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.
Here is the answer.We can solve this equation using any other methods also.
Recurrence equation is : T(n)=2T(n/2)+theta(n)
Time Complexity is:Theta(nlogn)[It means for best and worst cases it gives same time complexity that's why we use theta notation here]
If you have any doubt regarding this,feel free to comment on comment section.
A divide-and-conquer algorithm solves a problem by dividing the input (of size n>1, T(1) =0) into...
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.
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)
2. 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...
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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....
The steps in divide-and-conquer approach are: A) Divide an instance of a problem into one or more smaller instances. B) Use recursion until the instances are sufficiently small. C) Conquer (solve) these small and manageable instances. D) Combine the solutions to obtain the solution of the original instance. Select one: True False
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