Which of the following algorithms is NOT a divide & conquer algorithm by nature?a)Euclidean algorithm to compute the greatest common divisorb)Heap Sortc)Cooley-Tukey fast Fourier transformd)Quick SortCorrect answer is option 'B'. Can you explain this answer?

Question

Which of the following algorithms is NOT a divide &#38; conquer algorithm by nature?a)Euclidean algorithm to compute the greatest common divisorb)Heap Sortc)Cooley-Tukey fast Fourier transformd)Quick SortCorrect answer is option 'B'. Can you explain this answer?

Answer

Explanation:

Divide and Conquer Algorithm: It is a problem-solving approach that breaks a problem into smaller sub-problems, solves the sub-problems individually, and then combines them to obtain the solution to the original problem. The divide and conquer algorithm consists of three steps:

1. Divide the problem into smaller sub-problems
2. Conquer the sub-problems by solving them recursively
3. Combine the solutions to the sub-problems to obtain the solution to the original problem.

Euclidean algorithm to compute the greatest common divisor: It is a divide and conquer algorithm. It is used to find the greatest common divisor (GCD) of two positive integers. The algorithm works by dividing the larger number by the smaller number, and then dividing the remainder by the smaller number, and so on, until the remainder is zero. The GCD is the last non-zero remainder.

Heap Sort: It is not a divide and conquer algorithm. It is a comparison-based sorting algorithm that works by dividing the input array into a sorted and an unsorted region, and iteratively shrinking the unsorted region by extracting the largest element and moving that to the sorted region.

Cooley-Tukey fast Fourier transform: It is a divide and conquer algorithm. It is used to compute the discrete Fourier transform (DFT) of a sequence. The algorithm works by recursively breaking down the DFT into smaller DFTs, and then combining the results to obtain the final DFT.

Quick Sort: It is a divide and conquer algorithm. It is a sorting algorithm that works by partitioning an array into two sub-arrays, according to a pivot element, and then recursively sorting the sub-arrays. The pivot element is selected such that all elements in one sub-array are less than or equal to the pivot, and all elements in the other sub-array are greater than the pivot.

Conclusion: From the above explanation, it is clear that Heap Sort is not a divide and conquer algorithm.

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