Step (D) of the divide-and-conquer strategy (i.e. combine the solutions to smaller instances of the problem...

Step (D) of the divide-and-conquer strategy (i.e. combine the solutions to smaller instances of the problem to obtain the solution of the original instance) is not a necessary step for this design strategy. Mergesort is an example of such cases.

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True

False

Expert Solution

FALSE

Divide-and-conquer:

Both merge sort and quicksort employ a common algorithmic paradigm based on recursion. This paradigm, divide-and-conquer, breaks a problem into subproblems that are similar to the original problem, recursively solves the subproblems, and finally combines the solutions to the subproblems to solve the original problem. Because divide-and-conquer solves subproblems recursively, each subproblem must be smaller than the original problem, and there must be a base case for subproblems. You should think of a divide-and-conquer algorithm as having three parts:

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.

Colby Messinger answered 1 year ago

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