Q1.Design an iterative algorithm to multiply odd integers. For example, if a given n is an odd integer, then the product is 1 * 3 * 5 * 7 * … * n; if n is an even integer, then the product is 1 * 3 * 5 * 7 * … * (n-1).
Q2.mplement your above iterative algorithm in Java with the following method header.
public static int oddProduct(int n)
Selected Answer:
public class Main
{
public static int oddProduct(int n)
{
int i = 1;
int product = 1;
if(i%2==0)
{
while(i<(n-1))
{
product*=i;
i+=2;
}
}
else{
while(i<(n))
{
product*=i;
i+=2;
}
}
}
public static void main(String[] args)
{
int product;
int n = 9;
product= oddProduct(n);
System.out.println(product);
}
}
Response Feedback:
off by one
Q3.Design a recursive algorithm to multiply odd integers as specified in the previous question (Q1).
Q4.
Implement your above recursive algorithm in Java with the following method header:
public static int oddProduct(int n)
Selected Answer:
public class Main
{
public static int oddProduct(int n)
{
if (n == 1)
return 1;
else
return n*oddProduct(n-2);
}
public static void main(String[] args)
{
int product;
int n = 9;
product= oddProduct(n);
System.out.println(product);
}
}
Response Feedback:
What if n is even?
Q16.
Solve the recurrence relation using master’s theorem: T(n) = 9T(n/3) + n. Show all steps.
Q17.
| Solve the recurrence relation: T(n) = 2T(n/2) + n, T(1) = 1, using the substitution method. Your answer must contain the following 3 parts. 1) detailed steps leading to the closed form; 2) the exact closed formula; 3) complexity in big O notation. Write an answer without steps will receive zero point. You can either use the Math editor in Blackboard, or write on a separate paper (don’t forget your name). |
Q19.
You just realized that homework for CPS 340 is due in just 8 hours, yet you have not started. There are four questions in the homework, and each question with different points require certain number of hours to complete (see below). Use a brute-force strategy to maximize your points for the homework.
For your Problem:
hours left – 8
hours -[1,5,3,4]
points -[15,10,9,5]
Hours Left ->
0 1 2 3 4 5 6 7 8 -> hours left
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 |
| 0 | 15 | 15 | 15 | 15 | 15 | 25 | 25 | 25 |
| 0 | 15 | 15 | 15 | 24 | 24 | 25 | 25 | 25 |
| 0 | 15 | 15 | 15 | 24 | 24 | 25 | 25 | 29 |
so for [1,3,4] hour combination you can get the best points 29. questions -> [1,3,4]
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