproduct(a, b) that takes two arguments: the lists a and b. It returns the result of performing the dot product of a times b. The dot product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number obtained by multiplying corresponding entries and then summing those products:

   $$ a \cdot b = \sum_{i=1}^{n} a_i b_i=a_1 b_1 + a_2 b_2 + \cdots + a_n b_n $$

   Test your program with the following main() function:

   def main():
       print(dotproduct([], []))
       print(dotproduct([1, 2, 3], [4, 5, 6]))
       print(dotproduct([1.3, 3.4, 5.7, 9.5, 10.4],
                        [-4.5, 3.0, 1.5, 0.9, 0.0]))
       print(dotproduct([92, -39, 82, 16, -64, -1, -16, -45, -7, 39,
                         45, 0, 34, -3, -51, 71, 23, -8, 41, -40],
                        [-50, -81, 94, -84, 47, 86, 52, 19, -57, 36,
                         -20, 11, -42, 48, 14, 13, 9, -67, 92, 96]))
   
   

   The expected program output should be:

   0
   32
   21.45
   357

3. Write a program called replicate.py. Define in this program a function called replicate(n, x) that takes two arguments: a list x and an integer number n, where n ≥ 0. It returns a new list that replicates n times each element contained in x.

   Test your program with the following main() function:

   def main():
       print(replicate(7, []))
       print(replicate(0, ['a', 'b', 'c']))
       print(replicate(3, ['a']))
       print(replicate(3, ['a', 'b', 'c']))
       print(replicate(4, [1, 2, 3, 4]))
   

   The expected program output should be:

   []
   []
   ['a', 'a', 'a']
   ['a', 'a', 'a', 'b', 'b', 'b', 'c', 'c', 'c']
   [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4]
   

4. The Fibonacci sequence is:

   $$ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, \ldots $$

   The sequence starts with 0 and 1. Any number that follows is calculated by adding the previous two numbers.

   Write a program called fibo.py. Define in this program a function called fibo(n) that returns a list with the first n Fibonacci numbers.

   Test your program with the following main() function:

   def main():
       print(fibo(0))
       print(fibo(1))
       print(fibo(2))
       print(fibo(5))
       print(fibo(10))
       print(fibo(20))
       print(fibo(30))
       print(fibo(100))
   

   The expected program output should be:

   []
   [0]
   [0, 1]
   [0, 1, 1, 2, 3]
   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610,
   987, 1597, 2584, 4181]
   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610,
   987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025,
   121393, 196418, 317811, 514229]
   [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610,
   987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368,
   75025, 121393, 196418, 317811, 514229, 832040, 1346269,
   2178309, 3524578, 5702887, 9227465, 14930352, 24157817,
   39088169, 63245986, 102334155, 165580141, 267914296,
   433494437, 701408733, 1134903170, 1836311903, 2971215073,
   4807526976, 7778742049, 12586269025, 20365011074, 32951280099,
   53316291173, 86267571272, 139583862445, 225851433717,
   365435296162, 591286729879, 956722026041, 1548008755920,
   2504730781961, 4052739537881, 6557470319842, 10610209857723,
   17167680177565, 27777890035288, 44945570212853, 72723460248141,
   117669030460994, 190392490709135, 308061521170129,
   498454011879264, 806515533049393, 1304969544928657,
   2111485077978050, 3416454622906707, 5527939700884757,
   8944394323791464, 14472334024676221, 23416728348467685,
   37889062373143906, 61305790721611591, 99194853094755497,
   160500643816367088, 259695496911122585, 420196140727489673,
   679891637638612258, 1100087778366101931, 1779979416004714189,
   2880067194370816120, 4660046610375530309, 7540113804746346429,
   12200160415121876738, 19740274219868223167,
   31940434634990099905, 51680708854858323072,
   83621143489848422977, 135301852344706746049,
   218922995834555169026]
   

5. In statistics, the standard deviation \(\sigma\) is a measure of how spread out numbers are. It has the following formula:

   $$ \sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2} $$

   Where \(\bar{x}\) is the arithmetic mean and is defined as follows:

   $$ \bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_i $$
   Write a program called deviation.py. Define in this program a function called deviation(x) that returns the standard deviation of the list of numbers contained in x.

   Test your program with the following main() function:

   def main():
       print(deviation([42]))
       print(deviation([10, 20]))
       print(deviation([1, 2, 3, 4, 5]))
       print(deviation([7, 7, 7, 7, 7, 7, 7]))
       print(deviation([32, 88, 20, 26, 14, 24, 26, 44, 14, 94,
                        94, 72, 8, 46, 92, 50, 38, 56, 60, 84]))
   

   The expected program output should be:

   0.0
   5.0
   1.4142135623730951
   0.0
   28.673855687716646
   

6. Write a program called compress.py. Define in this program a function called compress(x) that takes a list x as its argument. If x contains consecutive repeated elements, they should be replaced with a single copy of that element. The order of the elements should not be changed.

   Test your program with the following main() function:

   def main():
       print(compress(['a', 'a', 'a', 'a', 'b', 'c', 'c', 'a',
                       'a', 'd', 'e', 'e', 'e', 'e']))
       print(compress(['a', 'a', 'a', 'a', 'a', 'a', 'a', 'a',
                       'a', 'a']))
       print(compress(['a', 'b', 'c', 'd']))
       print(compress([]))
   

   The expected program output should be:

   ['a', 'b', 'c', 'a', 'd', 'e']
   ['a']
   ['a', 'b', 'c', 'd']
   []