objectives - cs.trinity.eduthicks/2320-2004-s/lecture-pdf/infixprefix... · # 1 1 2 3 objectives 1....
TRANSCRIPT
# 1
1 2
3
Objectives1. Evaluate Mathematical Expressions
2. Infix Expression Operators, Operands, Scope Openers, Scope Closers
3. Mathematical Order Of Operations
4. Generate Postfix From Infix
5. Generate Prefix From Infix
6. Evaluate Infix Expression With Respect To Parentheses, Brackets, & Braces
7. Create Prefix Expression From Infix Expression
8. Evaluate Postfix Expression
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5 66
# 2
7 8
Evaluate Mathematical ExpressionStep 1 –Is It A Valid Infix
Is It Valid With Respect To Parentheses, Brackets, & Braces
# | Expression | Valid | Invalid
1 | 5 + 2 ^ 3 ^ 2 | |
2 | (2 + 3) * (5 – 2) | |
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | |
X
X
X
What makes a Mathematical Expression valid with respectto Parentheses, Brackets, and Braces?
4 | 3 * )2 + 3 ( | | X
5 | 3 * (2 + 12 / {4 * [5 – 4} -1 ]) | | X
96 | ( 3 + 2 ^ 3 ^ 2 / {4 * [5 – 4] * 1 } * 2 | | X10
Now that we can manually verify valid infix parenthese,
brackets, and braces, how do we get the computer to do so?
Info
Max
Top-1
5
0
1
2
3
4
5
11
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top-1
5
0
1
2
3
4
5“2 + (3 * 5 )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Define Scope Openers: ( { [
Define Scope Closers: ) } ]
Stack <char> ValidParen(5);
Traverse Infix String One Character At A Time
•If the character is a Scope Opener Push It To The Stack
•If the character is a Scope Closer, Pop the Stack; if the Closer and the top element of the stack are a pair, continue; otherwise return Invalid!
•When done, return Valid if stack is empty; otherwise return Invalid!
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# 3
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top-1
5
0
1
2
3
4
5“2+ (3 * 5 )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the 2?
Skip Constants/OperandsNothing –Skip to next Character
13
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top-1
5
0
1
2
3
4
5“2 +(3 * 5 )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the +?
Skip OperatorsNothing –Skip to next Character
14
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top-1
5
0
1
2
3
4
5“2 + (3 * 5 )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the (?
Push Scope Openers
15
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top0
5
0
1
2
3
4
5“2 + (3* 5 )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the 3?(
Skip Constants/OperandsNothing –Skip to next Character
16
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top0
5
0
1
2
3
4
5“2 + (3 *5 )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the *?(
Skip OperatorsNothing –Skip to next Character
17
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top0
5
0
1
2
3
4
5“2 + (3 * 5)”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the 5?(
Skip Constants/OperandsNothing –Skip to next Character
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# 4
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top0
5
0
1
2
3
4
5“2 + (3 * 5 )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the )?
(Pop The Stack And See If Set
) Goes With (If the Set Matches ContinueReturn INVALID If No Match
19
# | Expression [Infix String] | Valid | Invalid
0 | 2 + (3 * 5) | | X
Info
Max
Top-1
5
0
1
2
3
4
5“2 + (3 * 5 )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
Done With The Infix String
If Stack Empty Return VALID
If Stack Not Empty Return INVALID
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21
# | Expression [Infix String] | Valid | Invalid
X
Info
Max
Top-1
5
0
1
2
3
4
5
“5 + 2 ̂ 3 ̂ 2”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the 5?
Skip Constants/OperandsNothing –Skip to next Character
1 | 5 + 2 ^ 3 ^ 2 | | X
22
# | Expression [Infix String] | Valid | Invalid
X
Info
Max
Top-1
5
0
1
2
3
4
5
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the +?
Skip OperatorsNothing –Skip to next Character
1 | 5 + 2 ^ 3 ^ 2 | | X
“5 +2 ̂ 3 ̂ 2”
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# | Expression [Infix String] | Valid | Invalid
X
Info
Max
Top-1
5
0
1
2
3
4
5
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the 2?
X
Skip Constants/OperandsNothing –Skip to next Character
1 | 5 + 2 ^ 3 ^ 2 | |
“5 + 2 ̂3 ̂ 2”
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# 5
# | Expression [Infix String] | Valid | Invalid
X
Info
Max
Top-1
5
0
1
2
3
4
5
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the ^?
Skip OperatorsNothing –Skip to next Character
1 | 5 + 2 ^ 3 ^ 2 | | X
“5 + 2 ^3 ̂ 2”
^ or $ often represents exponenation 25
# | Expression [Infix String] | Valid | Invalid
X
Info
Max
Top-1
5
0
1
2
3
4
5
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the 3?
X
Skip Constants/OperandsNothing –Skip to next Character
1 | 5 + 2 ^ 3 ^ 2 | |
“5 + 2 ^ 3 ̂2”
26
# | Expression [Infix String] | Valid | Invalid
X
Info
Max
Top-1
5
0
1
2
3
4
5
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the ^?
Skip OperatorsNothing –Skip to next Character
X1 | 5 + 2 ^ 3 ^ 2 | |
“5 + 2 ^ 3 ^2”
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# | Expression [Infix String] | Valid | Invalid
X
Info
Max
Top-1
5
0
1
2
3
4
5
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the 2?
X
Skip Constants/OperandsNothing –Skip to next Character
1 | 5 + 2 ^ 3 ^ 2 | |
“5 + 2 ^ 3 ^ 2”
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# | Expression [Infix String] | Valid | Invalid
X
Info
Max
Top-1
5
0
1
2
3
4
5
“2 + 3 * 5 -2”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
Infix Expression CompleteWhat Is Returned?
VALID –Stack is Empty!
X1 | 5 + 2 ^ 3 ^ 2 | |
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# 6
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top-1
5
0
1
2
3
4
5
“(2 + 3) * (5 –2)”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
What do we do with the (?
2 | (2 + 3) * (5 – 2) | | X
Push Scope Openers
31
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top0
5
0
1
2
3
4
5
(
“(2 + 3) * (5 –2)”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
Skip
2 | (2 + 3) * (5 – 2) | | X
Skip
SkipPop Scope
Closer
Set Match( )
Continue32
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top-1
5
0
1
2
3
4
5
“(2 + 3) * (5 –2)”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
2 | (2 + 3) * (5 – 2) | | X
Skip
Push
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# | Expression [Infix String] | Valid | Invalid
Info
Max
Top0
5
0
1
2
3
4
5
(
“(2 + 3) * (5–2)”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
2 | (2 + 3) * (5 – 2) | | X
Skip
Skip
Skip
Pop
Set Match( )
Continue
34
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top-1
5
0
1
2
3
4
5
“(2 + 3) * (5 –2)”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Stack <char> ValidParen(5);
2 | (2 + 3) * (5 – 2) | | X
Infix Expression CompleteWhat Is Returned?
VALID –Stack is Empty!
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# 7
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top-1
5
0
1
2
3
4
5“3 * (2 + [ 12 / [ 4 * {5 –4} -1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Skip Skip Push
37
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top0
5
0
1
2
3
4
5
(
“3 * (2 + [ 12 / [ 4 * {5 –4} -1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Skip Skip Push
38
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top1
5
0
1
2
3
4
5
(
[
“3 * (2 + [ 12 / [ 4 * {5 –4} -1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Skip Skip Push
39
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top2
5
0
1
2
3
4
5
(
[
[
“3 * (2 + [ 12 / [ 4 * { 5 –4} -1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Skip Skip Push
40
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top3
5
0
1
2
3
4
5
(
[
[
{
“3 * (2 + [ 12 / [ 4 * { 5–4 } -1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Skip Skip PopSkip
Set Match{ }
Continue
41
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top2
5
0
1
2
3
4
5
(
[
[
“3 * (2 + [ 12 / [ 4 * { 5 –4 } - 1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Skip Skip Pop
Set Match[ ]
Continue
42
# 8
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top1
5
0
1
2
3
4
5
(
[
“3 * (2 + [ 12 / [ 4 * { 5 –4 } - 1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Skip Skip Pop
Set Match[ ]
Continue
43
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top0
5
0
1
2
3
4
5
(
“3 * (2 + [ 12 / [ 4 * { 5 –4 } - 1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Pop
Set Match( )
Continue
44
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top-1
5
0
1
2
3
4
5“3 * (2 + [ 12 / [ 4 * { 5 –4 } - 1 ] –1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
3 | 3 * (2 + [ 12 / [ 4 * {5 – 4} -1 ] – 1 ] ) | | X
Infix Expression CompleteWhat Is Returned?
VALID –Stack is Empty!
45 46
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top-1
5
0
1
2
3
4
5“3 * ) 2 + 3 (”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Skip Skip Pop
4 | 3 * ) 2 + 3 ( | | X
UnsuccessfulPop –Return
INVALID
47 48
# 9
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top-1
5
0
1
2
3
4
5“3 * ( 2 + 12 / { 4 * [ 5 –4 } -1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Skip Skip Push
5 | 3 * (2 + 12 / {4 * [5 – 4} -1 ]) | | X
49
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top0
5
0
1
2
3
4
5
(
“3 * ( 2 + 12 / { 4 * [ 5 –4 } -1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Skip Skip
Push
5 | 3 * (2 + 12 / {4 * [5 – 4} -1 ]) | | X
Skip Skip
50
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top1
5
0
1
2
3
4
5
( {
“3 * ( 2 + 12 / { 4 * [ 5 –4 } -1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Push
5 | 3 * ( 2 + 12 / { 4 * [ 5 – 4 } -1 ] ) | | X
SkipSkip
51
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top1
5
0
1
2
3
4
5
( {[
“3 * ( 2 + 12 / { 4 * [ 5–4 } -1 ] )”
We are going to evaluate expressions with constants –Extrapolate it to variables!
5 | 3 * ( 2 + 12 / { 4 * [ 5 – 4 } -1 ] ) | | X
Skip Skip PopSkip
[ } Not Match Return INVALID
52
53
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top-1
5
0
1
2
3
4
5“( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 –4 ] * 1 } * 2”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Push
X6 | ( 3 + 2 ^ 3 ^ 2 / {4 * [5 – 4] * 1 } * 2 | |
54
# 10
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top0
5
0
1
2
3
4
5
(
“( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 –4 ] *1 } * 2”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Skip Skip
Push
X6 | ( 3 + 2 ^ 3 ^ 2 / {4 * [5 – 4] -1 } * 2 | |
Skip Skip
Skip Skip Skip Skip
55
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top1
5
0
1
2
3
4
5
( {
“( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 –4 ] *1 } * 2”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Push
X6 | ( 3 + 2 ^ 3 ^ 2 / {4 * [5 – 4] -1 } * 2 | |
Skip
Skip
56
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top2
5
0
1
2
3
4
5
( { [
“( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } * 2”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Pop
X6 | ( 3 + 2 ^ 3 ^ 2 / {4 * [5 – 4] -1 } * 2 | |
Skip
Skip Skip
[ ] Set Match Continue
57
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top1
5
0
1
2
3
4
5
( {
“( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } * 2”
We are going to evaluate expressions with constants –Extrapolate it to variables!
Pop
X6 | ( 3 + 2 ^ 3 ^ 2 / {4 * [5 – 4] -1 } * 2 | |
Skip
Skip
{ } Set Match Continue
58
# | Expression [Infix String] | Valid | Invalid
Info
Max
Top0
5
0
1
2
3
4
5
(
“( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } * 2”
We are going to evaluate expressions with constants –Extrapolate it to variables!
X6 | ( 3 + 2 ^ 3 ^ 2 / {4 * [5 – 4] -1 } * 2 | |
Skip
SkipIf Stack Empty Return VALID
If Stack Not Empty Return INVALID
59
Stack <char> ValidParen(5);
What type of stack was to Verify A Valid Infix?
Is It Correct Parentheses, Brackets,
and Braces?
60
# 11
6161
62
Must Get Same Answer As Manual Solution!
Preserve The Mathematical Order Of Operations
5 + 2 ^ 3 ^ 2 = _______69 ?
517 ?Other ?
63
Maybe A Spreadsheet Will Help?
69 ?
517 ?Maybe Not!
5 + 2 ^ 3 ^ 2 = _______
64
Create Valid Postfix ExpressionStep 3
Preserve The Mathematical Order Of Operations
+
-* /
^
( ) # 1 Innermost First
Parenthes, Brackets, Braces
# 2 Right To Left# 4 Left To Right
# 4 Left To Right
# 3 Left To Right# 3 Left To Right
65
Create Valid Postfix Expression Step 2 Preserve The Mathematical Order Of Operations
1 | 5 + 2 ^ 3 ^ 2
2 | ( 2 + 3 ) * (5 – 2)
3 | 3 * 2 + 3 – 4 / 2 / 2 - 3
66
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] -1 } ) * 2
5 + 2 ^ 3 ^ 2
Create Postfix By Hand –Must Be Able To Do So To Verify Correctness Of Algorithm
Infix
Prefix
Postfix
5 2 3 2
5 2 3 2
# 12
67
5 2 3 2
68
5 + 2 ^ 3 ^ 2
1 –Write Down All Of The Operands
Infix
Prefix
Postfix
5 2 3 2
5 2 3 2^
69
5 + 2 ^ 3 ^ 2
2 –Solve As If Doing Mathematically –Order Of Operations
Infix
Prefix
Postfix
5 2 ^3 2
Put Operator In Front Of Respective Operands For Prefix
Put Operator In Rear Of Respective Operands For Prefix
5 + 2 ^ 3 ^ 2
5 2 3 2^^
70
2 –Solve As If Doing Mathematically –Order Of Operations
Infix
Prefix
Postfix
5 ^2 ^3 2
5 2 3 2^
5 2 ^3 2
5 2 3 2^^+
71
5 + 2 ^ 3 ^ 2
2 –Solve As If Doing Mathematically –Order Of Operations
Infix
Prefix
Postfix
+5 ^2 ^3 2
5 2 3 2^^
5 ^2 ^3 2
72
# 13
( 2 + 3 ) * ( 5 – 2 )
73
Infix
Prefix
Postfix
+ 2 3 5 2
2 3 + 5 2
2 3 5 2
2 3 5 2
Solve As If Doing Mathematically –Order Of Operations
( 2 + 3 ) * ( 5 – 2 )
74
Infix
Prefix
Postfix
+ 2 3 -5 2
2 3 + 5 2-
+ 2 3 5 2
2 3 + 5 2
Solve As If Doing Mathematically –Order Of Operations
( 2 + 3 ) * ( 5 – 2 )
75
Infix
Prefix
Postfix
* + 2 3 -5 2
2 3 + 5 2 - *
+ 2 3 -5 2
2 3 + 5 2-
Solve As If Doing Mathematically –Order Of Operations
76
77
Infix
Prefix
Postfix
3 * 2 + 3 – 4 / 2 / 2 - 3
3 2 3 4 2 2 3
3 2 3 4 2 2 3
* 3 2 3 4 2 2 3
3 2* 3 4 2 2 3
Solve As If Doing Mathematically –Order Of Operations
* 3 2 3 4 2 2 3
78
Infix
Prefix
Postfix
3 * 2 + 3 – 4 / 2 / 2 - 3
3 2* 3 4 2 2 3
* 3 2 3 /4 2 2 3
3 2* 3 4 2/ 2 3
Solve As If Doing Mathematically –Order Of Operations
# 14
79
Infix
Prefix
Postfix
3 * 2 + 3 – 4 / 2 / 2 - 3
* 3 2 3 //4 2 2 3
3 2* 3 4 2/ 2/ 3
* 3 2 3 /4 2 2 3
3 2* 3 4 2/ 2 3
Solve As If Doing Mathematically –Order Of Operations
80
Infix
Prefix
Postfix
3 * 2 + 3 – 4 / 2 / 2 - 3
+* 3 2 3 //4 2 2 3
3 2* 3+ 4 2/ 2/ 3
* 3 2 3 //4 2 2 3
3 2* 3 4 2/ 2/ 3
Solve As If Doing Mathematically –Order Of Operations
81
Infix
Prefix
Postfix
3 * 2 + 3 – 4 / 2 / 2 - 3
- +* 3 2 3 //4 2 2 3
3 2* 3+ 4 2/ 2/- 3
+* 3 2 3 //4 2 2 3
3 2* 3+ 4 2/ 2/ 3
Solve As If Doing Mathematically –Order Of Operations
82
Infix
Prefix
Postfix
3 * 2 + 3 – 4 / 2 / 2 - 3
- - +* 3 2 3 //4 2 2 3
3 2* 3+ 4 2/ 2/- 3 -
- +* 3 2 3 //4 2 2 3
3 2* 3+ 4 2/ 2/- 3
Solve As If Doing Mathematically –Order Of Operations
83
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
84
Infix
Prefix
Postfix
Solve As If Doing Mathematically –Order Of Operations
3 2 3 2 4 5 4 1 2
3 2 3 2 4 5 4 1 2
3 2 3 2 4 -5 4 1 2
3 2 3 2 4 5 4- 1 2
# 15
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
85
Infix
Prefix
Postfix
Solve As If Doing Mathematically –Order Of Operations
3 2 3 2 4 -5 4 1 2
3 2 3 2 4 5 4- 1 2
3 2 3 2 *4 -5 4 1 2
3 2 3 2 4 5 4-* 1 2
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
86
Infix
Prefix
Postfix
Solve As If Doing Mathematically –Order Of Operations
3 2 3 2 **4 -5 4 1 2
3 2 3 2 4 5 4-* 1* 2
3 2 3 2 *4 -5 4 1 2
3 2 3 2 4 5 4-* 1 2
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
87
Infix
Prefix
Postfix
Solve As If Doing Mathematically –Order Of Operations
3 2 3 2 **4 -5 4 1 2
3 2 3 2 4 5 4-* 1* 2
3 2 ^3 2 **4 -5 4 1 2
3 2 3 2^ 4 5 4-* 1* 2
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
88
Infix
Prefix
Postfix
Solve As If Doing Mathematically –Order Of Operations
3 2 ^3 2 **4 -5 4 1 2
3 2 3 2^ 4 5 4-* 1* 2
3 ^2 ^3 2 **4 -5 4 1 2
3 2 3 2^^ 4 5 4-* 1* 2
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
89
Infix
Prefix
Postfix
Solve As If Doing Mathematically –Order Of Operations
3 ^2 ^3 2 **4 -5 4 1 2
3 2 3 2^^ 4 5 4-* 1* 2
3 /^2 ^3 2 **4 -5 4 1 2
3 2 3 2^^ 4 5 4-* 1*/ 2
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
90
Infix
Prefix
Postfix
Solve As If Doing Mathematically –Order Of Operations
+3 /^2 ^3 2 **4 -5 4 1 2
3 2 3 2^^ 4 5 4-* 1*/+ 2
3 /^2 ^3 2 **4 -5 4 1 2
3 2 3 2^^ 4 5 4-* 1*/ 2
# 16
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
91
Infix
Prefix
Postfix
Solve As If Doing Mathematically –Order Of Operations
*+3 /^2 ^3 2 **4 -5 4 1 2
3 2 3 2^^ 4 5 4-* 1*/+ 2*
+3 /^2 ^3 2 **4 -5 4 1 2
3 2 3 2^^ 4 5 4-* 1*/+ 2
92
Now that we can manually create the postfix expressions,
how do we do this with a computer program?
Info
Max
Top-1
5
0
1
2
3
4
5
93 94
95 96
Info
Max
Top-1
5
0
1
2
3
4
5( 2 + 3 ) * ( 5 – 2 )
( ICP = 7 Always PUSH opener to stack)
( ISP of Empty Stack = -1)
Stack <char> Postfix(5);
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
# 17
97
Info
Max
Top0
5
0
1
2
3
4
5
(
( 2 + 3 ) * ( 5 – 2 )
Write Operand To Postfix String
( ISP = That Of Top Char = 0
Postfix = 2
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
98
Info
Max
Top0
5
0
1
2
3
4
5
(
( 2 + 3 ) * ( 5 – 2 )
ICP = 1 > ISP = 0 Push Operator
( ISP = That Of Top Char = 0
Postfix = 2
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
99
Info
Max
Top1
5
0
1
2
3
4
5
(+
( 2 + 3 ) * ( 5 – 2 )
( ISP = That Of Top Char = 2
Postfix = 2
Write Operand To Postfix String
3
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
100
Info
Max
Top1
5
0
1
2
3
4
5
(+
( 2 + 3 ) * ( 5 – 2 )
( ISP = That Of Top Char = 2
Postfix = 2 3
Scope Closer –Pop & Add To Postfix
+
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
101
Info
Max
Top-1
5
0
1
2
3
4
5( 2 + 3 ) * ( 5 – 2 )
( ISP -1
Postfix = 2 3 +
ICP = 3 > ISP = -1 Push
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
102
Info
Max
Top0
5
0
1
2
3
4
5
*
( 2 + 3 ) * ( 5 – 2 )
( ISP 4
Postfix = 2 3 +
( ICP = 7 Always PUSH opener to stack)
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
# 18
103
Info
Max
Top1
5
0
1
2
3
4
5
*(
( 2 + 3 ) * ( 5 – 2 )
( ISP 0
Postfix = 2 3 +
Write Operand To Postfix String
5
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
104
Info
Max
Top1
5
0
1
2
3
4
5
*(
( 2 + 3 ) * ( 5 – 2 )
( ISP 0
Postfix = 2 3 + 5
ICP = 1 > ISP = 0 Push
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
105
Info
Max
Top2
5
0
1
2
3
4
5
*( -
( 2 + 3 ) * ( 5 – 2 )
( ISP 1
Postfix = 2 3 + 5
Write Operand To Postfix String
2
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
106
Info
Max
Top2
5
0
1
2
3
4
5
*( -
( 2 + 3 ) * ( 5 – 2 )
( ISP 1
Postfix = 2 3 + 5 2
Scope Closer –Pop & Add To Postfix
-
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
107
Info
Max
Top0
5
0
1
2
3
4
5
*
( 2 + 3 ) * ( 5 – 2 )
( ISP 2
Postfix = 2 3 + 5 2 -
Done –Pop Stack & Add To Postfix
*
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
108
Info
Max
Top-1
5
0
1
2
3
4
5
( 2 + 3 ) * ( 5 – 2 )
( ISP 2
Postfix = 2 3 + 5 2 - *
To Form Postfix•Examine one Infix character at a time –left to right
•If Operand, Write it to the Postfix String•If Scope Opener or Operator
•If the In-Coming Priority (ICP) is greater than the In-StackPriority (ISP) Push
•If ICP < ISP Pop –Write Values To Postfix Until Can Push•If Scope Closer, Pop till find opener –Write values to
Postfix –Throw out scope opener!•Empty Stack –Write Values To Postfix
2 3 + 5 2 - *
It is finished –Success! –Stack Is Empty!
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
# 19
109 110
Info
Max
Top-1
5
0
1
2
3
4
5
Infix = 5 + 2 ^ 3 ^ 2
ISP = -1
5 2 3 2 ^ ^ +
Postfix =
Write Operand To Postfix String
5
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
111
Info
Max
Top-1
5
0
1
2
3
4
5
Infix = 5 + 2 ^ 3 ^ 2
ISP = -1
5 2 3 2 ^ ^ +
Postfix = 5
ICP = 1 > ISP -1 PUSH
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
112
Info
Max
Top0
5
0
1
2
3
4
5
+
Infix = 5 + 2 ^ 3 ^ 2
ISP = 1
5 2 3 2 ^ ^ +
Postfix = 5
Write Operand To Postfix String
2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
113
Info
Max
Top0
5
0
1
2
3
4
5
+
Infix = 5 + 2 ^ 3 ^ 2
ISP = 2
5 2 3 2 ^ ^ +
Postfix = 5 2
ICP = 6 > ISP 2 PUSH
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
114
Info
Max
Top1
5
0
1
2
3
4
5
+^
Infix = 5 + 2 ^ 3 ^ 2
ISP = 5
5 2 3 2 ^ ^ +
Postfix = 5 2
Write Operand To Postfix String
3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
# 20
115
Info
Max
Top1
5
0
1
2
3
4
5
+^
Infix = 5 + 2 ^ 3 ^ 2
ISP = 5
5 2 3 2 ^ ^ +
Postfix = 5 2 3
ICP = 6 > ISP 5 Push
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
116
Info
Max
Top2
5
0
1
2
3
4
5
+^ ^
Infix = 5 + 2 ^ 3 ^ 2
ISP = 5
5 2 3 2 ^ ^ +
Postfix = 5 2 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
Write Operand To Postfix String
2
117
Info
Max
Top2
5
0
1
2
3
4
5
+^ ^
Infix = 5 + 2 ^ 3 ^ 2
ISP = 5
5 2 3 2 ^ ^ +
Postfix = 5 2 3 2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
^ ^ +
Done –Pop Stack & Add To Postfix
118
119
Info
Max
Top-1
5
0
1
2
3
4
5
Infix = 3 * 2 + 3 – 4 / 2 / 2 – 3
ISP = -1
3 2 * 3 + 4 2 / 2 / - 3 -
Postfix =
Write Operand To Postfix String
3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
120
Info
Max
Top-1
5
0
1
2
3
4
5
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = -1
Postfix = 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
ICP = 3 > ISP = -1 Push *
3 2 * 3 + 4 2 / 2 / - 3 -
# 21
121
Info
Max
Top-1
5
0
1
2
3
4
5
*
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 4
Postfix = 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
Write Operand To Postfix String
2
3 2 * 3 + 4 2 / 2 / - 3 -
122
Info
Max
Top-1
5
0
1
2
3
4
5
*
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 4
Postfix = 3 2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
ICP = 1 < ISP = 4 Pop * Add To Postfix & Try Again! Push +
*
3 2 * 3 + 4 2 / 2 / - 3 -
123
Info
Max
Top-1
5
0
1
2
3
4
5
+
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 2
Postfix = 3 2 *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
3
Write Operand To Postfix String
3 2 * 3 + 4 2 / 2 / - 3 -
124
Info
Max
Top-1
5
0
1
2
3
4
5
+
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 2
Postfix = 3 2 * 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
+
ICP = 1 < ISP = 2 Pop + Add To Postfix & Try Again! Push -
3 2 * 3 + 4 2 / 2 / - 3 -
125
Info
Max
Top-1
5
0
1
2
3
4
5
-
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 2
Postfix = 3 2 * 3 +
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
4
Write Operand To Postfix String
3 2 * 3 + 4 2 / 2 / - 3 -
126
Info
Max
Top-1
5
0
1
2
3
4
5
-
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 2
Postfix = 3 2 * 3 + 4
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
ICP = 3 > ISP = 2 Push /
3 2 * 3 + 4 2 / 2 / - 3 -
# 22
127
Info
Max
Top0
5
0
1
2
3
4
5
-/
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 2
Postfix = 3 2 * 3 + 4
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
2
3 2 * 3 + 4 2 / 2 / - 3 -
Write Operand To Postfix String
128
Info
Max
Top1
5
0
1
2
3
4
5
-/
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 4
Postfix = 3 2 * 3 + 4 2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
/
3 2 * 3 + 4 2 / 2 / - 3 -
ICP = 3 < ISP = 4 Pop / Add To Postfix & Try Again! Push /
129
Info
Max
Top1
5
0
1
2
3
4
5
-/
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 4
Postfix = 3 2 * 3 + 4 2 /
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
2
3 2 * 3 + 4 2 / 2 / - 3 -
Write Operand To Postfix String
130
Info
Max
Top1
5
0
1
2
3
4
5
-/
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 4
Postfix = 3 2 * 3 + 4 2 / 2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
/
3 2 * 3 + 4 2 / 2 / - 3 -
ICP = 1 < ISP = 4 Pop / Add To Postfix & Try Again! Pop Add To Postfix & Try Again! Push -
-
131
Info
Max
Top0
5
0
1
2
3
4
5
-
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 2
Postfix = 3 2 * 3 + 4 2 / 2 / -
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
3
3 2 * 3 + 4 2 / 2 / - 3 -
Write Operand To Postfix String
132
Info
Max
Top0
5
0
1
2
3
4
5
-
Infix = 3 * 2 + 3 – 4 / 2 / 2 - 3
ISP = 2
Postfix = 3 2 * 3 + 4 2 / 2 / - 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2
-
3 2 * 3 + 4 2 / 2 / - 3 -
Done Pop Stack & Add To Postfix
# 23
133 134
Info
Max
Top-1
5
0
1
2
3
4
5
ISP = -1
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix =
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
( ICP = 7 Always PUSH opener to stack)
135
Info
Max
Top0
5
0
1
2
3
4
5
(
ISP = 0
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
Write Operand To Postfix String
136
Info
Max
Top0
5
0
1
2
3
4
5
(
ISP = 0
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
ICP = 1 > ISP = 0 Push +
137
Info
Max
Top1
5
0
1
2
3
4
5
( +
ISP = 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
2
Write Operand To Postfix String
138
Info
Max
Top1
5
0
1
2
3
4
5
( +
ISP = 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
ICP = 6 > ISP = 2 Push ^
# 24
139
Info
Max
Top2
5
0
1
2
3
4
5
( +^
ISP = 5
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
Write Operand To Postfix String
3
140
Info
Max
Top2
5
0
1
2
3
4
5
( +^
ISP = 5
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
ICP = 6 > ISP = 5 Push ^
141
Info
Max
Top2
5
0
1
2
3
4
5
( +^
ISP = 5
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
2
Write Operand To Postfix String
^
142
Info
Max
Top3
5
0
1
2
3
4
5
( +^
ISP = 5
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
^
^
ICP = 3 < ISP = 5 Pop ^Add To Postfix & Try Again! Pop ^Add To Postfix & Try Again! Push /
^
143
Info
Max
Top2
5
0
1
2
3
4
5
( +/
ISP = 4
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
(ICP = 7 > ISP = 4 PushAlways PUSH opener to stack
144
Info
Max
Top3
5
0
1
2
3
4
5
( +/
ISP = 0
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
4
{
Write Operand To Postfix String
# 25
145
Info
Max
Top3
5
0
1
2
3
4
5
( +/
ISP = 0
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{
ICP = 3 > ISP = 0 Push *
146
Info
Max
Top4
5
0
1
2
3
4
5
( +/
ISP = 4
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{*
(ICP = 7 > ISP = 4 PushAlways PUSH opener to stack
147
Info
Max
Top5
5
0
1
2
3
4
5
( +/
[
ISP = 0
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{*
5
Write Operand To Postfix String
148
Info
Max
Top5
5
0
1
2
3
4
5
( +/
[
ISP = 0
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4 5
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{*
(ICP = 1 > ISP = 0 PushAlways PUSH opener to stack
149
Info
Top5
0
1
2
3
4
5
( +/
[
ISP = 1
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4 5
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{*
4
6 -
Write Operand To Postfix String
150
Info
Top5
0
1
2
3
4
5
( +/
[
ISP = 1
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4 5
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{*
-
6 -
Pop Stack Till Find Matching Opener Add - To Postfix
# 26
151
Info
Top4
0
1
2
3
4
5
( +/
ISP = 4
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4 5 -
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{*
6
(ICP = 1 > ISP = 4 Pop *Add To Postfix & Try Again! Push -
*
152
Info
Top4
0
1
2
3
4
5
( +/
ISP = 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4 5 - *
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{-
6
1
Write Operand To Postfix String
153
Info
Top4
0
1
2
3
4
5
( +/
ISP = 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4 5 - * 1
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
{-
6
-
Pop Stack Till Find Matching Opener Add - To Postfix
154
Info
Top2
0
1
2
3
4
5
( +/
ISP = 4
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix = 3 2 3 2 ^ ^ 4 5 - * 1 -
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
6
/
Pop Stack Till Find Matching Opener Add - To Postfix
+
155
Info
Top-1
0
1
2
3
4
5
ISP = -1
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix =
3 2 3 2 ^ ^ 4 5 - * 1 - / +
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
6
(ICP = 3 > ISP = -1 Push *
156
Info
Top0
0
1
2
3
4
5
*
ISP = 4
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix =
3 2 3 2 ^ ^ 4 5 - * 1 - / +
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
6
Write Operand To Postfix String
2
# 27
157
Info
Top0
0
1
2
3
4
5
*
ISP = 4
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Postfix =
3 2 3 2 ^ ^ 4 5 - * 1 - / + 2
ICP ISP
+ -* /^({[)}]
1
3
6
7
-
0
5
4
2( 3 + 2 ^ 3 ^ 2 / { 4 * [ 5 – 4 ] * 1 } ) * 2
6
*
Done Pop Stack & Add To Postfix
Stack <char> Postfix(5);
What type of stack was to
create the Postfix from the Infix?
158
159 160
Create Valid Postfix ExpressionStep 3
Preserve The Mathematical Order Of Operations
+
-* /
^
( ) # 1 Innermost First
Parenthes, Brackets, Braces
# 2 Right To Left# 4 Left To Right
# 4 Left To Right
# 3 Left To Right# 3 Left To Right
161
Evaluate Postfix Expression Step 2 Preserve The Mathematical Order Of Operations
1 | 5 + 2 ^ 3 ^ 2
2 | ( 2 + 3 ) * (5 – 2)
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
5 2 3 2 ^ ^ +
2 3 + 5 2 - *
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
3 2 * 3 + 4 2 / 2 / - 3 -
= _______
= _______
= _______
= _______
15
517
5
262
162
# 28
163
1 | 5 + 2 ^ 3 ^ 2
5 2 3 2 ^ ^ += _______517
Info
Max
Top-1
5
0
1
2
3
4
5
5 2 3 2 ^ ^ +
Push Operands To Stack
Stack <double> Eval (5);
164
1 | 5 + 2 ^ 3 ^ 2
5 2 3 2 ^ ^ += _______517
Info
Max
Top0
5
0
1
2
3
4
5
5
5 2 3 2 ^ ^ +
Push Operands To Stack
Stack <double> Eval (5);
165
1 | 5 + 2 ^ 3 ^ 2
5 2 3 2 ^ ^ += _______517
Info
Max
Top1
5
0
1
2
3
4
5
52
5 2 3 2 ^ ^ +
Push Operands To Stack
Stack <double> Eval (5);
166
1 | 5 + 2 ^ 3 ^ 2
5 2 3 2 ^ ^ += _______517
Info
Max
Top2
5
0
1
2
3
4
5
52 3
5 2 3 2 ^ ^ +
Push Operands To Stack
Stack <double> Eval (5);
167
1 | 5 + 2 ^ 3 ^ 2
5 2 3 2 ^ ^ += _______517
Info
Max
Top3
6
0
1
2
3
4
5
52 3 2
5 2 3 2 ^ ^ +
Operator –Pop Stack Twice
Stack <double> Eval (5);
23 ^
Apply Operator
Evaluate Expression & Push
= 9
Push 9
Info
Max
Top2
5
0
1
2
3
4
5
52 9
168
# 29
1 | 5 + 2 ^ 3 ^ 2
5 2 3 2 ^ ^ += _______517
5 2 3 2 ^ ^ +
Operator –Pop Stack Twice
Stack <double> Eval (5);
Pop –Evaluate 2 ^ 9Push 512
Info
Max
Top2
5
0
1
2
3
4
5
52 9
169
1 | 5 + 2 ^ 3 ^ 2
5 2 3 2 ^ ^ += _______517
5 2 3 2 ^ ^ +
Operator –Pop Stack Twice
Stack <double> Eval (5);
Pop –Evaluate 5 + 512Push 517
Info
Max
Top1
5
0
1
2
3
4
5
5512
170
1 | 5 + 2 ^ 3 ^ 2
5 2 3 2 ^ ^ += _______517
5 2 3 2 ^ ^ +
Done –Only Item In Stack Contains Evaluated Expression
Stack <double> Eval (5);
Info
Max
Top0
5
0
1
2
3
4
5
517
171 172
= _______
Info
Max
Top-1
5
0
1
2
3
4
5
Push
2 | ( 2 + 3 ) * (5 – 2)
2 3 + 5 2 - * 15
2 3 + 5 2 - *
173
= _______
Info
Max
Top0
5
0
1
2
3
4
5
2Push
2 | ( 2 + 3 ) * (5 – 2)
2 3 + 5 2 - * 15
2 3 + 5 2 - *
174
# 30
= _______
Info
Max
Top1
5
0
1
2
3
4
5
23
Pop Evaluate 2 + 3 Push 5
2 | ( 2 + 3 ) * (5 – 2)
2 3 + 5 2 - * 15
2 3 + 5 2 - *
175
= _______
Info
Max
Top0
5
0
1
2
3
4
5
5
2 | ( 2 + 3 ) * (5 – 2)
2 3 + 5 2 - * 15
2 3 + 5 2 - *
Push
176
= _______
Info
Max
Top1
5
0
1
2
3
4
5
55
2 | ( 2 + 3 ) * (5 – 2)
2 3 + 5 2 - * 15
2 3 + 5 2 - *
Push
177
= _______
Info
Max
Top2
5
0
1
2
3
4
5
55 2
2 | ( 2 + 3 ) * (5 – 2)
2 3 + 5 2 - * 15
2 3 + 5 2 - *
Pop –Evaluate 5 - 2 Push 3
178
= _______
Info
Max
Top1
5
0
1
2
3
4
5
53
2 | ( 2 + 3 ) * (5 – 2)
2 3 + 5 2 - * 15
2 3 + 5 2 - *
Pop –Evaluate 5 * 3 Push 15
179
= _______
Info
Max
Top0
5
0
1
2
3
4
5
15
2 | ( 2 + 3 ) * (5 – 2)
2 3 + 5 2 - * 15
2 3 + 5 2 - *
Done –Only Item In Stack Contains Evaluated Expression
180
# 31
181
= _______
Info
Max
Top-1
5
0
1
2
3
4
5
Push
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
182
= _______
Info
Max
Top0
5
0
1
2
3
4
5
3 Push
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
183
= _______
Info
Max
Top1
5
0
1
2
3
4
5
3 2
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Pop Evaluate 3 * 2 Push 6
184
= _______
Info
Max
Top0
5
0
1
2
3
4
5
6
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Push
185
= _______
Info
Max
Top1
5
0
1
2
3
4
5
6 3
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Pop Evaluate 6 + 3 Push 9
186
# 32
= _______
Info
Max
Top0
5
0
1
2
3
4
5
9
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Push
187
= _______
Info
Max
Top1
5
0
1
2
3
4
5
9 4
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Push
188
= _______
Info
Max
Top2
5
0
1
2
3
4
5
9 4 2
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Pop Evaluate 4 / 2 Push 2
189
= _______
Info
Max
Top1
5
0
1
2
3
4
5
9 2
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Push
190
= _______
Info
Max
Top2
5
0
1
2
3
4
5
9 2 2
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Pop Evaluate 2 / 2 Push 1
191
= _______
Info
Max
Top1
5
0
1
2
3
4
5
9 1
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Pop Evaluate 9 - 1 Push 8
192
# 33
= _______
Info
Max
Top0
5
0
1
2
3
4
5
8
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Push
193
= _______
Info
Max
Top1
5
0
1
2
3
4
5
8 3
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -
Pop Evaluate 8 - 3 Push 5
194
= _______
Info
Max
Top0
5
0
1
2
3
4
5
5
3 2 * 3 + 4 2 / 2 / - 3 -
3 | 3 * 2 + 3 – 4 / 2 / 2 – 3
3 2 * 3 + 4 2 / 2 / - 3 -
5
3 2 * 3 + 4 2 / 2 / - 3 -Done –Only Item In Stack Contains Evaluated Expression
195 196
= _______
Info
Max
Top-1
5
0
1
2
3
4
53 2 * 3 + 4 2 / 2 / - 3 -
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
197
= _______
Info
Max
Top0
5
0
1
2
3
4
5
3
3 2 * 3 + 4 2 / 2 / - 3 -
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
198
# 34
= _______
Info
Max
Top1
5
0
1
2
3
4
5
32
3 2 * 3 + 4 2 / 2 / - 3 -
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
199
= _______
Info
Max
Top2
5
0
1
2
3
4
5
323
3 2 * 3 + 4 2 / 2 / - 3 -
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
200
= _______
Info
Max
Top3
5
0
1
2
3
4
5
3232
3 2 * 3 + 4 2 / 2 / - 3 -
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Pop Evaluate 3 ^ 2 Push 9
201
= _______
Info
Max
Top2
5
0
1
2
3
4
5
329
3 2 * 3 + 4 2 / 2 / - 3 -
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Pop Evaluate 2 ^ 9 Push 512
202
= _______
Info
Max
Top1
5
0
1
2
3
4
5
3512
3 2 * 3 + 4 2 / 2 / - 3 -
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
203
= _______
Info
Max
Top2
5
0
1
2
3
4
5
3512
4
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
204
# 35
= _______
Info
Max
Top3
5
0
1
2
3
4
5
3512
45
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
205
= _______
Info
Max
Top4
5
0
1
2
3
4
5
3512
454
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Pop Evaluate 5 - 4 Push 1
206
= _______
Info
Max
Top3
5
0
1
2
3
4
5
3512
41
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Pop Evaluate 4 * 1 Push 4
207
= _______
Info
Max
Top2
5
0
1
2
3
4
5
3512
4
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
208
= _______
Info
Max
Top3
5
0
1
2
3
4
5
3512
41
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Pop Evaluate 4 * 1 Push 4
209
= _______
Info
Max
Top2
5
0
1
2
3
4
5
3512
4
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Pop Evaluate 512 / 4 Push 128
210
# 36
= _______
Info
Max
Top1
5
0
1
2
3
4
5
3128
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Pop Evaluate 3 +128 Push 131
211
= _______
Info
Max
Top0
5
0
1
2
3
4
5
131
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Push
212
= _______
Info
Max
Top1
5
0
1
2
3
4
5
1312
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Pop Evaluate 131 * 2 Push 262
213
= _______
Info
Max
Top0
5
0
1
2
3
4
5
262
4 | ( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *262
3 2 3 2 ^ ^ 4 5 4 - * 1 * / + 2 *
Done –Only Item In Stack Contains Evaluated Expression
214
Stack <double> Eval(5);
What type of stack was to Evaluate The
Postfix?
215 216
# 37
Extra Credit LabNot A Team - Individual
You will have lots of programming to do this semester, but you may program this and submit it by the first reading day to replace your
two lowest quizzes with 100%
Main Program is to continue to prompt the user for an Infix until
the user enters QUIT.
If the infix is Invalid, say so. If it is Valid, Evaluate it and display the evaluated value.
217
This Lab Can Be Easily Expanded To Process Multiple Digit Floating Point Numbers: 1.2 *
5.43
This Lab Can Be Expanded To Process Variables More Difficult!
Lots of string processing practice!
Right to left string processing will enable you to create algorithm to evaluate prefix! 218
Software Engineering I
Be able to create an algorithm that you can walk through manually prior to
sitting at the computer.
219
Software Engineering II
Create and test well ADT’s, such as the Stack, that can be used with multiple
datatypes in many programs.
220
Software Engineering III
Implement & Test one part of a program at a time. Major components for this lab might be to (1) verify the Infix, (2) create the Postfix, and (3) evaluate the Postfix.
221