Prove that f(n)=5n2+6n+7f(n)=5n2+6n+7f( n ) = 5n^2+6n+7 is O(n2)O(n2)O( n^2 )

Matching each statement with the correct sequence in a formal proof.

If an algorithm with input integer nn can return the result in f(n)=3.3×10−8×nf( n ) = 3.3 \times 10^{-8} \times n seconds.

How long can this algorithm finish when n=230n=2^{30}?

If an algorithm with input integer nn can return the result in f(n)=3.3×10−10×2nf( n ) = 3.3 \times 10^{-10} \times 2^n seconds.

How long can this algorithm finish when n=63n=63?

If an algorithm with input integer nn can return the result in f(n)=3.3×10−10×n2f( n ) = 3.3 \times 10^{-10} \times n^2 seconds.

How long can this algorithm finish when n=230n=2^{30}?

Suppose a sequence is defined as:

a0a0a_0 = 9

ai=2×ai−1+5a_i = 2 \times a_{i-1} + 5 for all i≥1i \geq 1

Determine aia_i when ii is 3.

Let A=[a0,a1,⋯,am−1]A=[a0,a1,⋯,am−1]A=[a_0, a_1, \cdots, a_{m-1}] be a list of mmm distinct integers. 

Let B=[b0,b1,⋯,bn−1]B=[b_0, b_1, \cdots, b_{n-1}] be a list of nn distinct integers. 

Find the correct sequence of statements for an algorithm that return the intersection A∩BA \cap B.

Given the algorithm below and an input A=[1,6,2,7,5,8,4,3]A=[1,6,2,7,5,8,4,3], determine the return when the input value xx is 5.

procedure Alg2(x, A): A is a list of n integers

1    i = 0

2    while (i < n)

3        if (x == A[i])

4            break

5        end of if

6        i = i + 1

7    end of while

8    if (i < n)

9        location = i

a    else:

b        location = -1

c    end of if

d    return location

Given the algorithm below and an input A=[1,6,2,7,5,8,4,3]A=[1,6,2,7,5,8,4,3]A=[1,6,2,7,5,8,4,3], determine the return when the input value xxx is 0.

procedure Alg2(x, A): A is a list of n integers

1    i = 0

2    while (i < n)

3        if (x == A[i])

4            break

5        end of if

6        i = i + 1

7    end of while

8    if (i < n)

9        location = i

a    else:

b        location = -1

c    end of if

d    return location

Given the algorithm below and an input [1,6,2,7,5,8,4,3][1,6,2,7,5,8,4,3][1,6,2,7,5,8,4,3], determine the value of mmm after the body of the "for loop" (line 2 to line 6) is executed 3 times.

procedure Alg1(A): A is a list of n integers

1    m = A[0]

2    for i = 1 to n-1

3        if m < A[i] then 

4            m = A[i]

5        end of if

6    end of for

7    return m