Give an efficient algorithm to compute the union of sets A and B, where n =...
Give an efficient algorithm to compute the union of sets
A and B, where n = max(|A|,
|B|). The
output should be an array of distinct elements that form the union
of the sets, such that they
appear exactly once in the union. Assume that A and
B are unsorted. Give an O(n log
n) time
algorithm for the problem.
Homework Answers
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Give an efficient algorithm to compute the union of sets
A and B, where n =...
Design an algorithm for the following description. Solution can be done in pseudo-code or steps of...
Design an algorithm for the following description. Solution can
be done in pseudo-code or steps of the algorithm.
Describe and analyze an algorithm that takes an unsorted array A of n integers (in an unbounded range) and an integer k, and divides A into k equal-sized groups, such that the integers in the first group are lower than the integers in the second group, and the integers in the second group are lower than the integers in the third group,...
Question3 10 pts Let A [L.n] be a max-heap with n > 1 and consider the index ị such that l 〈 i 〈 n . Assume that a...
Question3 10 pts Let A [L.n] be a max-heap with n > 1 and consider the index ị such that l 〈 i 〈 n . Assume that all the elements of A are distinct. Write the pseudocode of an algorithm which replaces A [i] by A i 100 and then re-arranges the elements of A into a max-heap. The running time of your algorithm must be O (log, n Upload Choose a File
Question3 10 pts Let A [L.n]...
ALGORITHM PROBLEM: A) Significant Inversions: We are given a sequence of n arbitrary but distinct real...
ALGORITHM PROBLEM: A) Significant Inversions: We are given a sequence of n arbitrary but distinct real numbers <a1 , a2 ,..., an>. We define a significant inversion to be a pair i < j such that ai > 2 aj . Design and analyze an O(n log n) time algorithm to count the number of significant inversions in the given sequence. [Hint: Use divide-&-conquer. Do the “combine” step carefully] B) The Maximum-Sum Monotone Sub-Array Problem: Input: An array A[1..n] of...
Given an unsorted array of distinct positive integers A [ 1......n ] in the range between...
Given an unsorted array of distinct positive integers A [ 1......n ] in the range between 1 and 10000 and an integer i in the sane range. Here n can be arbitrary large You want to find out whether there are 2 elements of the array that add up to i. Give an algorithm that runs in time (O(n).
Suppose you have two data sets, each of which contain n comparable elements. As an basic...
Suppose you have two data sets, each of which contain n comparable elements. As an basic operation, you may ask one set to tell you the kth largest element of that set, for a value k you choose. Give an algorithm that, with O(log n) queries, determines the median value of the union of the two sets.
Do problem 4-20: Give an efficient algorithm to rearrange an array of n keys so that...
Do problem 4-20: Give an efficient algorithm to rearrange an array of n keys so that all the negative keys precede all the nonnegative keys. Your algorithm must be in-place, meaning you cannot allocate another array to temporarily hold the items. How fast is your algorithm?
Please answer this in python pseudocode. It's an algorithm question. 1. [10 marks] Consider the function...
Please answer this in python
pseudocode. It's an algorithm question.
1. [10 marks] Consider the function SumKSmallest(A[0..n – 1), k) that returns the sum of the k smallest elements in an unsorted integer array A of size n. For example, given the array A=[6,-6,3,2,1,2,0,4,3,5] and k=3, the function should return -5. a. [3 marks) Write an algorithm in pseudocode for SumKSmallest using the brute force paradigm. Indicate and justify (within a few sentences) the time complexity of your algorithm. b....
Explain the space-time tradeoff implemented in efficient hash tables? b) Use hashing to design and algorithm...
Explain the space-time tradeoff implemented in efficient hash tables? b) Use hashing to design and algorithm to identify all duplicate elements in an array, e.g., for the following array [ “r6i”, “opd”, “r6i”, “ydg”, “x5s”, “pc1”, “tni”, “594”, “ wi5”, “ip0”, “vvj”, “oad”, “ydg”, “‘opd” ] the elements [“r6i”, “opd”, “ydg”] are duplicates. The time complexity of the algorithm must be O(n)
(a) Give the pseudo-code for a recursive algorithm called Find_Smallest(A, n) that returns the value of...
(a) Give the pseudo-code for a recursive algorithm called Find_Smallest(A, n) that returns the value of the smallest element in an array of n integers called A. Assume the elements in the array are at locations A[1]..A[n]. (b) Give a recurrence T(n) for the running time of your algorithm. (c) Solve the recurrence in part (b)
Consider the following pseudocode: Algorithm RecursiveFunction (a, b) // a and b are integers if (as1...
Consider the following pseudocode: Algorithm RecursiveFunction (a, b) // a and b are integers if (as1 ) return b; else return RecursiveFunction (a-2, a/2); endif a. What is the time complexity of the RecursiveFunction pseudocode shown above? b What is the space complexity of the RecursiveFunction pseudocode shown above? n(n+1) C. What is the time complexity of the following algorithm (Note that 21-, i = n(n+1)(2n+1). and Σ.,1 ): Provide both T(n) and order, Ofn)). int A=0; for (int i=0;i<n;i++)...
Design an algorithm for the following description. Solution can
be done in pseudo-code or steps of the algorithm.
Describe and analyze an algorithm that takes an unsorted array A of n integers (in an unbounded range) and an integer k, and divides A into k equal-sized groups, such that the integers in the first group are lower than the integers in the second group, and the integers in the second group are lower than the integers in the third group,...
Question3 10 pts Let A [L.n] be a max-heap with n > 1 and consider the index ị such that l 〈 i 〈 n . Assume that all the elements of A are distinct. Write the pseudocode of an algorithm which replaces A [i] by A i 100 and then re-arranges the elements of A into a max-heap. The running time of your algorithm must be O (log, n Upload Choose a File
Question3 10 pts Let A [L.n]...
Please answer this in python
pseudocode. It's an algorithm question.
1. [10 marks] Consider the function SumKSmallest(A[0..n – 1), k) that returns the sum of the k smallest elements in an unsorted integer array A of size n. For example, given the array A=[6,-6,3,2,1,2,0,4,3,5] and k=3, the function should return -5. a. [3 marks) Write an algorithm in pseudocode for SumKSmallest using the brute force paradigm. Indicate and justify (within a few sentences) the time complexity of your algorithm. b....
Consider the following pseudocode: Algorithm RecursiveFunction (a, b) // a and b are integers if (as1 ) return b; else return RecursiveFunction (a-2, a/2); endif a. What is the time complexity of the RecursiveFunction pseudocode shown above? b What is the space complexity of the RecursiveFunction pseudocode shown above? n(n+1) C. What is the time complexity of the following algorithm (Note that 21-, i = n(n+1)(2n+1). and Σ.,1 ): Provide both T(n) and order, Ofn)). int A=0; for (int i=0;i<n;i++)...
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