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 1 year 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...

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.

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.

Consider the following recursive algorithm for computing the sum of the first n squares: S(n) =...

Consider the following recursive algorithm for computing the sum of the first n squares: S(n) = 12 +22 +32 +...+n2 . Algorithm S(n) //Input: A positive integer n //Output: The sum of the first n squares if n = 1 return 1 else return S(n − 1) + n* n a. Set up and solve a recurrence relation for the number of times the algorithm’s basic operation is executed. b. How does this algorithm compare with the straightforward non-recursive algorithm...

Give pseudocode for a recursive function that sorts all letters in a string. For example, the...

Give pseudocode for a recursive function that sorts all letters in a string. For example, the string "goodbye" would be sorted into "bdegooy". Java

Give pseudocode for a recursive function that sorts all letters in a string. For example, the...

Give pseudocode for a recursive function that sorts all letters in a string. For example, the string "goodbye" would be sorted into "bdegooy". Python

write a recursive method that returns the product of all elements in java linked list

Recall the Matrix-Multiplication Algorithm for determining all-pairs distances in a graph. Provide a linear-time recursive implementation...

Recall the Matrix-Multiplication Algorithm for determining all-pairs distances in a graph. Provide a linear-time recursive implementation of the function void print_path(Matrix D[], int n, int i, int j); that takes as input the array of matrices D[1], D[2], . . . , D[n − 1] that have been computed by the algorithm, and prints the optimal path from vertex i to vertex j. Hint: for convenience you may use the notation Dr ij to denote the value D[r][i, j], i.e....

PYTHON: Write a recursive function named linear_search that searches a list to find a given element....

PYTHON: Write a recursive function named linear_search that searches a list to find a given element. If the element is in the list, the function returns the index of the first instance of the element, otherwise it returns -1000. Sample Output >> linear_search(72, [10, 32, 83, 2, 72, 100, 32]) 4 >> linear_search(32, [10, 32, 83, 2, 72, 100, 32]) 1 >> linear_search(0, [10, 32, 83, 2, 72, 100, 32]) -1000 >> linear_search('a', ['c', 'a', 'l', 'i', 'f', 'o', 'r',...

Subjects