As you know from Discrete Math, a permutation is any possible ordering of the distinct items of a set S. If |S| = n, there are n! permutations. This means that for large sets, it is computationally infeasible to generate all possible permutations. One well-known algorithm for generating set permutations (at least for small sets) is presented below: ALGORITHM Johnson-Trotter(n) // Input: a positive integer n // Output: A list of all permutations of {1, 2, ..., n} initialize the first permutation as 1 2 ... n with directions pointing left while the last permutation has a mobile element find its largest mobile element k swap k and the element to which k is directed reverse the direction of all elements that are larger than k add the new permutation to the list Note: an element is mobile if its direction points to a smaller adjacent element. Example: 1 2 3 13 2 3 1 2 3 2 1 2 3 1 2 1 3 REQUIREMENTS: Design and implement a program to generate all permutations of the set of least n positive integers. INPUT: an integer n with 1 < n < 25. OUTPUT: The tag "There are x permutations of the set {1, 2, ..., n}:", where x = n! a list of all permutations of the set {1, 2, n}, one per line. .... EXAMPLE OUTPUT:
As you know from Discrete Math, a permutation is any possible ordering of the distinct items of a set S. If |S| = n, there are n! permutations. This means that for large sets, it is computationally infeasible to generate all possible permutations. One well-known algorithm for generating set permutations (at least for small sets) is presented below: ALGORITHM Johnson-Trotter(n) // Input: a positive integer n // Output: A list of all permutations of {1, 2, ..., n} initialize the first permutation as 1 2 ... n with directions pointing left while the last permutation has a mobile element find its largest mobile element k swap k and the element to which k is directed reverse the direction of all elements that are larger than k add the new permutation to the list Note: an element is mobile if its direction points to a smaller adjacent element. Example: 1 2 3 13 2 3 1 2 3 2 1 2 3 1 2 1 3 REQUIREMENTS: Design and implement a program to generate all permutations of the set of least n positive integers. INPUT: an integer n with 1 < n < 25. OUTPUT: The tag "There are x permutations of the set {1, 2, ..., n}:", where x = n! a list of all permutations of the set {1, 2, n}, one per line. .... EXAMPLE OUTPUT:
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Transcribed Image Text:As you know from Discrete Math, a permutation is any possible ordering of the distinct
items of a set S. If |S| = n, there are n! permutations. This means that for large sets, it is
computationally infeasible to generate all possible permutations. One well-known
algorithm for generating set permutations (at least for small sets) is presented below:
ALGORITHM Johnson-Trotter(n)
// Input: a positive integer n
// Output: A list of all permutations of {1, 2, ..., n}
initialize the first permutation as 1 2
while the last permutation has a mobile element
find its largest mobile element k
swap k and the element to which k is directed
reverse the direction of all elements that are larger than k
add the new permutation to the list
n with directions pointing left
Note: an element is mobile if its direction points to a smaller adjacent element.
Example:
1 2 3
1 3 2
3 1 2
3 2 1
2 3 1
2 1 3
REQUIREMENTS:
Design and implement a program to generate all permutations of the set of least n
positive integers.
INPUT:
an integer n with 1 < n< 25.
OUTPUT:
The tag "There are x permutations of the set {1, 2, ..., n}:", where x = n!
a list of all permutations of the set {1, 2,
n}, one per line.
...
EXAMPLE OUTPUT:
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