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Below is the BinarySearch Algorithm..!!!!!


1. (16 pts.) Sorted Array Given a sorted array A of n (possibly negative) distinct integers,...
Design and analysis of algorithms
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Problem 5. Given a sorted array of distinct integers A[1- -n], you want to find out whether there is an index I for which Ai-i. Give a divide-and-conquer algorithm that runs in time O(log n)
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.
6. Let T(1..n] be a sorted array of distinct integers, some of which may be negative. Give an algorithm that can find an index i such that 1 <i<n and T[i] = i, provided such an index exists. Your algorithm should take a time in O(lg n) in the worst case. Answers must be proven (or at least well justified)
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.
Suppose you are given an array A holding n distinct integers (negative values are allowed) in sorted order; in other words, A[i] < A[i + 1] for each i ∈ [0, n − 2]. We say the ith element is self referential if A[i] = i. Design an O(log n) time algorithm to determine if there is a self referencial element in the array. Your solution must include a) Statement of your algorithm in plain English. (Pseudo-code is optional.) b)...
Given an unsorted array of distinct positive integers A [ 1......n ] in the range between 1 and 10000 and an integer i in the sane range. Here n can be arbitrary large You want to find out whether there are 2 elements of the array that add up to i. Give an algorithm that runs in time (O(n).
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.
(13 pts) Given an array AlI,2,. .. ,n] integers, design and analyze an efficient Divide-and-Conquer algorithm to find some i and j, where j > 1, such that A[j]-Ali] is maximized. For example, given A 6, 1,3,8,4,5, 12,6], the maximum value of AL] - Ali] for j > i is 12-1 11 where j -7 and i 2. Give the underlying recurrence relation for your algorithm and analyze its running time. You should carefully state all details of your algorithm:...
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. Please write a Divide-and-Conquer Java algorithm solving the following problem: Given an "almost sorted" array of distinct integers, and an integer x, return the index of x in the array. If the element x is not present in the array, return -1. "Almost sorted" means the following. Assume you had a sorted array A[0…N], and then split it into two pieces A[0…M] and A[M+1…N], and move the second piece upfront to get the following: A[M+1]…A[N]A[0]…A[M]. Thus, the "almost sorted"...