9. Consider the following algorithm for finding the distance between the two closest elements in an array of numbers.
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#9
![Introduction
17
8. Give an example of a problem other than computing the greatest common
divisor for which you know more than one algorithm. Which of them is
simpler? Which is more efficient?
9. Consider the following algorithm for finding the distance between the two
closest elements in an array of numbers.
ALGORITHM MinDistance (A[0..n-1])
Input: Array A[0..n - 1] of numbers
//Output: Minimum distance between two of its elements
dmin <o
for i 0 to n - 1 do
-0
for j←0 to n - 1 do
return dmin
AL
if i ‡ j and \A[i] – A[j] <dmin
dmin A[i]- A[j]|
Make as many improvements as you can in this algorithmic solution to the
problem. If you need to, you may change the algorithm altogether; if not,
improve the implementation given.
Find
10. One of the most influential books on problem solving, titled How To Solve
It [Pol57], was written by the Hungarian-American mathematician George
Pólya (1887-1985). Pólya summarized his ideas in a four-point summary.
the plan outlined in Sectio
this summary on the Internet or, better yet. in his book and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26fe8f9d-a829-4ffe-94fa-74d9058056a0%2Fbf0dc606-4f97-4daa-b18e-4b8f12ef78c7%2F6utajnm_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps
- IN JAVA Exploration: Test the sorting algorithms as follows. For input sizes n = 500, n = 1,000, n = 1,500, …, n = 10,000 [That’s 20 different values of n]. For each n, create an array I of size n. Fill the array with n random integers. Create a copy M of the array I. Pass the array I to your insertion sort and record the number of comparisons. Pass the array M to your mergesort and record the number of comparisons.A) Starting with a dynamic array of length = 32 and numElements = 30, the length after we execute 90 insert at end operations is [answer]Group of answer choices 120 122 128 none of the above B) In each of the following cases, we start with a dynamic array of length = 128 and numElements = 64. After we execute 30 delete last operations, the number of elements isand the length isAfter we execute 32 delete last operations, the number of elements isand the length isAfter we execute 60 delete last operations, the number of elements isand the length is no hand written1. Consider a problem of computing the prefix average of a sequence of numbers stored in an array P consisting of P integers. We want to compute an array P such that P is the average of P for P . Consider the two algorithms related to the above problem. Answer the questions given below
- Given an integer array [A], efficiently find a descending sorted triplet such that: A[i]> A[i]> A[k] and 0 <=i<j <k <n, where n is the array size. For example, Input: A[] = {9, 1, 6, 7, 3, 4, 5) Output: Any one of the following triplets: (9, 7,5) (9, 7, 4) (9, 7, 3) (9, 6, 5) (9, 6, 4) (9, 6, 3) a) Design a brute-force algorithm to solve this problem complexity of your solution b) Design a more efficient algorithm to do the same task with less complexity and analyse the complexity of your solution. c) Develop a python code to implement your efficient algorithm. depend on the correctness of the code, indentation, comments, test-case] d) Prepare a brief report (250 words) comparing the two algorithmsLet A and B be two arrays of length n, each containing a random permutation of the numbers from 1 to n. An inversion between the two permutations A and B is a pair of values (x, y) where the index of x is less than the index of y in array A, but the index of x is more than the index of y in array B. Design an algorithm which counts the total number of inversions between A and B that runs in O(n log n) time.Euclid’s algorithm (or the Euclidean algorithm) is an algorithm that computes thegreatest common divisor, denoted by gcd, of two integers. Below are the original versions ofEuclid’s algorithm that uses repeated subtraction and another one that uses the remainder.int gcd_sub(int a, int b){ if (!a) return b; while (b) if (a > b) a = a – b; else b = b – a; return a;}int gcd_rem(int a, int b){ int t; while (b) { t = b; b = a % b; a = t; } return a;}1. Trace each of the above algorithm using specific values for a and b.2. Compare both algorithms.
- 1. Consider the algorithm for the sorting problem that sorts an array by counting,for each of its elements, the number of smaller elements and then uses thisinformation to put the element in its appropriate position in the sorted array:ALGORITHMComparisonCountingSort(A[0..n − 1])//Sorts an array by comparison counting//Input: Array A[0..n//Output: Array S[0..n− 1] of orderable values− 1] of A’s elements sorted// in nondecreasing orderfor i ← 0 to nCount− 1 do[i]←0for i ← 0 to n − 2 dofor j ← i +1 to n − 1 doif A[i] < A[j ]Count[j ]← Count[j ] + 1else Count[i]← Count[i] + 1for i ←0 to n−1 doS[Count[i]]←A[i]return Sa. Apply this algorithm to sorting the list 60, 35, 81, 98, 14, 47.b. Is this algorithm stable?c. Is it in-place?a. Write a version of the sequential search algorithm that can be used to search a sorted list. (1, 2) b. Consider the following list: 2, 20, 38, 41, 49, 56, 62, 70, 88, 95, 100, 135, 145 Using a sequential search on ordered lists, that you designed in (a), how many comparisons are required to determine whether the following items are in the list? (Recall that comparisons mean item comparisons, not index comparisons.) (1, 2) 2 57 88 70 135 Write a program to test the function you designed. Note: Have the function,seqOrdSearch, return -1 if the item is not found in the list. (return the index of the item if found).Implement the following algorithms in Java: 3-WAY-QUICKSORT (slide 25). Explain in the report how yourimplementation operates.slide 25 : In 3-WAY-QUICKSORT, an array A[p..r] is divided in 3 parts −A[p..i] elements less than pivot −A[i+1..j-1] elements equal to pivot −A[j..r] elements greater than pivot. −Based on Dutch National Flag algorithm −Good when input has many duplicates
- you are given integers A = [a0, a1, a2, · · · an], where a are integers. We want to determine the largest sum of a portion of consecutive values in the array. array A = [3, 13, −20, 9, −3, 30, 9, −70], largest sum of a portion of consecutive values is 9-3+30+9 = 45. a) you must write an iterative algorithm that can determine the largest sum of a portion of consecutive values / show the time complexity b)Write a dynamic programming-based algorithm that determines the largest sum of a portion of consecutive values/show its time complexityWrite a Java program that• Define an integer array with length of 10.• Populate the array with random integer numbers.• Sort this array into non-decreasing order based on three sorting algorithms.o bubble sorto selection sorto insertion sort• Test these 3 sorting methods• Give a big-Oh characterization, in terms of n, of the running time of these three algorithms.• I mprove the bubble sort so that the time complexity of them are O(N) for the best case Write a Java program that• Define an integer array with length of 100.• Populate the array with random numbers in {1, 2, ..., 30}.• Count and output the frequency of each number occurred in the array.• Give a big-Oh characterization, in terms of n, of the running time of this algorithm.You are given an array A[1..n] of positive numbers where Ai] is the stock price on day i. You are allowed to buy the stock once and sell it at some point later. For each day you own the stock you pay S1 fee. Design a divide-and-conquer algorithm that will return a pair (i,j) such that buying the stock on day i and selling it on day j will maximize your gain The complexity of the algorithm has to be O(n log n) You are given an array A[1..n] of positive numbers where Ai] is the stock price on day i. You are allowed to buy the stock once and sell it at some point later. For each day you own the stock you pay S1 fee. Design a divide-and-conquer algorithm that will return a pair (i,j) such that buying the stock on day i and selling it on day j will maximize your gain The complexity of the algorithm has to be O(n log n)