If a problem can be solved by combining optimal solutions to non-overlapping problems, the strategy is called _____________a)Dynamic programmingb)Greedyc)Divide and conquerd)RecursionCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Divide and conquer is a problem-solving strategy that involves breaking a problem into smaller subproblems, solving each subproblem independently, and then combining the solutions to the subproblems to obtain the solution to the original problem. This approach is especially useful when the problem can be divided into non-overlapping subproblems and the optimal solutions to these subproblems can be combined to solve the original problem.

Algorithm:
1. Divide the problem into smaller subproblems.
2. Solve each subproblem independently.
3. Combine the solutions to the subproblems to obtain the solution to the original problem.

Example:

Suppose we have a problem of finding the maximum element in an array. We can divide the array into two halves, find the maximum element in each half, and then compare the two maximum elements to find the overall maximum.

Here is the algorithm for finding the maximum element using the divide and conquer strategy:
1. If the array has only one element, return that element.
2. Divide the array into two halves.
3. Recursively find the maximum element in each half.
4. Compare the two maximum elements and return the larger one.

By dividing the problem into smaller subproblems and finding the maximum element in each subproblem, we can solve the original problem efficiently.

Advantages:

1. Efficiency: The divide and conquer strategy can often lead to efficient algorithms, especially when the subproblems are non-overlapping and can be solved independently.
2. Modularity: By breaking the problem into smaller subproblems, the overall problem becomes easier to understand and solve.
3. Scalability: The divide and conquer strategy is scalable and can be applied to problems of various sizes.

Using the divide and conquer strategy can lead to optimal solutions by combining the optimal solutions to non-overlapping subproblems. This approach is widely used in various algorithms and problem-solving techniques.

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