W(n) = 2W(n/2) + n - 1 for n > 1 and n a power of 2.W(n) = 2 W(n/2) + n-1for n > 1 and n a power of 2.W(n) = time to sort U + time to sort V + time to merge.Algorithm 1.5:Binary Search void binSearch (int n, constkeytype S, keytype x, index& loc) Basic operation: Comparison Worst-case time complexity: W(merge) = W(h, m) = h+m-1 comparisons.Obtain the solution to the array from the solution to the sub-arrayĪlgorithms with Pseudocode pass by reference.Conquer(solve) the sub-array: Determine if x in the sub-array using recursion until the sub-array is sufficiently small ?.If x is larger than the middle item, select right sub-array.If x is smaller than the middle item, select left sub-array.Divide the Array into two sub-arrays approximately half as large.Compare x with the middle element : If equal, done – quit.Locate key x in an array of size n sorted in non-decreasing order.In this approach, a problem is divided into sub-problems and the same algorithm is applied ( usually recursively) to every sub-problem.Divide an instance of a problem into 2 or more smaller instances.Recall that when multiplying two matrices, Aa ij and Bb jk, the resulting matrix C c ik is given by c ik å j a ijb jk: In the case of multiplying together two n by n matrices, this gives us an Q(n3) algorithm computing each c ik. Napoleon split the Austro-Russian Army and was able to conquer 2 weaker armies Strassen’s algorithm Divide and conquer algorithms can similarly improve the speed of matrix multiplication.Contrast worst-case and average-case complexity analysis.Determine complexity analysis of divide and conquer algorithms.Determine when the divide-and-conquer approach is an appropriate solution approach.The structure of a divide-and-conquer algorithm follows the structure of a proof by (strong) induction. Apply the divide-and-conquer approach to solve a problem 1 Divide and Conquer Algorithms Divide and conquer algorithms generally have 3 steps: divide the problem into subproblems, re-cursively solve the subproblems and combine the solutions of subproblems to create the solution to the original problem.Describe the divide-and-conquer approach to solving problems.
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