Consider the following array representation of a min binary heap: [1, 3, 5, 7, 10, 6, 8].

If we perform an extract-min operation on this heap, what will be the resulting array after the heap property is restored according to our lectures?

What is the worst-case time complexity of the selection sort algorithm, and what is its primary operation?

• f ( n ) = O (g ( n )) implies  f ( n ) = Ω (g ( n )) 

• f ( n ) = Θ (g ( n )) implies f ( n ) = O (g ( n )) and  f( n ) = Ω (g ( n ))

• f ( n ) = Ω (g ( n )) implies f ( n ) = O (g ( n ))

• f ( n ) = O (g ( n )) implies f ( n ) = Θ (g ( n ))

• f ( n ) = Θ (g ( n )) implies f ( n ) = O (g ( n )) but not f( n ) = Ω (g ( n ))

How many statement(s) shown above is/are correct? 

Consider the following array: [3, 6, 8, 10, 1, 2, 4].

Suppose we perform quicksort on this array using the first element as the pivot. What is the state of the array after the first partitioning step based on our discussion in lectures?

What does asymptotic analysis focus on?

Find the asymptotic running time for the recurrence relation T[n]=8T[n/4]+n^1.51 and then select every correct answer below (more than one choice could be selected).

Which of the following is NOT a characteristic of an algorithm?

What is the primary difference between a queue used in BFS and a stack used in DFS?

Consider a double hashing scheme in which the primary hash function is

h₁(k) = (2k+3)mod  29

and the secondary hash function is

h₂(k) = 1+(3k mod  23).

Assume that the table size is 29.

Find the address returned by probe 1 in the probe sequence for the key value k = 75. Assume that the probe sequence begins at probe 0.

Suppose you inserted the keys 1, 3, 4, 7, 12, 14, 16, 17, 30, 39 (exactly in this order) into a hash table of size 13 using the hash function:

h(x)=(3x+5) mod  13 also insert key 27 and 43 after that

using chaining for collision resolution.