Extend the function to num_permutation (n, k=None) which takes in an additional optional keyword argument...

 

  
 
 

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Extend the function to num_permutation (n, k=None) which • takes in an additional optional keyword argument k, and • returns the INTEGER number of k -permutations of n items. The number is given by the formula Osk <n Pn. Pak = { (5) otherwise. In [26]: def num_permutation(n,k=None): # YOUR CODE HERE executed in 4ms, finished 19:44:08 2020-11-02 In [27]: # tests assert isinstance(num_permutation (0), int) assert num_permutation(3) == 6 assert num_permutation(3,0) == 1 assert num_permutation(3,2) == 6 assert num_permutation(10,5) == 30240 executed in 20ms, finished 19:44:09 2020-11-02 Unfortunately, there is not much improvement. Nevertheless, we can efficiently compute the number of k-permutations based on the previously computed number of k – 1-permutations: For k from 0 ton, Pat-1 if k>0 Pn.k = nx (n – 1) x ...x (n – k + 1). (6) k terms in the product. Exercise Use the yield statement to write the function num_permutation_sequence(n) that returns a generator of Pnk with k from 0 to n. In [ ]: - def num_permutation_sequence (n): output = 1 for k in range (0, n + 1) : # YOUR CODE HERE executed in 3ms, finished 12:00:19 2020-10-25 In [ ]: # tests executed in 201ms, finished 12:00:19 2020-10-25 Exercise (Challenge) Extend the function num_permutation_sequence(n) so that calling send (0) method causes the generator to increment n instead of k for the next number to generate. İ.e., for 0 < k < n, send(0) ... Pnk-1 → Pk P+1.k → Pr+1,k+1 ... (7) where → without labels is the normal transition without calling the send method. Hint: n+1 Pn+1,k = Pn.k X (8) n-k +1 In [ ]: def num_permutation_sequence (n): # YOUR CODE HERE raise NotImplementedError() executed in 14ms, finished 12:00:19 2020-10-25 In [ ]: # tests executed in 20ms, finished 12:00:19 2020-10-25 Exercise: Create a decorator to eliminate duplicate input positional arguments instead of the ouput, i.e., permutation (1,1,2) will return the same result as permutation(1,2). In [ ]: - def deduplicate_input (f): ''Takes in a function f that takes a variable number of arguments possibly with duplicates, returns a decorator that remove duplicates in the positional argument.''' @functools.wraps (f) def wrapper(*args, **kwargs): # YOUR CODE HERE raise NotImplementedError() return wrapper executed in 9ms, finished 12:00:19 2020-10-25 In [ 1: # tests executed in 12ms, finished 12:00:24 2020-10-25 Extend the function to num_permutation (n, k=None) which • takes in an additional optional keyword argument k, and • returns the INTEGER number of k -permutations of n items. The number is given by the formula Osk <n Pn. Pak = { (5) otherwise. In [26]: def num_permutation(n,k=None): # YOUR CODE HERE executed in 4ms, finished 19:44:08 2020-11-02 In [27]: # tests assert isinstance(num_permutation (0), int) assert num_permutation(3) == 6 assert num_permutation(3,0) == 1 assert num_permutation(3,2) == 6 assert num_permutation(10,5) == 30240 executed in 20ms, finished 19:44:09 2020-11-02 Unfortunately, there is not much improvement. Nevertheless, we can efficiently compute the number of k-permutations based on the previously computed number of k – 1-permutations: For k from 0 ton, Pat-1 if k>0 Pn.k = nx (n – 1) x ...x (n – k + 1). (6) k terms in the product. Exercise Use the yield statement to write the function num_permutation_sequence(n) that returns a generator of Pnk with k from 0 to n. In [ ]: - def num_permutation_sequence (n): output = 1 for k in range (0, n + 1) : # YOUR CODE HERE executed in 3ms, finished 12:00:19 2020-10-25 In [ ]: # tests executed in 201ms, finished 12:00:19 2020-10-25 Exercise (Challenge) Extend the function num_permutation_sequence(n) so that calling send (0) method causes the generator to increment n instead of k for the next number to generate. İ.e., for 0 < k < n, send(0) ... Pnk-1 → Pk P+1.k → Pr+1,k+1 ... (7) where → without labels is the normal transition without calling the send method. Hint: n+1 Pn+1,k = Pn.k X (8) n-k +1 In [ ]: def num_permutation_sequence (n): # YOUR CODE HERE raise NotImplementedError() executed in 14ms, finished 12:00:19 2020-10-25 In [ ]: # tests executed in 20ms, finished 12:00:19 2020-10-25 Exercise: Create a decorator to eliminate duplicate input positional arguments instead of the ouput, i.e., permutation (1,1,2) will return the same result as permutation(1,2). In [ ]: - def deduplicate_input (f): ''Takes in a function f that takes a variable number of arguments possibly with duplicates, returns a decorator that remove duplicates in the positional argument.''' @functools.wraps (f) def wrapper(*args, **kwargs): # YOUR CODE HERE raise NotImplementedError() return wrapper executed in 9ms, finished 12:00:19 2020-10-25 In [ 1: # tests executed in 12ms, finished 12:00:24 2020-10-25

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