Algorithms Test...

From the given options, which of the following sorting algorithm has the lowest-best case complexity?

I. Merge Sort

II. Quick sort

In Hash table H, collision is resolved by using chaining. There are 29 slots in H. The average number of elements stored in a chain is 130. What is the total number of elements stored in H?

The number of swappings needed to sort the numbers 8, 22, 7, 9, 31, 5, 13 in ascending order, using bubble sort is

Consider an empty Hash table of size 13 (0 -12). The keys inserted are 121, 142, 169, 30, 24, 78, 53, and 154. Hash Function is H(K) = K mod 13.Open addressing is the method used for collision resolution in a hash table with linear probing. What is the index of the key 154?

In a binary min -heap with ‘n’ elements, the 7-th smallest element can be found in the time of _________.

Let the length of sorted arrays of A₁, A₂, A₃, A₄, A₅, and A₆ be 41, 30, 15, 80, 25 and 50 respectively. To merge them into a single array A by merging two arrays at a time using optimal algorithm. In worst case, the maximum number of comparisons needed is _____.

In an array A of 63 numbers consisting of a sequence of 0’s followed by a sequence of 1’s. The problem is to find the smallest index i such that A[i] is 1 by probing the minimum number of locations in A. The worst-case number of probes performed by an optimal algorithm is _____.

An array of 50 distinct elements is to be sorted using quick sort. Assume that the pivot element is chosen uniformly at random. What is the probability that the pivot element gets placed in the worst possible location in the first round of partitioning?

In a double hashing scheme, the primary function is H₁(K) = K mod 31, and the secondary hash function is H₂(K) = 1 + (K mod 17). Hash table size is 31. If the probe sequence begins at probe 0 then the address returned by probe 1 in the probe sequence for key value K = 100 is _____.