Construct a Divide and Conquer-based algorithm for the following problem and analyze the same in the worst case. Input: An ordered array L with n elements and item X that is to be searched in the array L. Output: Index j where L[j]=X, if X is found or else j = 0, if X not found.

Find a sorted matrix: The input is a real number x and a matrix A[1..n, 1..m] of nm real numbers, with each row A[i, 1..m] and column A[1..n, j] sorted. The objective is to locate the largest array entry A[i, j] that is less than or equal to x, or to report that all components of A are greater than x. Create and test an iterative method that analyses as few matrix elements as feasible. Be cautious if you assume a simple binary search would fix the problem. Find a sorted matrix: The input is a real number x and a matrix A[1..n, 1..m] of nm real numbers, with each row A[i, 1..m] and column A[1..n, j] sorted. The objective is to locate the largest array entry A[i, j] that is less than or equal to x, or to report that all components of A are greater than x. Create and test an iterative method that analyses as few matrix elements as feasible. Be cautious if you assume a simple binary search would fix the problem.

2. An interpolation search assumes that the data in an array is sorted and uniformly distributed.Whereas a binary search always looks at the middle item in an array, an interpolation searchlooks where the sought-for item is more likely to occur. For example, if you searched yourtelephone book for Victoria Appleseed, you probably would look near its beginning ratherthan its middle. And if you discovered many Appleseeds, you would look near the lastAppleseed. Instead of looking at the element a[mid] of an array a, as the binary search would,an interpolation search examines a[index], where p = (desiredElement - a[first]) / (a[last] - a[first]) index = first + [(last – first) × p]Implement an interpolation search of an array. For particular arrays, compare the outcomesof an interpolation search and of a binary search. Consider arrays that have uniformlydistributed entries and arrays that do not. Modify and save the file asSearchComparerYourlastname.java.

Search a sorted matrix: The input consists of a real number x and a matrix A[1..n, 1..m] of nm real values, where A[i, 1..m] and A[1..n, j] are the rows and columns, respectively, of the matrix. The objective is to either state that all of the members of A are greater than x or to locate the largest array entry A[i, j] that is less than or equal to x. Create and evaluate an iterative approach for this issue that looks at the least amount of matrix entries feasible. If you think the issue can be resolved with a straightforward binary search, think twice.

Question 2: Recurrences (a) Below is the pseudo-code for two algorithms: Practicel (A,s,f) and Practice2(A,s,f), which take as input a sorted array A, indexed from s to f. The algorithms make a call to Bsearch(A,s,f,k) which we saw in class. Determine the worst-case runtime recurrece for each algorithm: T1(n) and T2(n). Show that T(n) is O((log n)²) and T2(n) is O(n log n). Practicel (A,s,f) if s< f ql = L(s+ f)/2] if BSearch(A,s,ql,1) = true Practice2(A,s,f) if s < f if BSearch(A,s+1,f,1) = true return true return true else else return Practice2(A, s, f-1) return Practicel(A, ql+1, f) else else return false return false

The algorithm below searches for the maximum in an input array A. Assume A is a random sequence containing n distinguishable real numbers, what is the probability for line #4 to be executed exactly once? (The phrase "random sequence" here means the n numbers can appear in any order with equal chance.) mymax(A, n) { 1: max = A[1]; 2: for i = 2:n 3: if A[i] > max 4: max = A[i); 5: end; 6: end; 7: return max; }

Question 2: The game of "FastestPath" consists of a path (a 1-D array) with n positive integers to represent n cities in a path (except the first index which has always value 0). The aim of the game is to move from the source city (located at index 0) to destination (located at last index) in the shortest time. The value at each index shows the travel time to enter the city located in the corresponding index. Here is a sample path where there are 6 cities (n is 6): 0 5 90 7 61 12 Always start the game from the first city and there are two types of moves. You can either move to the adjacent city or jump over the adjacent city to land two cities over. The total travel time of a game is the sum of the travel times of the visited cities. In the path shown above, there are several ways to get to the end. Starting in the first city, our time so far is 0. We could travel to city 2, then travel to city 4, then travel to last city for a total travel time of 90 + 61 + 12 = 163. However, a…

Consider the following algorithm that uses a sorted list of n elements (alist). What is the worst case runtime of this algorithm? for each element in alist    1. ask the user for an input, call it value    2. search value in alist using binary search    3. if value exists in alist, print "successful"       otherwise print "unsuccessful"      Question options: a. O(log n) b. O(n) c. O(n log n) d. O(2^n) e. O(n^2) f. O(1)

Many computer applications involve searching through a set of data and sorting the data. A number of effi cient searching and sorting algorithms have been devised in order to reduce the runtime of these tedious tasks. In this problem we will consider how best to parallelize these tasks.Consider the following binary search algorithm (a classic divide and conquer algorithm) that searches for a value X in a sorted N-element array A and returns the index of matched entry:BinarySearch(A[0..N−1], X) {low = 0high = N −1while (low <= high) {mid = (low + high) / 2if (A[mid] >X)high = mid −1else if (A[mid] <X)low = mid + 1elsereturn mid // found}return −1 // not found}Assume that you have Y cores on a multi-core processor to run BinarySearch. Assuming that Y is much smaller than N, express the speedup factor you might expect to obtain for values of Y and N. Plot these on a graph.Next, assume that Y is equal to N. How would this affect your conclusions in your previous answer? If you…

Question: Design an algorithm for this problem with worst-case runtime of O(n).