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Given an array A containing 0s and 1s, such that all the 0s appear in the...
Let A = [A[1], A[2],…..,A[n]] be an array of n distinct integers. For 1 <= j...
Let A = [A[1], A[2],…..,A[n]] be an array of n distinct integers. For 1 <= j <= n, the index j is a happy index if A[i] < A[j] for all 1 <= i < j. Describe an O(n)- time algorithm that finds all the happy indices in the array A. Partial credit will be given for an O(n log(n))-time algorithm and a minimal credit will be given for an O(n^2) –time algorithm. What is the running time of your...
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct...
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct integers which is already sorted into ascending order, will find if there is some i such that Ali] in worst-case 0(log n) time.
4) [15 points total (5 points each)] Assume you are given a sorted array A of n numbers, where A is indexed from 1 up t...
4) [15 points total (5 points each)] Assume you are given a sorted array A of n numbers, where A is indexed from 1 up to n, anda number num which we wish to insert into A, in the proper sorted position. The function Search finds the minimum index i such that num should be inserted into Ali]. It searches the array sequentially until it finds the location i. Another function MakeRoom moves A[i], .., AIn] to Ali+1]...AIn+1] same sort...
Suppose that we are given a sorted array of distinct integers A[1, ......, n] and we want...
Suppose that we are given a sorted array of distinct integers A[1, ......, n] and we want to decide whether there is an index i for which A[i] = i. Describe an efficient divide-and-conquer algorithm that solves this problem and explain the time complexity. 1. Describe the steps of your algorithm in plain English. 2. Write a recurrence equation for the runtime complexity. 3. Solve the equation by the master theorem.
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.
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
The worst-case complexity of the Quicksort is O(n2). (a) Use the selection algorithm to modify Quicksort...
The worst-case complexity of the Quicksort is O(n2). (a) Use the selection algorithm to modify Quicksort and reduce its worst-case complexity to O( n*log(n) ) (b) Write the recurrence equation for the modified Quicksort algorithm.
Array manipulation (a) Write Java code for a method exchange (int [] a, int i, int...
Array manipulation (a) Write Java code for a method exchange (int [] a, int i, int j) that exchanges the values stored at indices i and j in the array a. You do not need to worry about cases where either i or j is an invalid index. Give the best estimate you can for its time complexity (b) In an ordered array of n items, how can we determine whether or not an item belongs to the list using...
the programming language is in java Problem 2 You are given an array A with n...
the
programming language is in java
Problem 2 You are given an array A with n distinct elements. Implement an (n log n)-time algorithm that creates an array B where all elements are in range from 0 to n - 1 and where the order of elements is the same as in A. That is, 0 has the same index in B as the smallest element in A, 1 has the same index in B as the second smallest element...
2) Given an array of n nonzero real numbers a[0]…a[n-1], write a function to partition the...
2) Given an array of n nonzero real numbers a[0]…a[n-1], write a function to partition the array (not sort) so that all its negative elements come before all its positive elements. Your algorithm should have O(n) time complexity. The function prototype is void negpospartition(float a[], int n) Please use C language
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct integers which is already sorted into ascending order, will find if there is some i such that Ali] in worst-case 0(log n) time.
4) [15 points total (5 points each)] Assume you are given a sorted array A of n numbers, where A is indexed from 1 up to n, anda number num which we wish to insert into A, in the proper sorted position. The function Search finds the minimum index i such that num should be inserted into Ali]. It searches the array sequentially until it finds the location i. Another function MakeRoom moves A[i], .., AIn] to Ali+1]...AIn+1] same sort...
Array manipulation (a) Write Java code for a method exchange (int [] a, int i, int j) that exchanges the values stored at indices i and j in the array a. You do not need to worry about cases where either i or j is an invalid index. Give the best estimate you can for its time complexity (b) In an ordered array of n items, how can we determine whether or not an item belongs to the list using...
the
programming language is in java
Problem 2 You are given an array A with n distinct elements. Implement an (n log n)-time algorithm that creates an array B where all elements are in range from 0 to n - 1 and where the order of elements is the same as in A. That is, 0 has the same index in B as the smallest element in A, 1 has the same index in B as the second smallest element...
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