Homework Answers
In hashing we will first create hash function and then we will compute hash value for all the elements which involves O(n) complexity and then each element will compare against the hash values if there is only one match for all the elements are distinct and it involves O(n)
total complexity is O(n+n) == O(n)
for brute force algorithm it takes complexity of O(n^n);
for pre-sorting algorithm it takes complexity of O(nlogn);// because it involves sorting and then binary search
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thoblerm 1: (25 pts) Explain how the time efficieney of this a to use hashing to...
a. Use pseudocode to specify a brute-force algorithm that takes as input a list of n...
a. Use pseudocode to specify a brute-force algorithm that takes as input a list of n positive integers and determines whether there are two distinct elements of the list that have as their sum a third element of the list. That is, whether there exists i, j.k such that iヂj, i关k,j关k and ai + aj = ak. The algorithm should loop through all triples of elements of the list checking whether the sum of the first two is the third...
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)
1. Let A = {a1, ..., an} and B = {b1, ..., bm} be two sets...
1. Let A = {a1, ..., an} and B = {b1, ..., bm} be two sets of numbers. Consider the problem of finding their intersection, i.e., the set C of all the numbers that are in both A and B. a. Design a presorting based algorithm for solving this problem and determine its efficiency class. 2. Estimate how many searches will be needed to justify time spent on presorting an array of 103 elements if sorting is done by mergesort...
Subject: Algorithm. solve only part 3 and 4 please. 2.2 Selection- 5 points each 1. Run the simultaneous min-and-max algorithm on the array A 4, 2, 12, 6, 13,9,15). (16, 7, 10, 1,5, 11,3,8, 14, 2....
Subject: Algorithm.
solve only part 3 and 4 please.
2.2 Selection- 5 points each 1. Run the simultaneous min-and-max algorithm on the array A 4, 2, 12, 6, 13,9,15). (16, 7, 10, 1,5, 11,3,8, 14, 2. Explain why the above algorithm is better than the naive algorithm for finding minimum and maximum separately. How many comparisons does the naive algorithm do? How many comparisons does the simultaneous min and max do? 3. Use the randomized select algorithm based on partition...
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]...
problem 2 can use Det-Selection(A, p, q, r) as a sub-routine (i.e, you don't need to...
problem 2
can use Det-Selection(A, p, q, r) as a sub-routine (i.e, you don't need to write its pseudo-code). To sort an array A, you will then call Det-QuickSort(A, 1, n). You also need to provide the worst case time complexity analysis of your algorithm. 2. (20 points) Given a set of n distinct numbers, we wish to find the k largest in sorted order using a comparison-based algorithm. Give an algorithm that implements each of the following methods, and...
Exercise 3 (2 pts). Consider the following decision problem: Given a list of integers, deter- mine...
Exercise 3 (2 pts). Consider the following decision problem: Given a list of integers, deter- mine whether all elements of the list are distinct. Is this problem in P? Yes, no, unknown? Justify your answer (if your answer is "yes", briefly describe a polynomial-time algorith)
1. State and explain the definition of big-O. 2. Explain why we use big-O to compare...
1. State and explain the definition of big-O. 2. Explain why we use big-O to compare algorithms. 3. Explain why binary search runs in O(log n) time. 4. Under what conditions is it possible to sort a list in less than O(nlog n) time? 5. List and explain the worst-case and average-case running times for each Vector method below: (a) insert(iterator here, Object item) (b) insertAtHead (c) insertAtTail (aka push back) (d) get(iterator here) (e) get(index i) (f) remove(iterator here)...
2. Here is a sorting algorithm that I like to use. Given an unsorted list of...
2. Here is a sorting algorithm that I like to use. Given an unsorted list of size n, let Xx represent the data in location k of the unsorted list. Compare xi to X2 and switch if necessary so that they are in sorted order, smallest first. Compare Xn-1 and Xn and switch if necessary so that they are in sorted order, smallest first. • Compare x3 with its left neighbors, switching if necessary so that the 3 first entries...
a. Use pseudocode to specify a brute-force algorithm that takes as input a list of n positive integers and determines whether there are two distinct elements of the list that have as their sum a third element of the list. That is, whether there exists i, j.k such that iヂj, i关k,j关k and ai + aj = ak. The algorithm should loop through all triples of elements of the list checking whether the sum of the first two is the third...
Subject: Algorithm.
solve only part 3 and 4 please.
2.2 Selection- 5 points each 1. Run the simultaneous min-and-max algorithm on the array A 4, 2, 12, 6, 13,9,15). (16, 7, 10, 1,5, 11,3,8, 14, 2. Explain why the above algorithm is better than the naive algorithm for finding minimum and maximum separately. How many comparisons does the naive algorithm do? How many comparisons does the simultaneous min and max do? 3. Use the randomized select algorithm based on partition...
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]...
problem 2
can use Det-Selection(A, p, q, r) as a sub-routine (i.e, you don't need to write its pseudo-code). To sort an array A, you will then call Det-QuickSort(A, 1, n). You also need to provide the worst case time complexity analysis of your algorithm. 2. (20 points) Given a set of n distinct numbers, we wish to find the k largest in sorted order using a comparison-based algorithm. Give an algorithm that implements each of the following methods, and...
Exercise 3 (2 pts). Consider the following decision problem: Given a list of integers, deter- mine whether all elements of the list are distinct. Is this problem in P? Yes, no, unknown? Justify your answer (if your answer is "yes", briefly describe a polynomial-time algorith)
2. Here is a sorting algorithm that I like to use. Given an unsorted list of size n, let Xx represent the data in location k of the unsorted list. Compare xi to X2 and switch if necessary so that they are in sorted order, smallest first. Compare Xn-1 and Xn and switch if necessary so that they are in sorted order, smallest first. • Compare x3 with its left neighbors, switching if necessary so that the 3 first entries...
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