For this task, save your work in allperm.py Remember the set data type? Well, you can look it up in Python's documentation. 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) == {(1,)} • all_perm (2) == {(1,2), (2,1)} • all perm(3) == {(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)}
For this task, save your work in allperm.py Remember the set data type? Well, you can look it up in Python's documentation. 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) == {(1,)} • all_perm (2) == {(1,2), (2,1)} • all perm(3) == {(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)}
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
![For this task, save your work in allperm.py
Remember the set data type? Well, you can look it up in Python's documentation.
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) == {(1,)}
• all_perm(2)
• all_perm (3) == {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)}
=
{(1,2), (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)}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28e2e603-ecab-45a4-8f55-ede3fe263a81%2F25b24ea0-136f-43da-bfe5-7c20a3f386d7%2Fkmtzf2_processed.png&w=3840&q=75)
Transcribed Image Text:For this task, save your work in allperm.py
Remember the set data type? Well, you can look it up in Python's documentation.
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) == {(1,)}
• all_perm(2)
• all_perm (3) == {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)}
=
{(1,2), (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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