Binary Search (Ternary Search)
Ternary Search is a generalization of Binary Search that can be used to find an element in an array. Itdivides the array withnelements into three parts and determines, with two comparisons, which partmay contain the value we are searching for. For instance, initially, the array is divided into three thirdsby taking mid1=(n−1)/3 and mid2=((2(n−1))/3. Write a recurrence for the running time of Ternary Search and solve this recurrence.
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Consider an ordered array A of size n and the following ternary search algorithm for finding...
Consider an ordered array A of size n and the following ternary search algorithm for finding the index i such that A[i] = K. Divide the array into three parts. If A[n/3] > K. the first third of the array is searched recursively, else if A[2n/3] > K then the middle part of the array is searched recursively, else the last thud of the array is searched recursively. Provisions are also made in the algorithm to return n/3 if A[n/3]...
Write the recurrence equation for ternary search and solve it.
Write the recurrence equation for the Worst Case complexity function for TernarySearch (counting 4 comparisons per recursive call, and assuming W(1) = 1) and solve thisequation. You may assume that n is a power of 3.
Binary Search
Suppose we want to check if a sorted sequence A contains an element v. For this, we can use Binary Search. Binary Search compares the value at the midpoint of the sequence A with v and eliminates half of the sequence from further consideration. The Binary Search algorithm repeats this procedure, halving the size of the remaining portion of the sequence each time. Write a recurrence for the runningtime of Binary search and solve this recurrence.
We know that binary search on a sorted array of size n takes O(log n) time....
We know that binary search on a sorted array of size n takes O(log n) time. Design a similar divide-and-conquer algorithm for searching in a sorted singly linked list of size n. Describe the steps of your algorithm in plain English. Write a recurrence equation for the runtime complexity. Solve the equation by the master theorem.
Suppose that, even unrealistically, we are to search a list of 700 million items using Binary...
Suppose that, even unrealistically, we are to search a list of
700 million items using Binary Search, Recursive (Algorithm 2.1).
What is the maximum number of comparisons that this algorithm must
perform before finding a given item or concluding that it is not in
the list
“Suppose that, in a divide-and-conquer algorithm, we always
divide an instance of size n of a problem into n subinstances of
size n/3, and the dividing and combining steps take linear time.
Write a...
The purpose of this assignment is to familiarize you with sort algorithms. Problem Description is as follows: 8. Search Benchmarks Write a program that has at least 20 250 integers stored in an ar...
The purpose of this assignment is to familiarize you with sort algorithms. Problem Description is as follows: 8. Search Benchmarks Write a program that has at least 20 250 integers stored in an array in ascending order. It should call a function that uses the linear search algorithm to locate one of the values. The function should keep a count of the number of comparisons it makes until it finds the value. The program then should call a function that...
What is the maximum number of comparisons made when searching a 60 element array with Binary...
What is the maximum number of comparisons made when searching a 60 element array with Binary Search? 60 30 5 6 Question 3 (3 points) What is the average number of comparisons made when searching a 60 element array with Linear Search? 06 5 A selection sort algorithm is used to sort an array containing the following values into ascending order. Give the order of the elements after each pass of the sorting algorithm. 6 4 7 2 3 5...
The purpose of this assignment is to familiarize you with sort algorithms. Problem Description is as follows: 8. Search Benchmarks Write a program that has at least 20 250 integers stored in an ar...
The purpose of this assignment is to familiarize you with sort algorithms. Problem Description is as follows: 8. Search Benchmarks Write a program that has at least 20 250 integers stored in an array in ascending order. It should call a function that uses the linear search algorithm to locate one of the values. The function should keep a count of the number of comparisons it makes until it finds the value. The program then should call a function that...
Searching/sorting tasks and efficiency analysis - Binary Search Search for the character S using the binary...
Searching/sorting tasks and efficiency analysis - Binary Search Search for the character S using the binary search algorithm on the following array of characters: A E G K M O R S Z. For each iteration of binary search use a table similar to the table below to list: (a) the left index and (b) the right index of the array that denote the region of the array that is still being searched, (c) the middle point of the array,...
1. Randomized Binary Search Which are true of the randomized Binary Search algorithm? Multiple answers:You can...
1. Randomized Binary Search Which are true of the randomized Binary Search algorithm? Multiple answers:You can select more than one option A) It uses a Variable-Size Decrease-and-Conquer design technique B) Its average case time complexity is Θ(log n) C) Its worst case time complexity is Θ(n) D) It can be implemented iteratively or recursively E) None of the above 2. Randomized Binary Search: Example Assume you have an array, indexed from 0 to 9, with the numbers 1 4 9...
Consider an ordered array A of size n and the following ternary search algorithm for finding the index i such that A[i] = K. Divide the array into three parts. If A[n/3] > K. the first third of the array is searched recursively, else if A[2n/3] > K then the middle part of the array is searched recursively, else the last thud of the array is searched recursively. Provisions are also made in the algorithm to return n/3 if A[n/3]...
Suppose that, even unrealistically, we are to search a list of
700 million items using Binary Search, Recursive (Algorithm 2.1).
What is the maximum number of comparisons that this algorithm must
perform before finding a given item or concluding that it is not in
the list
“Suppose that, in a divide-and-conquer algorithm, we always
divide an instance of size n of a problem into n subinstances of
size n/3, and the dividing and combining steps take linear time.
Write a...
What is the maximum number of comparisons made when searching a 60 element array with Binary Search? 60 30 5 6 Question 3 (3 points) What is the average number of comparisons made when searching a 60 element array with Linear Search? 06 5 A selection sort algorithm is used to sort an array containing the following values into ascending order. Give the order of the elements after each pass of the sorting algorithm. 6 4 7 2 3 5...
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