Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Given an array A of integer type of length n (n > 7), write a pseudocode of an efficient algorithm for finding the seven smallest elements in A. What is the running time of your algorithm?
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Given an array A and a positive integer k, the selection problem amounts to finding the largestelement x ∈ A such that at most k elements of A are less than or equal to x, or nil if no suchelement exists. A simple way to implement it is as follows:SimpleSelection(A, k)1 if k > A.length2 return nil3 else sort A in ascending order4 return A[k]Example A = (29, 28, 35, 20, 9, 33, 8, 9, 11, 6, 21, 28, 18, 36, 1) k = 6
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- Write an algorithm for a divide-and-conquer algorithm for finding values of both the largest and smallest elements in an array of n numbers. Implement the above-designed algorithm using Java Programming Language. How does this algorithm compare with the brute-force algorithm for this problem?arrow_forwardUsing Java, Write an algorithm that finds both the smallest and largest numbers in a list of n numbers. Try to find a method that does at most 1.5n comparisons of array items. Also, provide every-case and worst-case- time complexityarrow_forwardWrite pseudocode for a divide-and-conquer algorithm for finding the position of the largest element in an array of n numbers.arrow_forward
- Let B be an array that is of size n >= 6 containing integers from 1 to n-5, inclusive, with exactly five repeated. Describe an O(n) algorithm for finding the five integers in B that are repeated.arrow_forwardWrite out the algorithm (pseudocode) to find K in the ordered array by the method that compares K to every fifth entry until K itself or an entry larger than K is found, and then, in the latter case, searches for K among the preceding four. How many comparisons does your algorithm do in the worst case?arrow_forwardLet A be an array of size n storing positive integers. Write an algorithm(pseudo code) that takes array A and replaced each unique element of A by-1. For example, if A=(5,20,41,5,35,6,6) then after you run the algorithm, A=(5,-1,-1,5,-1,6,6). Compute time complexity of your algorithm.arrow_forward
- Write a program that reads a[8]. Then find and print the repetition of EACH element on it?arrow_forwardLet A be an array of size n >= 6 containing integers from 1 to n - 5, inclusive, with excactly five repeated. Describe a good algorithm for finding the five integers in A that are repeated.arrow_forwardDescribe an algorithm for finding the 10 largest elements in an array of size n. What is the running time of your algorithm?arrow_forward
- You're given an array of N integers, and a number K.The maximum K-product of the array is the maximum product of any K length subsequence of the array. For example, the maximum 2-product of the array [-5, 3, 4, -6] is 30 because the product of the subsequence [-5, -6] is 30 and it is impossible to achieve larger subsequence product.What is the maximum K-product you can achieve? Using JAVA programming output the max K-product.Input:14 25 -3 -4 6Output:30arrow_forwardYou're given an array of N integers, and a number K. The maximum K-product of the array is the maximum product of any K length subsequence of the array. For example, the maximum 2-product of the array [-5, 3, 4, -6] is 30 because the product of the subsequence [-5, -6] is 30 and it is impossible to achieve larger subsequence product. What is the maximum K-product you can achieve? Using JAVA programming output the max K- product. Input: 1 42 5 -3 -4 6 Output: 30arrow_forwardGiven an array of integers, return the largest gap between the sorted elements of the array. For example, consider the array: [9, 4, 26, 26, 0, 0, 5, 20, 6, 25, 5] ... in which, after sorting, the array becomes: [0, 0, 4, 5, 5, 6, 9, 20, 25, 26, 26] so that we now see that the largest gap in the array is between 9 and 20 which is *** 11. Examples largestGap ([9, 4, 26, 26, 0, 0, 5, 20, 6, 25, 5]) → 11 // After sorting: [0, 0, 4, 5, 5, 6, 9, 20, 25, 26, 26] // Largest gap between 9 and 20 is 11arrow_forward
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