If Hibbard increments (h1= 1, h2= 3, h3= 7, …, hk = 2^k–1) are used in a Shell sort implementation, then the best case time complexity will be ________(a) O(nlogn)(b) O(n)(c) O(n^2)(d) O(logn)The question was asked in a national level competition.This interesting question is from Shell sort topic in portion Sorting of Data Structures & Algorithms II

If Hibbard increments (h1= 1, h2= 3, h3= 7, …, hk = 2^k–1) are use

1.	If Hibbard increments (h1= 1, h2= 3, h3= 7, …, hk = 2^k–1) are used in a Shell sort implementation, then the best case time complexity will be ________(a) O(nlogn)(b) O(n)(c) O(n^2)(d) O(logn)The question was asked in a national level competition.This interesting question is from Shell sort topic in portion Sorting of Data Structures & Algorithms II
Answer» The correct CHOICE is (a) O(nlogn) Explanation: The best case occurs when the array is already sorted. In best case the number of comparison for each of the increments-based insertion sorts is equal to length of array. Here 2k –1 < n, where n is the number of records. So K < log(n+1), thus the sorting time in best case is LESS the n * log(n+1). Therefore best case time COMPLEXITY is O(nlogn).

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