Question

In: Advanced Math

Give a recursive algorithm to compute a list of all permutations of a given set S....

Give a recursive algorithm to compute a list of all permutations of a given set S. (That is, compute a list of all possible orderings of the elements of S. For example, permutations({1, 2, 3}) should return {〈1, 2, 3〉, 〈1, 3, 2〉, 〈2, 1, 3〉, 〈2, 3, 1〉, 〈3, 1, 2〉, 〈3, 2, 1〉}, in some order.)

Prove your algorithm correct by induction.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Write a recursive algorithm in pseudo-code to compute the “power list” of a given list of...
Write a recursive algorithm in pseudo-code to compute the “power list” of a given list of integers. Assume that the List type has members: int List.length returns the length of the list. void List.push(T n) pushes an element n to the front of the list T List.pop() pops an element from the front of the list. List$$ List$$.concat(List$$ other) returns the concatenation of this list with other. Explain in plain English the reasoning behind your algorithm. Power Lists should be...
2. Give a recursive algorithm to compute the product of two positive integers, m and n,...
2. Give a recursive algorithm to compute the product of two positive integers, m and n, using only addition and subtraction. Java Language...
Given a stack S and an element x, write a recursive algorithm that returns True if...
Given a stack S and an element x, write a recursive algorithm that returns True if x is in S, or False otherwise. Note that your algorithm should not change the content in S. What is the time complexity of your algorithm?
Given a stack S and an element x, write a recursive algorithm that returns True if...
Given a stack S and an element x, write a recursive algorithm that returns True if x is in S, or False otherwise. Note that your algorithm should not change the content in S. What is the time complexity of your algorithm?
Consider the recursive formulation of the Binary Search algorithm. Given a sorted and non-decreasing list of...
Consider the recursive formulation of the Binary Search algorithm. Given a sorted and non-decreasing list of comparable objects L, and a new item x, find the location (index) of x or indicated that x is not in L. 5a) Give a recursive algorithm for binary search. No, while, for, repeat etc statements are allowed. Only if, if else and assignment statements are allowed. 5b) Write a difference equation for the running time of your Binary Search algorithm. Solve your equation...
Use java .Given a stack S and an element x, write a recursive algorithm that returns...
Use java .Given a stack S and an element x, write a recursive algorithm that returns True if x is in S, or False otherwise. Note that your algorithm should not change the content in S. What is the time complexity of your algorithm?
Use Recursive Algorithm to compute 5^23 Mod 8
Use Recursive Algorithm to compute 5^23 Mod 8
Give a recursive algorithm to solve the following recursive function. f(0) = 0;    f(1) = 1;...
Give a recursive algorithm to solve the following recursive function. f(0) = 0;    f(1) = 1;   f(2) = 4; f(n) = 2 f(n-1) - f(n-2) + 2; n > 2 b) Solve f(n) as a function of n using the methodology used in class for Homogenous Equations. Must solve for the constants as well as the initial conditions are given.
Generate all permutations of {3, 8, 2} by the Johnson-Trotter algorithm. Show the steps.
Generate all permutations of {3, 8, 2} by the Johnson-Trotter algorithm. Show the steps.
Let S be a non-empty set (finite or otherwise) and Σ the group of permutations on...
Let S be a non-empty set (finite or otherwise) and Σ the group of permutations on S. Suppose ∼ is an equivalence relation on S. Prove (a) {ρ ∈ Σ : x ∼ ρ(x) (∀x ∈ S)} is a subgroup of Σ. (b) The elements ρ ∈ Σ for which, for every x and y in S, ρ(x) ∼ ρ(y) if and only if x ∼ y is a subgroup of Σ.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT