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You are given an array of strings, where different strings may have different numbers of characters, but the total number of characters over all the strings is n. What is the worst case time complexity of the best algorithm to sort this array?
- a)O(n)
- b)O(n2)
- c)O(logn)
- d)O(loglogn)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
You are given an array of strings, where different strings may have d...
For the strings, we can do this
1. Groups the strings by length and order the groups
2. Starting i on the maximum length and going down to 1, perform counting sort on the ith character. Make sure to include only groups that have an ith character. If the groups are subsequent sub-arrays in the original array, we’re performing counting sort on a subarray ending on the last index of the original array.
So we ultimately using count sort, hence time complexity = O(n)
Most Upvoted Answer
You are given an array of strings, where different strings may have d...
Worst case time complexity of the best algorithm to sort the array
In order to determine the worst case time complexity of the best algorithm to sort the given array of strings, we need to analyze the characteristics of the array and the sorting algorithms.
Characteristics of the array
- The array contains strings with different numbers of characters.
- The total number of characters over all the strings is n.
Sorting algorithms
There are various sorting algorithms available, but the most commonly used ones are:
- Quicksort
- Mergesort
- Heapsort
- Insertion sort
- Selection sort
Analysis
We can analyze the time complexity of each sorting algorithm in the worst case scenario:
- Quicksort: The worst case time complexity of Quicksort is O(n^2), which occurs when the pivot chosen is either the smallest or largest element in the array, resulting in unbalanced partitions.
- Mergesort: The worst case time complexity of Mergesort is O(nlogn), as it consistently divides the array into halves until individual elements are reached, and then merges them back in sorted order.
- Heapsort: The worst case time complexity of Heapsort is O(nlogn), as it builds a heap data structure and repeatedly extracts the maximum element from it.
- Insertion sort: The worst case time complexity of Insertion sort is O(n^2), as it iterates over the array and repeatedly inserts each element into its correct position in the sorted portion of the array.
- Selection sort: The worst case time complexity of Selection sort is O(n^2), as it repeatedly selects the minimum element from the unsorted portion of the array and places it in its correct position.
Conclusion
Among the given sorting algorithms, the best algorithm in terms of worst case time complexity is Insertion sort with a time complexity of O(n^2). However, it is important to note that this time complexity is not optimal for large values of n. Other algorithms like Mergesort and Heapsort, with a time complexity of O(nlogn), are more efficient in practice.
Answer
The worst case time complexity of the best algorithm to sort the given array of strings is option 'A' - O(n).
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