from itertools import permutations, combinations def find_all_arc_diagrams (n): points = list(range(2 * n)) arc_diagrams = [] # Generate all combinations of n starting points start_combinations = combinations (points, n) for start_points in start_combinations: remaining points = [p for p in points if p not in start_points] # Generate all permutations of the remaining points end_permutations = permutations (remaining_points, n) # Generate all permutations of the remaining points end_permutations = permutations (remaining_points, n) for end points in end_permutations: # Check if all pairs (i_k, j_k) satisfy i_k < j_k if all(start_points[k] < end_points[k] for k in range(n)): arc_diagrams.append(list(zip(start_points, end_points))) return arc_diagrams
from itertools import permutations, combinations def find_all_arc_diagrams (n): points = list(range(2 * n)) arc_diagrams = [] # Generate all combinations of n starting points start_combinations = combinations (points, n) for start_points in start_combinations: remaining points = [p for p in points if p not in start_points] # Generate all permutations of the remaining points end_permutations = permutations (remaining_points, n) # Generate all permutations of the remaining points end_permutations = permutations (remaining_points, n) for end points in end_permutations: # Check if all pairs (i_k, j_k) satisfy i_k < j_k if all(start_points[k] < end_points[k] for k in range(n)): arc_diagrams.append(list(zip(start_points, end_points))) return arc_diagrams
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
By modifying or using the function find_all_arc_diagrams(attached picture), write two functions find_all_non_crossing_arc_diagrams and find_all_non_nesting_arc_diagrams that return lists of all non-crossing and non-nesting arc diagrams, respectively.
![from itertools import permutations, combinations
def find_all_arc_diagrams (n):
points = list(range(2 * n))
arc_diagrams = []
# Generate all combinations of n starting points
start_combinations = combinations (points, n)
for start_points in start_combinations:
remaining points = [p for p in points if p not in start_points]
# Generate all permutations of the remaining points
end_permutations = permutations (remaining_points, n)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c2f7f07-719c-4ae4-a72e-e6030dfbcb8c%2Fad1ccb76-c80e-4013-b977-cb6c26c470df%2Fp1gzbv_processed.png&w=3840&q=75)
Transcribed Image Text:from itertools import permutations, combinations
def find_all_arc_diagrams (n):
points = list(range(2 * n))
arc_diagrams = []
# Generate all combinations of n starting points
start_combinations = combinations (points, n)
for start_points in start_combinations:
remaining points = [p for p in points if p not in start_points]
# Generate all permutations of the remaining points
end_permutations = permutations (remaining_points, n)
![# Generate all permutations of the remaining points
end_permutations = permutations (remaining_points, n)
for end points in end_permutations:
# Check if all pairs (i_k, j_k) satisfy i_k < j_k
if all(start_points[k] < end_points[k] for k in range(n)):
arc_diagrams.append(list(zip(start_points, end_points)))
return arc_diagrams](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c2f7f07-719c-4ae4-a72e-e6030dfbcb8c%2Fad1ccb76-c80e-4013-b977-cb6c26c470df%2Fy2u10ro_processed.png&w=3840&q=75)
Transcribed Image Text:# Generate all permutations of the remaining points
end_permutations = permutations (remaining_points, n)
for end points in end_permutations:
# Check if all pairs (i_k, j_k) satisfy i_k < j_k
if all(start_points[k] < end_points[k] for k in range(n)):
arc_diagrams.append(list(zip(start_points, end_points)))
return arc_diagrams
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