Learning Objectives Gain some experience using dynamic data structures, which can grow and shrink at execution time. In this lab, you will use  Stacks , and  Maps . Learn to iterate through a dynamic data structures Setup Set up your directory: $ mkdir -p ~/cs180/lab14 $ cd ~/cs180/lab14 $ drjava & Evaluator Introduction Reverse Polish notation (RPN) is a mathematical notation in which every operator follows all of its operands, in contrast to Polish notation, which puts the operator in the prefix position. It is also known as postfix notation and is parenthesis-free as long as operator arities are fixed. The description “Polish” refers to the nationality of logician Jan Łukasiewicz, who invented (prefix) Polish notation in the 1920s. In reverse Polish notation the operators follow their operands; for instance, to add 3 and 4, one would write  3 4 +  rather than  3 + 4 . If there are multiple operations, the operator is given immediately after its second operand; so the expression written  3 − 4 + 5  in conventional notation would be written  3 4 − 5 +  in RPN: 4 is first subtracted from 3, then 5 added to it. An advantage of RPN is that it obviates the need for parentheses that are required by infix notation. While  3 − 4 × 5  can also be written  3 − (4 × 5) , that means something quite different from  (3 − 4) × 5 . In postfix, the former could be written  3 4 5 × − , which unambiguously means  3 (4 5 ×) −  which reduces to  3 20 − ; the latter could be written  3 4 − 5 ×  (or  5 3 4 − × , if keeping similar formatting), which unambiguously means (3 4 −) 5 × . Despite the name, reverse Polish notation is not exactly the reverse of Polish notation, for the operands of non-commutative operations are still written in the conventional order (e.g.  ÷ 6 3  in Polish notation and  6 3 ÷  in reverse Polish both evaluate to 2, whereas  3 6 ÷ ; in reverse Polish notation would evaluate to ½). Example The infix expression 5 + ((1 + 2) × 4) − 3 can be written down like this in RPN: 5 1 2 + 4 × + 3 − The expression is evaluated left-to-right, with the inputs interpreted as shown in the following table (the Stack is the list of values the algorithm is “keeping track of” after the Operation given in the middle column has taken place): Input Operation Stack Comment 5 Push value 5 - 1 Push value 1,5 - 2 Push value 2,1,5 - + Add 3,5 Pop two values (1, 2) and push result (3) 4 Push value 4,3,5 - x Multiply 12,5 Pop two values (3, 4) and push result (12) + Add 17 Pop two values (5, 12) and push result (17) 3 Push value 3,17 - - Subtract 14 Pop two values (17, 3) and push result (14) Result 14 - Your Task Now that we have explained the working of an RPN Calculator, it is time to make one ourselves. We will do that by using the  Stack  data structure, which is already implemented in the Java libraries. Use the push and pop functions as well as the constructor. Implement a class  Evaluator  with a  static  class method  evaluate  that takes a  String  argumen.

1. Learning Objectives
Gain some experience using dynamic data structures, which can
grow and shrink at execution time.
In this lab, you will use
Stacks
, and
Maps
.
Learn to iterate through a dynamic data structures
Setup
Set up your directory:
$ mkdir -p ~/cs180/lab14
$ cd ~/cs180/lab14
$ drjava &
Evaluator
Introduction
Reverse Polish notation (RPN) is a mathematical notation in
which every operator follows all of its operands, in contrast to
Polish notation, which puts the operator in the prefix position.
It is also known as postfix notation and is parenthesis-free as
long as operator arities are fixed. The description “Polish”
refers to the nationality of logician Jan Łukasiewicz, who
invented (prefix) Polish notation in the 1920s.
In reverse Polish notation the operators follow their operands;
for instance, to add 3 and 4, one would write
3 4 +
rather than
3 + 4
. If there are multiple operations, the operator is given
immediately after its second operand; so the expression written
3 − 4 + 5
in conventional notation would be written

2. 3 4 − 5 +
in RPN: 4 is first subtracted from 3, then 5 added to it.
An advantage of RPN is that it obviates the need for parentheses
that are required by infix notation. While
3 − 4 × 5
can also be written
3 − (4 × 5)
, that means something quite different from
(3 − 4) × 5
. In postfix, the former could be written
3 4 5 × −
, which unambiguously means
3 (4 5 ×) −
which reduces to
3 20 −
; the latter could be written
3 4 − 5 ×
(or
5 3 4 − ×
, if keeping similar formatting), which unambiguously means
(3 4 −) 5 ×
.
Despite the name, reverse Polish notation is not exactly the
reverse of Polish notation, for the operands of non-commutative
operations are still written in the conventional order (e.g.
÷ 6 3
in Polish notation and
6 3 ÷
in reverse Polish both evaluate to 2, whereas
3 6 ÷
; in reverse Polish notation would evaluate to ½).
Example
The infix expression
5 + ((1 + 2) × 4) − 3
can be written down like this in RPN:
5 1 2 + 4 × + 3 −

3. The expression is evaluated left-to-right, with the inputs
interpreted as shown in the following table (the Stack is the list
of values the algorithm is “keeping track of” after the Operation
given in the middle column has taken place):
Input
Operation
Stack
Comment
5
Push value
5
-
1
Push value
1,5
-
2
Push value
2,1,5
-
+
Add
3,5
Pop two values (1, 2) and push result (3)
4
Push value
4,3,5
-
x
Multiply
12,5
Pop two values (3, 4) and push result (12)
+
Add
17
Pop two values (5, 12) and push result (17)

4. 3
Push value
3,17
-
-
Subtract
14
Pop two values (17, 3) and push result (14)
Result
14
-
Your Task
Now that we have explained the working of an RPN Calculator,
it is time to make one ourselves.
We will do that by using the
Stack
data structure, which is already implemented in the Java
libraries.
Use the push and pop functions as well as the constructor.
Implement a class
Evaluator
with a
static
class method
evaluate
that takes a
String
argument comprising an RPN expression and returns the
int
result.
Make sure to test your evaluator — pass a
String
argument to calls to
evaluate
to check the results.

5. Stats
Introduction
In computing, a hash table (such as a Java
HashMap
) is a data structure used to implement an associative structure
that maps
keys
to
values
.
A hash table uses a hash function to compute an index into an
array of buckets or slots, from which the correct value can be
found.
In a well-dimensioned hash table, the average cost (number of
instructions) for each lookup is independent of the number of
elements stored in the table.
Many hash table designs also allow arbitrary insertions and
deletions of key-value pairs, at constant average cost per
operation.
In some situations, hash tables turn out to be more efficient than
search trees or any other table lookup structure. For this reason,
they are widely used in many kinds of computer software,
particularly for associative arrays, database indexing, caches,
and sets.
Here is the Java documentation for
HashMap
:
http://docs.oracle.com/javase/7/docs/api/java/util/HashMap.html
Creating a HashMap
To Create a HashMap in java, we first need to import the
required header files:
import
java.util.HashMap
;

6. import
java.util.Map
;
To Create a HashMap in java, we use the
HashMap
constructor.
HashMap
is a generic class, which means that we must indicate the types
of the keys and values it will use. For a map from
String
to
Integer
we use the constructor as follows:
Map
<
String
,Integer
>
map
=
new
HashMap
<
String
,Integer
>
(
)
;
The basic working of a
HashMap
used to track integer counts is:
Check if the element is present in the map.

7. If the element is present, increment its corresponding count.
If the element is not present, add the word to the map with its
corresponding count.
To look for an element in the map, use the method:
get()
For example, if we are looking for the word “the”:
Map
<
String
,Integer
>
map
=
new
HashMap
<
String
,Integer
>
(
)
;
String
word
=
"the"
;
Integer
count
=
map.
get

8. (
word
)
;
If the count in the above example is
null
, it simply means that the word doesn't exist in the map.
To add an element to the map, use the library function:
put()
:
map.
put
(
word, count
)
;
The arguments passed to the function
put
are the word (
String
) and count (
int
) which is the total number of times the number is seen. To
fetch the count of a given word, use the
get()
function.
Scenario
You work for an esteemed sports news website. The big story is
that the NBA is having a special all star league, in which teams
are assigned randomly before each game. The winner(s) of the
competition are the players who are in the most winning teams.
Your team has developed a way to organize a file so that your
reports come in faster than any other website.
File Format
Input file

9. The file is formatted as follows in which each line represents
one game: The first token is an integer that can be either
1
or
0
. It is
1
if the
first team
won and it is
0
if the
second team won
.
This token is followed by exactly five tokens representing the
player names of the first team (separated by spaces). After that,
the token
vs
token follows and finally five tokens for the player names of
the second team.
For example, this line means the second team with players
Prelich Murphy Wilkes Gall Greenberg
has won :
0 Chan Stine Neilson Curtis Kennedy vs Prelich Murphy Wilkes
Gall Greenberg
Your Task
Implement a class
Stats
with a
static
class method
wins
that reads lines of input from a
BufferedReader
and computes winner statistics for each of the players
mentioned in the input, by constructing a

10. HashMap
mapping the names of the players (
String
) to the number of wins (
Integer
) that player has accumulated, and returns the resulting
HashMap
.
Now, implement a
static
class method
winner
that iterates through a
HashMap
, such as returned by
wins
, returning the name of the player with the most wins (in the
case of a tie, return any such player).
Make sure to test your methods.