Table of Contents
How do you find the time complexity of divide and conquer?
The algorithm divides the array into two halves, recursively sorts them, and finally merges the two sorted halves. The time complexity of this algorithm is O(nLogn) , be it best case, average case or worst case. It’s time complexity can be easily understood from the recurrence equates to: T(n) = 2T(n/2) + n .
What is the time complexity of the divide part of the MergeSort algorithm?
Divide Part: The time complexity of the divide part is O(1) because calculating the middle index takes constant time. Conquer Part: We are recursively solving two sub-problems, each of size n/2.
What is the best case time complexity for sorting using MergeSort?
O(n log n)
What will be the best case time complexity of merge sort? Explanation: The time complexity of merge sort is not affected in any case as its algorithm has to implement the same number of steps. So its time complexity remains to be O(n log n) even in the best case.
How does divide and conquer reduce time complexity?
Divide and Conquer is a recursive problem-solving approach which break a problem into smaller subproblems, recursively solve the subproblems, and finally combines the solutions to the subproblems to solve the original problem. This method usually allows us to reduce the time complexity to a large extent.
What is meant by divide and conquer give the recurrence relation for divide and conquer?
the problem into subproblems that are smaller instances of the same problem. Conquer. the subproblems by solving them recursively.
How do you find the time complexity of a merge sort in Python?
Time complexity of Merge Sort is O(n*Log n) in all the 3 cases (worst, average and best) as merge sort always divides the array in two halves and takes linear time to merge two halves. It requires equal amount of additional space as the unsorted array.
Is divide and conquer an algorithm justify your answer?
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. Designing efficient divide-and-conquer algorithms can be difficult.
How do you write divide and conquer algorithm?
Divide-and-conquer
- Divide the problem into a number of subproblems that are smaller instances of the same problem.
- Conquer the subproblems by solving them recursively. If they are small enough, solve the subproblems as base cases.
- Combine the solutions to the subproblems into the solution for the original problem.