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A list of n strings, 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(n log n)
- 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 strings, each of length n, is sorted into lexicographic or...
The recurrence tree for merge sort will have height n and O (n2) work will be done at each level of the recurrence tree (Each level involves ncomparisons and a comparison takes O(n) time in worst case). So time complexity of this merge sort will be O(n2 logn).
Most Upvoted Answer
A list of n strings, each of length n, is sorted into lexicographic or...
Explanation:
Merge Sort Algorithm:
Merge Sort is a divide and conquer algorithm that divides the input array into two halves, recursively sorts the two halves, and then merges the sorted halves.
Worst Case Complexity:
In the worst case scenario, the input list is divided into two halves each time, resulting in log(n) levels of recursion. At each level, merging the two sorted lists takes O(n) time. Therefore, the worst case time complexity of Merge Sort is O(n log n).
Sorting n Strings of Length n:
In this case, we have n strings, each of length n. When sorting these n strings using lexicographic order, the comparison between strings takes O(n) time. Since there are n strings, the total time complexity of comparing all strings is O(n^2).
Combining the Complexities:
Considering the comparison of strings and the merge sort algorithm, the worst case running time of sorting n strings, each of length n, into lexicographic order using the merge sort algorithm is O(n^2 log n).
Therefore, the correct answer is option B) O(n^2 log n).
Merge Sort Algorithm:
Merge Sort is a divide and conquer algorithm that divides the input array into two halves, recursively sorts the two halves, and then merges the sorted halves.
Worst Case Complexity:
In the worst case scenario, the input list is divided into two halves each time, resulting in log(n) levels of recursion. At each level, merging the two sorted lists takes O(n) time. Therefore, the worst case time complexity of Merge Sort is O(n log n).
Sorting n Strings of Length n:
In this case, we have n strings, each of length n. When sorting these n strings using lexicographic order, the comparison between strings takes O(n) time. Since there are n strings, the total time complexity of comparing all strings is O(n^2).
Combining the Complexities:
Considering the comparison of strings and the merge sort algorithm, the worst case running time of sorting n strings, each of length n, into lexicographic order using the merge sort algorithm 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 strings, each of length n, is sorted into lexicographic order using the merge sort algorithm. The worst case running time of this computation isa)O(n log n)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 strings, each of length n, is sorted into lexicographic order using the merge sort algorithm. The worst case running time of this computation isa)O(n log n)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 strings, each of length n, is sorted into lexicographic order using the merge sort algorithm. The worst case running time of this computation isa)O(n log n)b)O(n2logn)c)O(n2 + logn)d)O(n2)Correct answer is option 'B'. Can you explain this answer?.
A list of n strings, each of length n, is sorted into lexicographic order using the merge sort algorithm. The worst case running time of this computation isa)O(n log n)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 strings, each of length n, is sorted into lexicographic order using the merge sort algorithm. The worst case running time of this computation isa)O(n log n)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 strings, each of length n, is sorted into lexicographic order using the merge sort algorithm. The worst case running time of this computation isa)O(n log n)b)O(n2logn)c)O(n2 + logn)d)O(n2)Correct answer is option 'B'. Can you explain this answer?.
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