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A list of n string, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation is
- a)O(nlogn)
- b)O(n2logn)
- c)O(n2+logn)
- d)O(n2)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A list of n string, each of length n, is sorted into lexicographic ord...
When we are sorting an array of n integers, Recurrence relation for Total number of comparisons involved will be,
T(n) = 2T(n/2) + (n) where (n) is the number of comparisons in order to merge 2 sorted subarrays of size n/2.
= (nlog2n)
Instead of integers whose comparison take O(1) time, we are given n strings. We can compare 2 strings in O(n) worst case. Therefore, Total number of comparisons now will be (n2log2n) where each comparison takes O(n) time now.
In general, merge sort makes (nlog2n) comparisons, and runs in (nlog2n) time if each comparison can be done in O(1) time.
To learn more about time complexity:
Most Upvoted Answer
A list of n string, each of length n, is sorted into lexicographic ord...
Explanation:
To understand why the worst case running time of the merge-sort algorithm for sorting a list of n strings, each of length n, is O(n^2 log n), let's break down the process of merge-sort and analyze its time complexity.
Merge-Sort Algorithm:
The merge-sort algorithm follows the divide-and-conquer approach to sort a list of elements. It consists of the following steps:
1. Divide: Divide the list into two halves until the base case is reached (when the list contains only one element).
2. Conquer: Sort the divided lists recursively.
3. Combine: Merge the sorted halves to obtain the final sorted list.
Time Complexity Analysis:
1. Divide: During the divide step, the list is divided into two halves repeatedly until the base case is reached. This process takes O(log n) time.
2. Conquer: In the conquer step, the sorted halves are merged together recursively. The time complexity of merging two lists of length n each is O(n). Since the conquer step is performed for each level of the recursive call stack (in this case, log n levels), the overall time complexity of the conquer step is O(n log n).
3. Combine: The combine step involves merging the sorted halves. Since the length of each string is n, the comparison between two strings can take up to O(n) time. In the worst case, the merge operation might need to compare every element in both halves, resulting in a time complexity of O(n^2).
4. Overall: Combining the time complexities of all the steps, the worst case running time of merge-sort for sorting a list of n strings, each of length n, is O(n^2 log n).
Therefore, the correct answer is option 'B' - O(n^2 log n).
To understand why the worst case running time of the merge-sort algorithm for sorting a list of n strings, each of length n, is O(n^2 log n), let's break down the process of merge-sort and analyze its time complexity.
Merge-Sort Algorithm:
The merge-sort algorithm follows the divide-and-conquer approach to sort a list of elements. It consists of the following steps:
1. Divide: Divide the list into two halves until the base case is reached (when the list contains only one element).
2. Conquer: Sort the divided lists recursively.
3. Combine: Merge the sorted halves to obtain the final sorted list.
Time Complexity Analysis:
1. Divide: During the divide step, the list is divided into two halves repeatedly until the base case is reached. This process takes O(log n) time.
2. Conquer: In the conquer step, the sorted halves are merged together recursively. The time complexity of merging two lists of length n each is O(n). Since the conquer step is performed for each level of the recursive call stack (in this case, log n levels), the overall time complexity of the conquer step is O(n log n).
3. Combine: The combine step involves merging the sorted halves. Since the length of each string is n, the comparison between two strings can take up to O(n) time. In the worst case, the merge operation might need to compare every element in both halves, resulting in a time complexity of O(n^2).
4. Overall: Combining the time complexities of all the steps, the worst case running time of merge-sort for sorting a list of n strings, each of length n, is O(n^2 log n).
Therefore, the correct answer is option 'B' - O(n^2 log n).
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A list of n string, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation isa)O(nlogn)b)O(n2logn)c)O(n2+logn)d)O(n2)Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 A list of n string, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation isa)O(nlogn)b)O(n2logn)c)O(n2+logn)d)O(n2)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A list of n string, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation isa)O(nlogn)b)O(n2logn)c)O(n2+logn)d)O(n2)Correct answer is option 'B'. Can you explain this answer?.
A list of n string, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation isa)O(nlogn)b)O(n2logn)c)O(n2+logn)d)O(n2)Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 A list of n string, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation isa)O(nlogn)b)O(n2logn)c)O(n2+logn)d)O(n2)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A list of n string, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation isa)O(nlogn)b)O(n2logn)c)O(n2+logn)d)O(n2)Correct answer is option 'B'. Can you explain this answer?.
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