Part 1
The function 'vbrf' (for very bad recursive function) is defined as follows:
vbrf(0) = 2
vbrf(1) = 3
vbrf(2) = 4
vbrf(3) = 5
vbrf(n) = vbrf(n-1) - vbrf(n-2) + 3*vbrf(n-3) - 2*vbrf(n-4) if n > 3
Your job for this problem is to implement the function vbrf as a method in Java. Then write a program that uses this method to compute the function for various values of the argument and time how long it takes to compute. Also, include in this program a part that computes the function for the arguments from 1 to 12 and displays the argument and the results. Once you have the program working and can examine the results, report the following in a comment near the beginning of your program file:
To determine how long it takes to compute vbrf, use code something like the following:
long t0 = System.nanoTime(); int x = vbrf(15); long t1 = System.nanoTime(); double timeInSeconds = (t1-t0)*1.0e-9;
Be aware, the time it takes to compute vbrf(n+1) is almost twice the time it takes to compute vbrf(n). Start with small values of n and work your way up.
Part 2
We will be studying one aspect of permutations in Assignment #5. We will make use of a function that is defined recursively. Your job for this part of the assignment is to implement this function and print the first few values. Implement the method as a static method that takes a long for an argument and returns a long. The method itself should do no printing.
We'll call the function h. It is defined by these conditions:
h(0) = 1
h(1) = 0
h(n) = (n-1)*(h(n-1) + h(n-2)) for n > 1
To check your work, here are the first few values of h:
n | h(n) |
---|---|
0 | 1 |
1 | 0 |
2 | 1 |
3 | 2 |
4 | 9 |
5 | 44 |
6 | 265 |
7 | 1854 |
8 | 14833 |
9 | 133496 |
10 | 1334961 |
11 | 14684570 |
12 | 176214841 |
13 | 2290792932 |
14 | 32071101049 |
15 | 481066515734 |
Your program should print the first 10 values or so of the function. Your program should not be interactive!
public class h{
public static void main(String[] args) {
int b = 6;
int c = h(b);
System.out.println("answer= " + c);
}
/** returns the minimum of two numbers */
public static int h(int n) {
int val;
val=(n-1)*(h(n-1)+h(n-2));
return val;
}
}
Part 1 The function 'vbrf' (for very bad recursive function) is defined as follows: vbrf(0) =...
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