In this task, you will implement a recursive function all_perm(n: int) -> set[tuple[int, that takes an integer n> 0 and returns a set containing all the permutations of 1,2,3,..., n. Each per- mutation must be represented as a tuple. For example: • all_perm(1) all_perm(2) • all_perm(3) {(1,)} == {(1,2), (2,1)} == {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)} == Restrictions: Do not write a helper function. Your function must be recursive, and must work with sets and tuples directly. You are not allowed to import anything. Hints: Consider how we can use all_perm(2) to create the answer for all_perm(3). Perhaps the following diagram will help (pay close attention to the color coding and numbers in boldface fonts): all_perm(2) == {(1,2), (2, 1)} all_perm(3) == {(3,1,2), (1,3,2), (1,2,3), (3,2, 1), (2,3, 1), (2, 1,3)} all_perm(4) == {(4,3,1,2), (3,4,1,2), (3, 1, 4, 2), (3, 1,2,4), (4, 1,3,2), (1,4,3,2), (1,3,4,2), (1,3,2,4), (4, 1,2,3), (1,4,2,3), (1,2,4,3), (1,2,3,4), (4,3,2, 1), (3,4,2, 1), (3,2, 4, 1), (3,2,1,4), (4, 2,3, 1), (2, 4,3, 1), (2,3, 4, 1), (2, 3, 1,4), (4,2, 1,3), (2,4, 1,3), (2, 1,4, 3), (2, 1,3,4)}
In this task, you will implement a recursive function all_perm(n: int) -> set[tuple[int, that takes an integer n> 0 and returns a set containing all the permutations of 1,2,3,..., n. Each per- mutation must be represented as a tuple. For example: • all_perm(1) all_perm(2) • all_perm(3) {(1,)} == {(1,2), (2,1)} == {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)} == Restrictions: Do not write a helper function. Your function must be recursive, and must work with sets and tuples directly. You are not allowed to import anything. Hints: Consider how we can use all_perm(2) to create the answer for all_perm(3). Perhaps the following diagram will help (pay close attention to the color coding and numbers in boldface fonts): all_perm(2) == {(1,2), (2, 1)} all_perm(3) == {(3,1,2), (1,3,2), (1,2,3), (3,2, 1), (2,3, 1), (2, 1,3)} all_perm(4) == {(4,3,1,2), (3,4,1,2), (3, 1, 4, 2), (3, 1,2,4), (4, 1,3,2), (1,4,3,2), (1,3,4,2), (1,3,2,4), (4, 1,2,3), (1,4,2,3), (1,2,4,3), (1,2,3,4), (4,3,2, 1), (3,4,2, 1), (3,2, 4, 1), (3,2,1,4), (4, 2,3, 1), (2, 4,3, 1), (2,3, 4, 1), (2, 3, 1,4), (4,2, 1,3), (2,4, 1,3), (2, 1,4, 3), (2, 1,3,4)}
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with python
![In this task, you will implement a recursive function all_perm(n: int) -> set[tuple[int, ...]]
that takes an integer n> 0 and returns a set containing all the permutations of 1,2,3,..., n. Each per-
mutation must be represented as a tuple. For example:
• all_perm(1)
• all_perm(2)
• all_perm(3)
{(1,)}
{(1,2), (2,1)}
==
{(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)}
%3D%3D
Restrictions: Do not write a helper function. Your function must be recursive, and must work with
sets and tuples directly. You are not allowed to import anything.
Hints: Consider how we can use all_perm(2) to create the answer for all_perm(3). Perhaps the
following diagram will help (pay close attention to the color coding and numbers in boldface fonts):
all_perm(2) == {(1,2), (2,1)}
all_perm(3) == {(3,1,2), (1,3,2), (1,2,3), (3,2,1), (2,3, 1), (2,1,3)}
all_perm(4) == {(4,3,1,2), (3,4, 1,2), (3, 1, 4, 2), (3, 1,2, 4),
(4, 1,3,2), (1,4,3, 2), (1,3,4,2), (1,3,2,4),
(4, 1,2,3), (1,4,2,3), (1,2,4,3), (1,2,3,4),
(4,3,2, 1), (3, 4, 2, 1), (3,2, 4, 1), (3,2, 1,4),
(4,2,3, 1), (2, 4, 3, 1), (2,3, 4, 1), (2,3,1,4),
(4,2, 1,3), (2,4, 1,3), (2,1,4, 3), (2,1,3,4)}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6954e458-8753-495c-94b2-cdcc9bbfd17e%2Fb1f8157f-6000-484c-b00e-53aa4b7e6c38%2Fl0sy5x_processed.png&w=3840&q=75)
Transcribed Image Text:In this task, you will implement a recursive function all_perm(n: int) -> set[tuple[int, ...]]
that takes an integer n> 0 and returns a set containing all the permutations of 1,2,3,..., n. Each per-
mutation must be represented as a tuple. For example:
• all_perm(1)
• all_perm(2)
• all_perm(3)
{(1,)}
{(1,2), (2,1)}
==
{(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)}
%3D%3D
Restrictions: Do not write a helper function. Your function must be recursive, and must work with
sets and tuples directly. You are not allowed to import anything.
Hints: Consider how we can use all_perm(2) to create the answer for all_perm(3). Perhaps the
following diagram will help (pay close attention to the color coding and numbers in boldface fonts):
all_perm(2) == {(1,2), (2,1)}
all_perm(3) == {(3,1,2), (1,3,2), (1,2,3), (3,2,1), (2,3, 1), (2,1,3)}
all_perm(4) == {(4,3,1,2), (3,4, 1,2), (3, 1, 4, 2), (3, 1,2, 4),
(4, 1,3,2), (1,4,3, 2), (1,3,4,2), (1,3,2,4),
(4, 1,2,3), (1,4,2,3), (1,2,4,3), (1,2,3,4),
(4,3,2, 1), (3, 4, 2, 1), (3,2, 4, 1), (3,2, 1,4),
(4,2,3, 1), (2, 4, 3, 1), (2,3, 4, 1), (2,3,1,4),
(4,2, 1,3), (2,4, 1,3), (2,1,4, 3), (2,1,3,4)}
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