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In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst case time complexity of the Insertion Sort algorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?
- a)Θ (n2)
- b)Θ (n log n)
- c)Θ (n1.5)
- d)Θ (n)
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a permutation a1.....an of n distinct integers, an inversion is a p...
Insertion sort runs in Θ(n + f(n)) time, where f(n) denotes the number of inversion initially present in the array being sorted.
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In a permutation a1.....an of n distinct integers, an inversion is a p...
Explanation:
Insertion Sort:
Insertion Sort is a simple sorting algorithm that builds the final sorted array one item at a time. It is efficient for small datasets but not suitable for large datasets due to its quadratic time complexity.
Permutations with at most n inversions:
When the input is restricted to permutations of 1.....n with at most n inversions, it means that the input array is almost sorted or has a limited number of inversions.
Worst case time complexity:
In the worst-case scenario, the Insertion Sort algorithm will have to swap each element with every element to its left until it reaches its correct position. This results in a time complexity of O(n) for almost sorted arrays with a limited number of inversions.
Therefore, the worst-case time complexity of the Insertion Sort algorithm for permutations of 1.....n with at most n inversions is O(n).
Insertion Sort:
Insertion Sort is a simple sorting algorithm that builds the final sorted array one item at a time. It is efficient for small datasets but not suitable for large datasets due to its quadratic time complexity.
Permutations with at most n inversions:
When the input is restricted to permutations of 1.....n with at most n inversions, it means that the input array is almost sorted or has a limited number of inversions.
Worst case time complexity:
In the worst-case scenario, the Insertion Sort algorithm will have to swap each element with every element to its left until it reaches its correct position. This results in a time complexity of O(n) for almost sorted arrays with a limited number of inversions.
Therefore, the worst-case time complexity of the Insertion Sort algorithm for permutations of 1.....n with at most n inversions is O(n).
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In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst case time complexity of theInsertion Sortalgorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?a)Θ (n2)b)Θ (n log n)c)Θ (n1.5)d)Θ (n)Correct answer is option 'D'. Can you explain this answer?
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In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst case time complexity of theInsertion Sortalgorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?a)Θ (n2)b)Θ (n log n)c)Θ (n1.5)d)Θ (n)Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst case time complexity of theInsertion Sortalgorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?a)Θ (n2)b)Θ (n log n)c)Θ (n1.5)d)Θ (n)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst case time complexity of theInsertion Sortalgorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?a)Θ (n2)b)Θ (n log n)c)Θ (n1.5)d)Θ (n)Correct answer is option 'D'. Can you explain this answer?.
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