## Basic Data Structures

Stacks Basic Data Structures Stacks Brad Miller David Ranum 1/25/06 Basic Data Structures Stacks Outline 1 Stacks What is a Stack? The Stack ...
Author: Jeffery Quinn
Stacks

Basic Data Structures Stacks Brad Miller

David Ranum

1/25/06

Basic Data Structures

Stacks

Outline

1

Stacks What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Outline

1

Stacks What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

A Stack of Books

Python Calculus Physics Music History

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

A Stack of Primitive Python Objects

8.4

Top

True “dog" 4 Base

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

The Reversal Property of Stacks

8.4 True

first

last "dog"

8.4

True

"dog" 4

first

4

last

Original Order

4

"dog"

True

Reversed Order

Basic Data Structures

8.

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Outline

1

Stacks What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stack() creates a new stack that is empty. It needs no parameters and returns an empty stack. push(item) adds a new item to the top of the stack. It needs the item and returns nothing. pop() removes the top item from the stack. It needs no parameters and returns the item. The stack is modified. peek() returns the top item from the stack but does not remove it. It needs no parameters. The stack is not modified. isEmpty() tests to see whether the stack is empty. It needs no parameters and returns a boolean value. size() returns the number of items on the stack. It needs no parameters and returns an integer. Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Outline

1

Stacks What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stack Implementation in Python I 1 2 3

c l a s s Stack: d e f __init__(self): self.items = []

4 5 6

d e f isEmpty(self): r e t u r n self.items == []

7 8 9

d e f push(self, item): self.items.append(item)

10 11 12

d e f pop(self): r e t u r n self.items.pop()

13 14

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stack Implementation in Python II

15 16

d e f peek(self): r e t u r n self.items[len(self.items)-1]

17 18 19

d e f size(self): r e t u r n len(self.items)

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Alternative ADT Stack Implementation in Python I 1 2 3

c l a s s Stack: d e f __init__(self): self.items = []

4 5 6

d e f isEmpty(self): r e t u r n self.items == []

7 8 9

d e f push(self, item): self.items.insert(0,item)

10 11 12

d e f pop(self): r e t u r n self.items.pop(0)

13 14

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Alternative ADT Stack Implementation in Python II

15 16

d e f peek(self): r e t u r n self.items[0]

17 18 19

d e f size(self): r e t u r n len(self.items)

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Outline

1

Stacks What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Basic Data Structures

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stacks

Matching Parentheses

Most recent open matches first close (

(

)

(

(

)

)

(

First open may wait until last close

Basic Data Structures

)

)

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Simple Balanced Parentheses I 1 2

d e f parChecker(symbolString): s = Stack()

3 4 5

balanced = True index = 0

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w h i l e index < len(symbolString) and balanced: symbol = symbolString[index] i f symbol == "(": s.push(symbol) else:

12 13 14

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Simple Balanced Parentheses II 15 16 17 18

i f s.isEmpty(): balanced = False else: s.pop()

19 20

index = index + 1

21 22 23 24 25

i f balanced and s.isEmpty(): r e t u r n True else: r e t u r n False

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Outline

1

Stacks What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Balanced Symbols–A General Case I 1

d e f parChecker(symbolString):

2 3

s = Stack()

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balanced = True index = 0

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w h i l e index < len(symbolString) and balanced: symbol = symbolString[index] i f symbol i n "([{": s.push(symbol) else:

13 14

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Balanced Symbols–A General Case II 15 16 17 18 19 20 21

i f s.isEmpty(): balanced = False else: top = s.pop() i f n o t matches(top,symbol): balanced = False

22 23

index = index + 1

24 25 26 27 28

i f balanced and s.isEmpty(): r e t u r n True else: r e t u r n False

29

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Balanced Symbols–A General Case III

30 31 32

d e f matches(open,close): opens = "([{" closers = ")]}"

33 34

r e t u r n opens.index(open) == closers.index(close)

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Outline

1

Stacks What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Basic Data Structures

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stacks

Decimal-to-Binary Conversion

1 rem = 1

1 rem = 0

58 / 2 = 29

rem = 0

29 / 2 = 14

rem = 1

14 / 2 = 7

rem = 0

7/2=3

rem = 1

3/2=1

Basic Data Structures

0 1 0 0

rem = 1

1/ 2 = 0

1

rem = 1

1

pop remainders

116 / 2 = 58

push remainders

233 / 2 = 116

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Decimal to Binary Conversion 1

d e f divideBy2(decNumber):

2 3

remstack = Stack()

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w h i l e decNumber > 0: rem = decNumber % 2 remstack.push(rem) decNumber = decNumber / 2

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binString = "" w h i l e n o t remstack.isEmpty(): binString = binString + str(remstack.pop())

13 14

r e t u r n binString Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Conversion to Any Base I 1

d e f baseConverter(decNumber,base):

2 3

digits = "0123456789ABCDEF"

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remstack = Stack()

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w h i l e decNumber > 0: rem = decNumber % base remstack.push(rem) decNumber = decNumber / base

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Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Conversion to Any Base II

15 16 17

newString = "" w h i l e n o t remstack.isEmpty(): newString = newString + digits[remstack.pop()]

18 19

r e t u r n newString

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Outline

1

Stacks What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Basic Data Structures

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stacks

Moving Operators to the Right for Postfix Notation

(

A

+

(

B

*

C

Basic Data Structures

)

)

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stacks

Moving Operators to the Left for Prefix Notation

(

A

+

(

B

*

C

Basic Data Structures

)

)

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Converting a Complex Expression to Prefix and Postfix Notations

(A + B) * C - (D - E) * (F + G)

(((A + B) * C) - ((D - E) * (F + G))) Prefix -*+A B C *- D E + F G

Postfix A B + C * D E - F G + * -

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

1

Create an empty stack called opstack for keeping operators. Create an empty list for output.

2

Convert the input infix string to a list by using the string method split.

Basic Data Structures

Stacks

3

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Scan the token list from left to right. If the token is an operand, append it to the end of the output list. If the token is a left parenthesis, push it on the opstack. If the token is a right parenthesis, pop the opstack until the corresponding left parenthesis is removed. Append each operator to the end of the output list. If the token is an operator, *, /, +, or -, push it on the opstack. However, first remove any operators already on the opstack that have higher or equal precedence and append them to the output list.

4

When the input expression has been completely processed, check the opstack. Any operators still on the stack can be removed and appended to the end of the output list. Basic Data Structures

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stacks

Converting A * B + C * D to Postfix Notation A*B+C*D A

A

*

B

+

*

*

*

B

C

*

D

*

*

*

+

+

+

+

+

*

C

D

AB*CD*+

Basic Data Structures

+

*

+

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Converting Infix Expressions to Postfix Expressions I 1 2

import string d e f infixToPostfix(infixexpr):

3 4 5 6 7 8 9

prec = {} prec["*"] prec["/"] prec["+"] prec["-"] prec["("]

= = = = =

3 3 2 2 1

10 11 12

opStack = Stack() postfixList = []

13 14

tokenList = infixexpr.split() Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Converting Infix Expressions to Postfix Expressions II 15 16 17 18 19 20 21 22 23 24 25

f o r token i n tokenList: i f token i n string.uppercase: postfixList.append(token) e l i f token == ’(’: opStack.push(token) e l i f token == ’)’: topToken = opStack.pop() w h i l e topToken != ’(’: postfixList.append(topToken) topToken = opStack.pop()

26 27 28 29

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Converting Infix Expressions to Postfix Expressions III 30 31 32 33

else: w h i l e ( n o t opStack.isEmpty()) and \ (prec[opStack.peek()] >= prec[token]): postfixList.append(opStack.pop())

34 35

opStack.push(token)

36 37 38

w h i l e n o t opStack.isEmpty(): postfixList.append(opStack.pop())

39 40

r e t u r n string.join(postfixList)

Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Stack Contents During Evaluation Left to Right Evaluation 4

push

5

6

*

push

push

pop twice and do math pop twice and do math

6

4

+

5

5

30

4

4

4

Basic Data Structures

34

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

A More Complex Example of Evaluation 7

8

+

3

2

+

/

2 8 7

7

15

3

3

5

15

15

15

Basic Data Structures

3

Stacks

1 2

3

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Create an empty stack called operandStack. Convert the string to a list by using the string method split. Scan the token list from left to right. If the token is an operand, convert it from a string to an integer and push the value onto the operandStack. If the token is an operator, *, /, +, or -, it will need two operands. Pop the operandStack twice. The first pop is the second operand and the second pop is the first operand. Perform the arithmetic operation. Push the result back on the operandStack.

4

When the input expression has been completely processed, the result is on the stack. Pop the operandStack and return the value. Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Postfix Evaluation I 1 2 3

d e f postfixEval(postfixExpr): operandStack = Stack() tokenList = postfixExpr.split()

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f o r token i n tokenList: i f token i n "0123456789": operandStack.push(int(token)) else: operand2 = operandStack.pop() operand1 = operandStack.pop() result = doMath(token,operand1,operand2) operandStack.push(result)

13 14

r e t u r n operandStack.pop() Basic Data Structures

Stacks

What is a Stack? The Stack Abstract Data Type Implementing a Stack in Python Simple Balanced Parentheses Balanced Symbols (A General Case) Converting Decimal Numbers to Binary Numbers Infix, Prefix and Postfix Expressions

Postfix Evaluation II 15 16 17 18 19 20 21 22 23 24 25 26

d e f doMath(op, op1, op2): i f op == "*": r e t u r n op1 * op2 else: i f op == "/": r e t u r n op1 / op2 else: i f op == "+": r e t u r n op1 + op2 else: r e t u r n op1 - op2

Basic Data Structures