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?

• 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? 

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

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 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.

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).

What does asymptotic analysis focus on?

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

Consider the following undirected graph:

If we perform Breadth-First Search (BFS) traversal starting from node 3, how many of the following traversal(s) is/are possible? 

3 → 2 → 4 → 6 → 7 → 1 → 8 → 5