The document outlines several programming tasks, each requiring the implementation of specific functions in Java. These include a power function using recursion and iteration, a file counting function that navigates directories, a recursive solution for the Tower of Hanoi puzzle, and a function to generate a mystery number based on input indices. It emphasizes understanding base cases and recursive steps for effective problem-solving.

1. 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

2. 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

3. 4
|
+--
dir
5
|
|
+--
dir
6
|
|
|
+--
file
7
|
|
+--
file
8
|

4. +--
file
9
+--
dir
10
|
+--
dir
11
|
|
+--
file
12
|
+--
file
13
+--
file
14
hanoi
Write a
public static
function named
hanoi

5. 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.

6. [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

7. 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

8. , 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

9. 1
1
2
1
2
1
3
1
3
3
1
4
1
4
6
4
1
5

10. 1
5
10
10
5
1
6
1
6
15
20
15
6
1
…
…
…
…
…
…
…
…
…