Problems
power
Write a
public static function named
power that takes in two integers,
a and
b, and returns
a^
b, the first argument to the power of the second argument. You may
NOT use
Math.pow(), because that would be boring.
The base case in this method is when the second argument is 0:
n^0 = 1, by definition.
Hint: 3^5 = 3*(3^4)
Why is recursion not the best solution for this problem? If you do not know, ask a TA.
Create a similar method named
power2 that is functionally identical but does not use recursion. It should still NOT use
Math.pow().
fileCount
Write a
public static function named
fileCount that takes as input a directory (as a File object) and returns the total number of files in all sub-directories
Directories count as files, too.
Your method should look through all files and sub-directories in the directory that was passed in. While searching through the directory, use the
java.io.File.isDirectory() method to check if the File you are looking at is a file or directory. If it is a normal file, count it. If it is a directory, count it and use a recursive call to count its contents.
Hint:
What is the base case?
What is the recursive step?
What is the combination?
You should consult the
java.io.File API for more information.
The following directory structure has 14 files:
root_dir 1
+–dir 2
| +–file 3
+–dir 4
| +–dir 5
| | +–dir 6
| | | +–file 7
| | +–file 8
| +–file 9
+–dir 10
| +–dir 11
| | +–file 12
| +–file 13
+–file 14
hanoi
Write a
public static function named
hanoi that recursively solves the Tower of Hanoi puzzle (see the description below).
Your function should take 1 integer and 3 chars as input (in this order):
n,
src,
dest,
aux.
n is the number of disks.
src (source),
dest (destination), and
aux (auxiliary) are tower letters.
For example, to solve the 3 disk puzzle, you would call
hanoi(3,’A’,’C’,’B’);
hanoi(3,’A’,’C’,’B’); means “move 3 disks from tower A to tower C using tower B”
Your function should print the solution to the puzzle to standard output in the following format:
“move [disk] from [tower1] to [tower2]”
[disk] is the number of the disk being moved. Disks are numbered 1 to
n, 1 being the smallest and
n being the largest.
[tower1] is the letter of the tower
from which the disk is being moved.
[tower2] is the letter of the tower
to which the disk is being moved.
For example: “move 1 from A to C” is the first step of solving the 3 disk problem.
Print each step on its own line.
The base case is the 0-disk problem, for which nothing must be done (just return).
What is the recursive step?
What is the combination?
Hints:
Solve the puzzle by hand (
one of many online versions or
another).
Divide and Conquer.
How do you use the solution to the 1-disk problem to help you solve the 2-disk problem?
How about using the 2-disk solution to solve the 3-disk problem?
And so on.
The whole function is just 5 lines of code.
2 of these are the base case
The other 3 are the steps to use the (n-1)-disk solution to solve the n-disk problem.
About the Tower of Hanoi
There is a temple in Kashi Vishwanath which contains a large room with three time-worn posts, on which are stacked 64 golden disks. Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks, in accordance with the immutable rules of the Brahma, since that time. When the last move of the puzzle is completed, the world will end. Despite the location of the legendary temple, the puzzle is most often called the Tower of Hanoi.
The objective of the puzzle is to move the entire stack of disks from the first post to the third post, obeying the following simple rules:
Only one disk may be moved at a time.
Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack.
No disk may be placed on top of a smaller disk.
mysterySeries
Figure out the pattern from the table below.
Write a
public static function named
mysterySeries that take integers
i and
j as input and returns the (
i,
j)-th mystery number (the number in the
i-th row and
j-th column).
mysterySeries(6,2) should return 15
Base Cases:
If
i < 0 or
j < 0 or
i <
j, then A(
i,
j) = 0
The above 3 base cases are
not sufficient, what other base case(s) do you need?
Hint: Each element of the
i-th row can be computed from elements in the (
i-1)-th row.
A(i,j)
0
1
2
3
4
5
6
…
0
1
1
1
1
2
1
2
1
3
1
3
3
1
4
1
4
6
4
1
5
1
5
10
10
5
1
6
1
6
15
20
15
6
1
…
…
…
…
…
…
…
…
…
Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount! Use Discount Code “Newclient” for a 15% Discount!NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you.
The post recursion program appeared first on Urgent Nursing Writers.
0 comments