Give an algorithm to determine whether or not the elements of an array of integers are...
Give an algorithm to determine whether or not the elements of
an array of integers are all unique. Argue that your algorithm is correct, and
that it terminates (doesn’t run forever). Give best and worst case run-time
analyses. That is, what are big-O and big-Omega for your algorithm?
Homework Answers
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Give an algorithm to determine whether or not the elements
of
an array of integers are...
Write a function to sort an array of integers and also determine and explain the worst...
Write a function to sort an array of integers and also determine and explain the worst case complexity (Big O notation) of your algorithm. (You may NOT use Collections.sort)
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark...
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...
The input is an array of N integers ( sorted ) and an integer X. The...
The input is an array of N integers ( sorted ) and an integer X. The algorithm returns true if X is in the array and false if X is not in the array. Describe an algorithm that solves the problem with a worst case of O(log N) time.
Computer Algorithm question 8) Give an algorithm for building a heap in O(n) 9) Prove the...
Computer Algorithm question
8) Give an algorithm for building a heap in O(n)
9) Prove the algorithm given in 8) runs in O(n) time.
10) What is the asymptotic runtime of an algorithm represented
by the following recurrence equation?
11) Suppose you have the following priority queue implemented as a (max) heap. What will the heap look like when the max node is removed and the heap is readjusted? Assume on each heapify operation the largest child node is selected...
Question 4 6 points You have to design an algorithm that verify if an array contains...
Question 4 6 points You have to design an algorithm that verify if an array contains duplicate values. This algorithm simply returns true as soon as two identical values are found. To perform this task you must not change the order of the elements in the array (so you cannot sort it) or use an auxiliary array. Write the pseudo-code of this algorithm and give the Big-2 complexity in the worst case.
For each problems segment given below, do the following: Create an algorithm to solve the problem...
For each problems segment given below, do the following: Create an algorithm to solve the problem Identify the factors that would influence the running time, and which can be known before the algorithm or code is executed. Assign names (such as n) to each factor. Identify the operations that must be counted. You need not count every statement separately. If a group of statements always executes together, treat the group as a single unit. If a method is called, and...
6. Let T(1..n] be a sorted array of distinct integers, some of which may be negative....
6. Let T(1..n] be a sorted array of distinct integers, some of which may be negative. Give an algorithm that can find an index i such that 1 <i<n and T[i] = i, provided such an index exists. Your algorithm should take a time in O(lg n) in the worst case. Answers must be proven (or at least well justified)
(d) Consider an algorithm A, whose runtime is dependent on some "size" variable n of the...
(d) Consider an algorithm A, whose runtime is dependent on some "size" variable n of the input. Explain the difference between the two statements below, and give an explicit example of an algorithm for which one statement is true but the other is false. 1. The worst case time complexity of A is n2. 2. A is O(n). (e) Give an example of an algorithm (with a clear input type) which has a Big-Oh (0) and Big-Omega (12) bound on...
Selection Sort is a common algorithm to sort the elements of an array. First, it scans...
Selection Sort is a common algorithm to sort the elements of an array. First, it scans the elements of the array to find the smallest value and places it at index 0, thus creating a sorted “subarray” of size 1 that contains the smallest value. Then it scans the remaining unsorted values for the new smallest value and places it at index 1, creating a sorted subarray of size 2 that contains the 2 smallest values. It continues in this...
Given two arrays A and B of n integers both of which are sorted in ascending...
Given two arrays A and B of n integers both of which are sorted in ascending order. Write an algorithm to check whether or not A and B have an element in common. Find the worst case number of array element comparisons done by this algorithm as a function of n and its Big-O complexity
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...
Computer Algorithm question
8) Give an algorithm for building a heap in O(n)
9) Prove the algorithm given in 8) runs in O(n) time.
10) What is the asymptotic runtime of an algorithm represented
by the following recurrence equation?
11) Suppose you have the following priority queue implemented as a (max) heap. What will the heap look like when the max node is removed and the heap is readjusted? Assume on each heapify operation the largest child node is selected...
Question 4 6 points You have to design an algorithm that verify if an array contains duplicate values. This algorithm simply returns true as soon as two identical values are found. To perform this task you must not change the order of the elements in the array (so you cannot sort it) or use an auxiliary array. Write the pseudo-code of this algorithm and give the Big-2 complexity in the worst case.
For each problems segment given below, do the following: Create an algorithm to solve the problem Identify the factors that would influence the running time, and which can be known before the algorithm or code is executed. Assign names (such as n) to each factor. Identify the operations that must be counted. You need not count every statement separately. If a group of statements always executes together, treat the group as a single unit. If a method is called, and...
6. Let T(1..n] be a sorted array of distinct integers, some of which may be negative. Give an algorithm that can find an index i such that 1 <i<n and T[i] = i, provided such an index exists. Your algorithm should take a time in O(lg n) in the worst case. Answers must be proven (or at least well justified)
(d) Consider an algorithm A, whose runtime is dependent on some "size" variable n of the input. Explain the difference between the two statements below, and give an explicit example of an algorithm for which one statement is true but the other is false. 1. The worst case time complexity of A is n2. 2. A is O(n). (e) Give an example of an algorithm (with a clear input type) which has a Big-Oh (0) and Big-Omega (12) bound on...
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