Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into 5 sub-instances of size n/3, and the dividing and combining steps take a time
in Θ(n n). Write a recurrence equation for the running time T (n) , and solve the
equation for T (n)
Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a...
A divide-and-conquer algorithm solves a problem by dividing the input (of size n>1, T(1) =0) into two inputs half as big using n/2-1 steps. The algorithm does n steps to combine the solutions to get a solution for the original input. Write a recurrence equation for the algorithm and solve it.
A divide-and-conquer algorithm solves a problem by dividing the input (of size n>1, T(1) =0) into two inputs half as big using n/2-1 steps. The algorithm does n steps to combine the solutions to get a solution for the original input. Write a recurrence equation for the algorithm and solve it.
Analysis Divide & Conquer: Analyze the complexity of algorithm A1 where the problem of size n is solved by dividing into 4 subprograms of size n - 4 to be recursively solved and then combining the solutions of the subprograms takes O(n2) time. Determine the recurrence and whether it is “Subtract and Conquer” or “Divide and Conquer“ type of problem. Solve the problem to the big O notation. Use the master theorem to solve, state which theorem you are using...
Suppose that, even unrealistically, we are to search a list of 700 million items using Binary Search, Recursive (Algorithm 2.1). What is the maximum number of comparisons that this algorithm must perform before finding a given item or concluding that it is not in the list “Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into n subinstances of size n/3, and the dividing and combining steps take linear time. Write a...
Suppose the following is a divide-and-conquer algorithm for some problem. "Make the input of size n into 3 subproblems of sizes n/2 , n/4 , n/8 , respectively with O(n) time; Recursively call on these subproblems; and then combine the results in O(n) time. The recursive call returns when the problems become of size 1 and the time in this case is constant." (a) Let T(n) denote the worst-case running time of this approach on the problem of size 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.
4.5-2 Professor Caesar wishes to develop a matrix-multiplication algorithm that is asymptotically faster than Strassen’s algorithm. His algorithm will use the divide- and-conquer method, dividing each matrix into pieces of size n/4 x n/4, and the divide and combine steps together will take O(n) time. He needs to determine how many subproblems his algorithm has to create in order to beat Strassen’s algo- rithm. If his algorithm creates a subproblems, then the recurrence for the running time T(n) becomes T(n)...
need help in this algorithm question Let A be an array containing n numbers (positive and negative). Develop a divide and conquer algorithm that finds the two indices 1 sisjsn such that A[k] (the sum of the elements from i to j) is maximized. For example, in the array A [10,-5,-6,5, 7,-2,4, -11], the sub-array A[4:6] has the sum 5+ 7-2+4-14 and no other sub-array contains elements that sum to a value greater than 14, so for this input the...
Provide a divide-and-conquer algorithm for determining the smallest and second smallest values in a given unordered set of numbers. Provide a recurrence equation expressing the time complexity of the algorithm, and derive its exact solution (i.e., not the asymptotic solution). For simplicity, you may assume the size of the problem to be an exact power of a the number 2
Provide a most efficient divide-and-conquer algorithm for determining the smallest and second smallest values in a given unordered set of numbers. Provide a recurrence equation expressing the time complexity of the algorithm, and derive its exact solution in the number of comparisons. For simplicity, you may assume the size of the problem to be an exact power of a the number 2