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33
4
Must Get Same Answer As Manual Solution! Preserve The Mathematical Order Of Operations
5 + 2 ^ 3 ^ 2 = _______69 ?517 ?Other ?
5
Maybe A Spreadsheet Will Help?
69 ?517 ?
Maybe Not!
5 + 2 ^ 3 ^ 2 = _______
6
Create A 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
7
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
8
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
9
5 2 3 2
10
5 + 2 ^ 3 ^ 2
1 – Write Down All Of The Operands
Infix
Prefix
Postfix
5 2 3 2
5 2 3 2^
11
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^^
12
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^^+
13
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
14
( 2 + 3 ) * ( 5 – 2 )
15
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 )
16
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 )
17
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
18
19
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
20
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
21
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
22
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
23
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
24
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
25
( 3 + 2 ^ 3 ^ 2 / {4 * [ 5 – 4 ] * 1 } ) * 2
26
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
27
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
28
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
29
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
30
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
31
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
32
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
33
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
34
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
35
36
37
38
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
39
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
40
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
41
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
42
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
43
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
44
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
45
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
46
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
47
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
48
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
49
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
50
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
51
52
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
53
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
54
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
55
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
56
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
57
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
58
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
59
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
60
61
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
62
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 -
63
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 -
64
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 -
65
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 -
66
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 -
67
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 -
68
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 -
69
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
70
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 /
71
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
72
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 -
-
73
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
74
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
75
76
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)
3 2 3 2^ ^ 4 5 4 - * 1* / + 2 *
77
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
78
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 +
79
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
80
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 ^
81
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
82
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 ^
83
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
^
84
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 /
^
85
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
86
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
87
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 *
88
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
89
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
90
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
91
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
92
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 4
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
93
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 4 -
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 -
*
94
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 4 - *
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
95
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 4 - * 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
96
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 4 - * 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
+
97
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 4 - * 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 *
98
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 4 - * 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
99
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 4 - * 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
Scala:var st = new charStack(50)
Stack <char> Postfix(5);
What type of stack was to
create the Postfix from the Infix?
100
You Must Have Function
def createPostfix (infix : String) : String =
{// You Do"2 3 +"
}
Test With Multiple Digit DoublesYou May Assume A Blank Between Each Token In The Infix ExpressionYou May Assume That The Infix Is Valid (Other Than ({[)
101
if ((diagnosticLevel == 20) || (diagnosticLevel == 99)){
var postfix = "?" var infix = "?" do{
println("\n\n\n====================================================")println("===== Interactive Testing createPostfix =====")println("===== diagnosticLevel = 20 =====")println("====================================================\n") printlnprint("\nEnter Infix <QUIT to Exit> : ")infix = readLine
if (postfix.toUpperCase != "QUIT"){
println ("\nInfix Expression = " + infix + "\n")var postfix = createPostfix(infix)println("\n===> Postfix Solution = " + postfix)
}
} while (infix.toUpperCase != "QUIT")102
Add Your Own Diagnostic TestingYou Must Include The Following Make Any Corrections Necessary!
Set Your Diagnostic
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