Algorithm Analysis
Worksheet
Program Analysis
1. Define assertion.
2. Define loop invariant?
3. What is the loop invariant for the following code segment?
public int summation(int n)
{
int sum = 0;
for(int i=0; i < n; i++)
{
sum += i:
}
return sum;
}
sum variable = _______________________________________
Loop control variable (i) = ______________________________
4. Define worst-case, best-case, and average case.
Big-O
5. What is the purpose of Big-O notation?
6. When classifying an algorithm using Big-O notation what is your principle
concern?
7. What is the Big-O for the following algorithm: _____________________
n(n – 1) 2
Common Algorithms
8. Place the following Big-O run-times in order from most efficient to least efficient.
O(log n), O(n3), O(1), O(n log n), O(n2)
____________________________________________________________
9. What is the Big-O for the following algorithms:
Linear Search –
Binary Search –
Selection Sort –
Insertion Sort –
Quick Sort –
Merge Sort –
Heap Sort –
Determining Big-O
Instructions: The following algorithms will display a different number of stars, depending
on the value in nNum. Classify the Big-O growth rate, and justify your answer with a
calculation.
Example
How many stars would be displayed by the following algorithm? 1000
constant
n times
int n = 10;
for(int nA = 0; nA < n; nA++) {
for(int nB = 0; nB < n; nB++) {
for(int nC = 0; nC < n; nC++) {
n times
System.out.println(“*”);
}
}
constant
}
Big-O notation: O(n3)
n times
Justify your answer: Total = c + n * n * n * c = c + cn3
10. How many stars would be displayed by the following algorithm? ________
int nNum = 10;
for(int nOuter = 0; nOuter < nNum; nOuter++)
for(int nInner = 0; nInner < nNum; nInner++)
System.out.print("*");
Big-O notation: __________________ Justify your answer: ______________________
11. How many stars would be displayed by the following algorithm? ________
int nNum = 10;
for(int nOuter = 0; nOuter < nNum; nOuter++)
System.out.print("*");
Big-O notation: __________________ Justify your answer: ______________________
12. How many stars would be displayed by the following algorithm? ________
int nNum = 10;
for(int nOuter = 1; nOuter <= nNum; nOuter*=2)
System.out.print("*");
Big-O notation: __________________ Justify your answer: ______________________
13. How many stars would be displayed by the following algorithm? ________
int nNum = 10;
char[] caStars = new char[100];
for(int nI = 0; nI < 100; nI++)
caStars[nI] = '*';
System.out.print("" + caStars[nNum]);
Big-O notation: __________________ Justify your answer: ______________________
14. How many stars would be displayed by the following algorithm? ________
int nNum = 5;
int nStars = 1;
while(nNum > 0)
{
nStars*=2;
nNum--;
}
for(int nI = 0; nI < nStars; nI++)
System.out.print("*");
Big-O notation: __________________ Justify your answer: ______________________
15. How many stars would be displayed by the following algorithm? ________
int nNum = 10;
for(int nOuter = 1; nOuter <= nNum; nOuter++)
for(int nInner = 1; nInner <= nNum; nInner*=2)
System.out.print("*");
Big-O notation: __________________ Justify your answer: ______________________
16. How many stars would be displayed by the following algorithm? ________
public static void main(String[] args) {
int nNum = 10;
printStar(nNum);
}
public static void printStar(int nNum){
if(nNum > 0){
System.out.print('*');
printStar(nNum - 1);
}
}
Big-O notation: __________________ Justify your answer: ______________________
17. How many stars would be displayed by the following algorithm? ________
public static void main(String[] args) {
int nNum = 10;
printStar(nNum);
}
public static void printStar(int nNum){
if(nNum > 0){
System.out.print('*');
printStar(nNum/2);
}
}
Big-O notation: __________________ Justify your answer: ______________________