Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Given an unsorted array. The array has this p...
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Given an unsorted array. The array has this property that every element in array is at most k distance from its position in sorted array where k is a positive integer smaller than size of array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity?
- a)Insertion Sort with time complexity O(kn)
- b)Heap Sort with time complexity O(nLogk)
- c)Quick Sort with time complexity O(kLogk)
- d)Merge Sort with time complexity O(kLogk)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Given an unsorted array. The array has this property that every elemen...
We can perform this in O(nlogK) time using heaps.
First, create a min-heap with first k+1 elements.Now, we are sure that the smallest element will be in this K+1 elements..Now,remove the smallest element from the min-heap(which is the root) and put it in the result array.Next,insert another element from the unsorted array into the mean-heap, now,the second smallest element will be in this..extract it from the mean-heap and continue this until no more elements are in the unsorted array.Next, use simple heap sort for the remaining elements.
Time Complexity---
O(k) to build the initial min-heap
O((n-k)logk) for remaining elements...
Thus we get O(nlogk)
Hence,B is the correct answer
First, create a min-heap with first k+1 elements.Now, we are sure that the smallest element will be in this K+1 elements..Now,remove the smallest element from the min-heap(which is the root) and put it in the result array.Next,insert another element from the unsorted array into the mean-heap, now,the second smallest element will be in this..extract it from the mean-heap and continue this until no more elements are in the unsorted array.Next, use simple heap sort for the remaining elements.
Time Complexity---
O(k) to build the initial min-heap
O((n-k)logk) for remaining elements...
Thus we get O(nlogk)
Hence,B is the correct answer
Most Upvoted Answer
Given an unsorted array. The array has this property that every elemen...
Explanation:
The given array has a property that every element in array is at most k distance from its position in sorted array where k is a positive integer smaller than size of array. This means that we can find the sorted position of any element in the array by checking only the adjacent k elements. Based on this property, we can modify the heap sort algorithm to sort the array efficiently.
Heap Sort:
Heap Sort is a comparison-based sorting algorithm that works by dividing the input into two parts: a sorted and an unsorted region. Initially, the entire input is considered as unsorted. The algorithm then repeatedly extracts the largest element from the unsorted region and adds it to the sorted region. This process continues until the entire input is sorted.
Modification for k-distance Property:
To modify Heap Sort for the given k-distance property, we can use a min-heap of size k+1. We start by inserting the first k+1 elements of the array into the heap. We then remove the minimum element from the heap and insert the next element from the array into the heap. This ensures that the minimum element of the first k+1 elements is always at the root of the heap.
We repeat this process for the remaining elements of the array. At each step, we remove the minimum element from the heap and insert the next element from the array. This ensures that the minimum element of the k+1 adjacent elements is always at the root of the heap.
After processing all the elements of the array, we will have k+1 sorted sub-arrays of length k+1 each. We can merge these sub-arrays to obtain the final sorted array.
Time Complexity:
The time complexity of Heap Sort with the modification for the k-distance property is O(nLogk). The insertion and removal of elements from the min-heap take O(Logk) time. We do this for each element of the array, which gives us a total time complexity of O(nLogk).
The given array has a property that every element in array is at most k distance from its position in sorted array where k is a positive integer smaller than size of array. This means that we can find the sorted position of any element in the array by checking only the adjacent k elements. Based on this property, we can modify the heap sort algorithm to sort the array efficiently.
Heap Sort:
Heap Sort is a comparison-based sorting algorithm that works by dividing the input into two parts: a sorted and an unsorted region. Initially, the entire input is considered as unsorted. The algorithm then repeatedly extracts the largest element from the unsorted region and adds it to the sorted region. This process continues until the entire input is sorted.
Modification for k-distance Property:
To modify Heap Sort for the given k-distance property, we can use a min-heap of size k+1. We start by inserting the first k+1 elements of the array into the heap. We then remove the minimum element from the heap and insert the next element from the array into the heap. This ensures that the minimum element of the first k+1 elements is always at the root of the heap.
We repeat this process for the remaining elements of the array. At each step, we remove the minimum element from the heap and insert the next element from the array. This ensures that the minimum element of the k+1 adjacent elements is always at the root of the heap.
After processing all the elements of the array, we will have k+1 sorted sub-arrays of length k+1 each. We can merge these sub-arrays to obtain the final sorted array.
Time Complexity:
The time complexity of Heap Sort with the modification for the k-distance property is O(nLogk). The insertion and removal of elements from the min-heap take O(Logk) time. We do this for each element of the array, which gives us a total time complexity of O(nLogk).
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Community Answer
Given an unsorted array. The array has this property that every elemen...
- To sort the array firstly create a min-heap with first k+1 elements and a separate array as resultant array.
- Because elements are at most k distance apart from original position so, it is guranteed that the smallest element will be in this K+1 elements.
- Remove the smallest element from the min-heap(extract min) and put it in the result array.
- Now,insert another element from the unsorted array into the mean-heap, now,the second smallest element will be in this, perform extract min and continue this process until no more elements are in the unsorted array.finally, use simple heap sort for the remaining elements
Time Complexity
- O(k) to build the initial min-heap.
- O((n-k)logk) for remaining elements.
- 0(1) for extract min.
So overall O(k) + O((n-k)logk) + 0(1) = O(nlogk)
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Given an unsorted array. The array has this property that every element in array is at most k distance from its position in sorted array where k is a positive integer smaller than size of array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity?a)Insertion Sort with time complexity O(kn)b)Heap Sort with time complexity O(nLogk)c)Quick Sort with time complexity O(kLogk)d)Merge Sort with time complexity O(kLogk)Correct answer is option 'B'. Can you explain this answer?
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Given an unsorted array. The array has this property that every element in array is at most k distance from its position in sorted array where k is a positive integer smaller than size of array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity?a)Insertion Sort with time complexity O(kn)b)Heap Sort with time complexity O(nLogk)c)Quick Sort with time complexity O(kLogk)d)Merge Sort with time complexity O(kLogk)Correct answer is option 'B'. 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 Given an unsorted array. The array has this property that every element in array is at most k distance from its position in sorted array where k is a positive integer smaller than size of array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity?a)Insertion Sort with time complexity O(kn)b)Heap Sort with time complexity O(nLogk)c)Quick Sort with time complexity O(kLogk)d)Merge Sort with time complexity O(kLogk)Correct answer is option 'B'. 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 Given an unsorted array. The array has this property that every element in array is at most k distance from its position in sorted array where k is a positive integer smaller than size of array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity?a)Insertion Sort with time complexity O(kn)b)Heap Sort with time complexity O(nLogk)c)Quick Sort with time complexity O(kLogk)d)Merge Sort with time complexity O(kLogk)Correct answer is option 'B'. Can you explain this answer?.
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