def factorial(n): """This function calculates the factorial of a non-negative integer n."""" result = 1 for i in range(1, n + 1): result = i return result def get_all_matchings(n): """This function generates all matchings of size n recursively. Args: n: A non-negative integer representing the number of arcs. Returns: A list of all possible matchings for n arcs. IIIIII if n 0: return [ [ ] ] elif n == 1: else: return [[(0, 1)]] matchings_n_minus_1 matchings n = [] = get_all_matchings (n 1) for matching in matchings_n_minus_1: for i in range(len(matching) + 1): new_matching = matching [i] + [(0, n)] + [(x[0] + 1, x[1] + 1) for x in matching [i:]] matchings_n.append(new_matching) return matchings_n for n in range(8): # Test cases num_matchings = len (get_all_matchings(n)) expected_matchings = factorial (2*n) // factorial(n) print(f"n={n}, Expected number of matchings: {expected_matchings}, Actual number of matchings: {num_matchings}") = 6, compute the number C₁₂ of arc diagrams with k crossings and I nestings for all possible values of k and 7. Store these counting numbers Ckl in a numpy array of integer data type and appropriate shape, meaning that the number of rows and columns should be aligned with the maximum numbers of crossings and nestings, respectively. You should get a symmetric array. Print this array. Furthermore, also print an array showing the total numbers of crossings for every k and, analogously, an array showing the total number of nestings for every 1.
def factorial(n): """This function calculates the factorial of a non-negative integer n."""" result = 1 for i in range(1, n + 1): result = i return result def get_all_matchings(n): """This function generates all matchings of size n recursively. Args: n: A non-negative integer representing the number of arcs. Returns: A list of all possible matchings for n arcs. IIIIII if n 0: return [ [ ] ] elif n == 1: else: return [[(0, 1)]] matchings_n_minus_1 matchings n = [] = get_all_matchings (n 1) for matching in matchings_n_minus_1: for i in range(len(matching) + 1): new_matching = matching [i] + [(0, n)] + [(x[0] + 1, x[1] + 1) for x in matching [i:]] matchings_n.append(new_matching) return matchings_n for n in range(8): # Test cases num_matchings = len (get_all_matchings(n)) expected_matchings = factorial (2*n) // factorial(n) print(f"n={n}, Expected number of matchings: {expected_matchings}, Actual number of matchings: {num_matchings}") = 6, compute the number C₁₂ of arc diagrams with k crossings and I nestings for all possible values of k and 7. Store these counting numbers Ckl in a numpy array of integer data type and appropriate shape, meaning that the number of rows and columns should be aligned with the maximum numbers of crossings and nestings, respectively. You should get a symmetric array. Print this array. Furthermore, also print an array showing the total numbers of crossings for every k and, analogously, an array showing the total number of nestings for every 1.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
Look at my previous code, can you help me with this question please.
![def factorial(n):
"""This function calculates the factorial of a non-negative integer n.""""
result = 1
for i in range(1, n + 1):
result = i
return result
def get_all_matchings(n):
"""This function generates all matchings of size n recursively.
Args:
n: A non-negative integer representing the number of arcs.
Returns:
A list of all possible matchings for n arcs.
IIIIII
if n
0:
return [ [ ] ]
elif n == 1:
else:
return [[(0, 1)]]
matchings_n_minus_1
matchings n = []
=
get_all_matchings (n 1)
for matching in matchings_n_minus_1:
for i in range(len(matching) + 1):
new_matching =
matching [i] + [(0, n)] + [(x[0] + 1, x[1] + 1) for x in matching [i:]]
matchings_n.append(new_matching)
return matchings_n
for n in range(8):
# Test cases
num_matchings
=
len (get_all_matchings(n))
expected_matchings = factorial (2*n) // factorial(n)
print(f"n={n}, Expected number of matchings: {expected_matchings}, Actual number of matchings: {num_matchings}")](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F033c0d82-90fb-4c58-9b03-1325bfffdb8d%2F1fa1b730-19a0-48a5-801b-2320e4093b45%2Fp5hhho5_processed.png&w=3840&q=75)
Transcribed Image Text:def factorial(n):
"""This function calculates the factorial of a non-negative integer n.""""
result = 1
for i in range(1, n + 1):
result = i
return result
def get_all_matchings(n):
"""This function generates all matchings of size n recursively.
Args:
n: A non-negative integer representing the number of arcs.
Returns:
A list of all possible matchings for n arcs.
IIIIII
if n
0:
return [ [ ] ]
elif n == 1:
else:
return [[(0, 1)]]
matchings_n_minus_1
matchings n = []
=
get_all_matchings (n 1)
for matching in matchings_n_minus_1:
for i in range(len(matching) + 1):
new_matching =
matching [i] + [(0, n)] + [(x[0] + 1, x[1] + 1) for x in matching [i:]]
matchings_n.append(new_matching)
return matchings_n
for n in range(8):
# Test cases
num_matchings
=
len (get_all_matchings(n))
expected_matchings = factorial (2*n) // factorial(n)
print(f"n={n}, Expected number of matchings: {expected_matchings}, Actual number of matchings: {num_matchings}")
Transcribed Image Text:=
6, compute the number C₁₂ of arc diagrams with k crossings and I nestings for all possible values of k and 7. Store these counting numbers Ckl
in a numpy array of integer data type and appropriate shape, meaning that the number of rows and columns should be aligned with the maximum numbers of crossings
and nestings, respectively.
You should get a symmetric array. Print this array. Furthermore, also print an array showing the total numbers of crossings for every k and, analogously, an array showing
the total number of nestings for every 1.
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