Q.1) What it the Bog O of the following equation?

10n3 + 24n2 + 3n log n + 144

O(n^3)

O(10n^3)

O(n^2)

O(n)

Q.2) What it the Bog O of the following equation?

n2 + n log n + 50

O(n)

O(n^2)

O(log n^2)

Q.3) What it the Bog O of the following equation?

5 log2n + 15 log n

O(n)

O(log n)

O(1)

Q.4) Exponential identity:

(ab)n = an + bn

True

False

Q.5) Match the following Big O notation with their respective operation.

O(1)

[ Choose ] Constant log n Logarithmic n log n quadratic Linear Cubic

O(log n)

[ Choose ] Constant log n Logarithmic n log n quadratic Linear Cubic

O(n)

[ Choose ] Constant log n Logarithmic n log n quadratic Linear Cubic

O(n^2)

[ Choose ] Constant log n Logarithmic n log n quadratic Linear Cubic

Q.6) What is the Big-O of the code snippet below?

#include <stdio.h>
int main()
{
printf(“Hello World”);
}

O(Cn)

O(n)

O(1)

O(n^2)

Q.7) What is n in the pseudocode below? What is the Big-O?

Pseudocode:

list_Sum(A,n) {

total =0

n = 8000

for i=0 to n-1

sum = sum + A[i]

return sum

}

n; O(1)

8000; O(A,i)

8000; O(n)

8000; O(n^2)

Q.8 ) Exponential identity:

aman = amn

True

False

Q.9) Logarithm identity:

logb M + logb N = logb (M/N)

True

False

Q.10) Say your and your coworkers write an algorithm that takes in an array of numbers and returns the highest one, select the the three (3) best analysis below that describes your algorithm.

The absolute slowest it can run is Linear time – O(n)

The absolute fastest it can run in Quadratic time – Ω(n^2)

The absolute fastest it can run is Linear time – Ω(n)

The absolute slowest it can run is constant time time – O(c)

This algorithm be tightly asymptotically bound – so we can also say it’s Θ(n)

Q.11) Match the analysis for Mileage problem:

How much gas does it take to go 200 miles?

Straight, downhill, wind at your back

[ Choose ]  Best case No difference (200 miles is 200 Miles) Worst case Average case Can not predict

“Average” terrain

[ Choose ]  Best case No difference (200 miles is 200 Miles) Worst case Average case Can not predict

Winding, uphill, gravel road, inclement weather

[ Choose ]  Best case No difference (200 miles is 200 Miles) Worst case Average case Can not predict

[ Choose ]  Best case No difference (200 miles is 200 Miles) Worst case Average case Can not predict

Q.12) Divide and Conquer

Divide ==> solve the problem recursively.

Conquer ==> put the problem into a number of sub-problems.

Combine ==> put the problem into one solution to give a solution to the original problem.

True

False

Q.13) Heap Sort:

Build the initial heap from the following array

[10, 16, 54, 17, 19, 65, 31]

Note: minimum 300 words.

Q.14) Heap Sort – max heap:

Build the initial heap from the following array

[10, 16, 54, 17, 19, 65, 31]

a. Show (draw) the max heap with the INITIAL max value

a. Show (draw) the max heap AFTER the FIRST max value is removed

b. Show (draw) the max heap AFTER the SECOND max value has been removed

Note: minimum 300 words

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