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An array of 25 distinct elements is to be sorted using quick sort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is
Correct answer is '(0.08)'. Can you explain this answer?
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An array of 25 distinct elements is to be sorted using quick sort. Ass...
The worst possible location for the pivot is either first place or the last place
Hence the probability is 2/25 = 0.08
Hence the probability is 2/25 = 0.08
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An array of 25 distinct elements is to be sorted using quick sort. Ass...
Explanation:
Quick sort is a popular sorting algorithm that uses the divide and conquer strategy to sort the array. The quick sort algorithm selects a pivot element, partitions the array around the pivot, and recursively sorts the subarrays. The choice of pivot element plays a crucial role in the efficiency of the algorithm.
Worst possible location for pivot element:
The worst possible location for the pivot element is when it is either the smallest or the largest element in the array. In such a case, the partitioning process will not divide the array into two subarrays of approximately equal size, but instead, one subarray will contain all the elements, and the other subarray will be empty.
Probability of choosing worst pivot element:
Since the pivot element is chosen uniformly at random, the probability of choosing the smallest or largest element as the pivot is 2/25. Therefore, the probability of selecting the worst possible pivot element is 2/25.
Probability of worst location in first round:
In the first round of partitioning, the pivot element divides the array into two subarrays. If the pivot element is the smallest or largest element in the array, then one of the subarrays will be empty, and the other subarray will contain all the remaining elements. The probability of choosing the worst pivot element in the first round is 2/25, and the probability of choosing the worst location for the pivot element in the first round is 1/2. Therefore, the probability of choosing the worst pivot element in the first round is (2/25)*(1/2) = 0.08.
Conclusion:
Therefore, the probability that the pivot element gets placed in the worst possible location in the first round of partitioning is 0.08.
Quick sort is a popular sorting algorithm that uses the divide and conquer strategy to sort the array. The quick sort algorithm selects a pivot element, partitions the array around the pivot, and recursively sorts the subarrays. The choice of pivot element plays a crucial role in the efficiency of the algorithm.
Worst possible location for pivot element:
The worst possible location for the pivot element is when it is either the smallest or the largest element in the array. In such a case, the partitioning process will not divide the array into two subarrays of approximately equal size, but instead, one subarray will contain all the elements, and the other subarray will be empty.
Probability of choosing worst pivot element:
Since the pivot element is chosen uniformly at random, the probability of choosing the smallest or largest element as the pivot is 2/25. Therefore, the probability of selecting the worst possible pivot element is 2/25.
Probability of worst location in first round:
In the first round of partitioning, the pivot element divides the array into two subarrays. If the pivot element is the smallest or largest element in the array, then one of the subarrays will be empty, and the other subarray will contain all the remaining elements. The probability of choosing the worst pivot element in the first round is 2/25, and the probability of choosing the worst location for the pivot element in the first round is 1/2. Therefore, the probability of choosing the worst pivot element in the first round is (2/25)*(1/2) = 0.08.
Conclusion:
Therefore, the probability that the pivot element gets placed in the worst possible location in the first round of partitioning is 0.08.
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An array of 25 distinct elements is to be sorted using quick sort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) isCorrect answer is '(0.08)'. Can you explain this answer?
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