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Stack ADT
Tiziana Ligorio
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Today’s Plan
Questons? Stack ADT
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Stack ADT Tiziana Ligorio 1 Todays Plan Questons? Stack ADT 2 - - PowerPoint PPT Presentation
Stack ADT Tiziana Ligorio 1 Todays Plan Questons? Stack ADT 2 - - PowerPoint PPT Presentation
Stack ADT Tiziana Ligorio 1 Todays Plan Questons? Stack ADT 2 Abstract Data Types Bag List Stack 3 Stack 34 A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack
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Abstract Data Types
Bag List Stack
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Stack
A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack
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34
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Stack
A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack
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34
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Stack
A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack
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127 34
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Stack
A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack
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34 127
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Stack
A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack
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13 34 127
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Stack
A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack
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34 127 13
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Stack
A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack
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13 34 127
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Stack
A data structure representing a stack of things Objects can be pushed onto the stack or popped from the stack LIFO: Last In First Out Only top of stack is accessible (top), no other
- bjects on the stack are visible
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34 127
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Applications
Very simple structure Many applications: program stack balancing parenthesis evaluating postfix expressions backtracking . . . and more
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Program Stack
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Program Stack
1 void f(int x, int y) 2 { 3 int a; 4 // stuff here 5 if(a<13) 6 a = g(a); 7 // stuff here 8 } 9 int g(int z) 10 { 11 int p ,q; 12 // stuff here 13 return q; 14 }
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Program Stack
1 void f(int x, int y) 2 { 3 int a; 4 // stuff here 5 if(a<13) 6 a = g(a); 7 // stuff here 8 } 9 int g(int z) 10 { 11 int p ,q; 12 // stuff here 13 return q; 14 }
Stack Frame for f() parameters return address local variables
a x y
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Address of instruction after call to f()
. . .
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Program Stack
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Stack Frame for f() Stack Frame for g() parameters parameters return address return address local variables local variables
a p q x y z
Address of instruction after call to f()
Address of instruction on line 7
. . . . . .
1 void f(int x, int y) 2 { 3 int a; 4 // stuff here 5 if(a<13) 6 a = g(a); 7 // stuff here 8 } 9 int g(int z) 10 { 11 int p ,q; 12 // stuff here 13 return q; 14 }
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Program Stack
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Stack Frame for f() parameters return address local variables
a x y
Address of instruction after call to f()
. . .
1 void f(int x, int y) 2 { 3 int a; 4 // stuff here 5 if(a<13) 6 a = g(a); 7 // stuff here 8 } 9 int g(int z) 10 { 11 int p ,q; 12 // stuff here 13 return q; 14 }
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Balancing Parentheses
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
push
(
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
pop
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
push
{
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} {
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} {
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{
Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} (
push
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { (
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { (
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{ (
Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} (
push
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { ( (
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { ( (
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { ( (
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{ ( (
Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} [
push
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { ( ( [
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
pop
{ ( (
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
pop
{ (
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { (
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { (
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { (
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
pop
{
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
push
{ {
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { {
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { {
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { {
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { {
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { {
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}} { {
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
pop
{
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}}
Finished reading Stack is empty Parentheses are balanced
pop
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Balancing Parentheses
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int f(){if(x*(y+z[i])<47){x += y}
Finished reading Stack not empty Parentheses NOT balanced
{
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Balancing Parentheses
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for(char ch : st) { if ch is an open parenthesis character push it on the stack else if ch is a close parenthesis character if it matches the top of the stack pop the stack else return unbalanced // else it is not a parenthesis } if stack is empty return balanced else return unbalanced
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Evaluating Postfix Expressions
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Postfix Expressions
Operator applies to the two operands immediately preceding it
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Infix: 2 * (3 + 4) 2 * 3 + 4 Postfix: 2 3 4 + * 2 3 * 4 +
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Evaluating Postfix Expressions
Operator applies to the two operands immediately preceding it Assumptions / simplifications:
- String is syntactically correct postfix expression
- No unary operators
- No exponentiation operation
- Operands in string are single integer values
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Postfix: 2 3 4 + *
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
2
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
2 3
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
2 3 4
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
2 3 4
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
4
+
2 3
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
3 4
+
2
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
3 4
+ = 7
2
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2
Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
7
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
2 7
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
7 2
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
2 7
*
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
2 7
* = 14
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Evaluating Postfix Expressions
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Postfix: 2 3 4 + *
14
Done reading string The top of the stack is the result
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Evaluating Postfix Expressions
Operator applies to the two operands immediately preceding it Assumptions / simplifications:
- string is syntactically correct postfix expression
- No unary operators
- No exponentiation operation
- Operands in string are single integer values
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Postfix: 2 3 * 4 +
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Evaluating Postfix Expressions
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Postfix: 2 3 * 4 +
2
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Evaluating Postfix Expressions
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Postfix: 2 3 * 4 +
2 3
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Evaluating Postfix Expressions
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Postfix: 2 3 * 4 +
3
*
2
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Evaluating Postfix Expressions
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3
Postfix: 2 3 * 4 +
2
* = 6
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Evaluating Postfix Expressions
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Postfix: 2 3 * 4 +
6
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4
Evaluating Postfix Expressions
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Postfix: 2 3 * 4 +
6
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Evaluating Postfix Expressions
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Postfix: 2 3 * 4 +
4
+
6
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Evaluating Postfix Expressions
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Postfix: 2 3 * 4 +
6 4 10
+ =
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Evaluating Postfix Expressions
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Postfix: 2 3 * 4 +
10
Done reading string The top of the stack is the result
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Evaluating Postfix Expressions
for(char ch : st) { if ch is an operand push it on the stack else // ch is an operator op { //evaluate and push the result
- perand2 = pop stack
- perand1 = pop stack
result = operand1 op operand2 push result on stack } }
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Lecture Activity
Describe an algorithm that translates the infix expression below into postfix (you can use drawings to explain): Hint: use 2 stacks, one for operators and parentheses another one for the operands and postfix expression. Once converted use the empty stack to invert the order
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Infix: 2 * (3 + 4) Postfix: 2 3 4 + *
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2 3 4 (
+
Infix: 2 * (3 + 4) Postfix: 2 3 4 + *
2 3 4 *
+
1. Read characters onto corresponding stack until ‘)’
- 2. Pop operator stack and push
it onto postfix stack ignoring ‘(‘
Postfix Stack Operator Stack Postfix Stack Operator Stack
*
Postfix Stack Operator Stack
- 3. Push everything onto empty
stack to invert Then read pop and print.
2 3 4 *
+
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2 3 (
Infix: (2 * 3 )+ 4 Postfix: 2 3 *4 +
2 3 4 *
+
1. Read characters
- nto corr. stack until ‘)’
- r end of string
- 2. If reading a ‘)’, move operators
to Postfix Stack until a ‘(‘ discard it and continue reading string
Postfix Stack Operator Stack Postfix Stack Operator Stack
* 2 3 *
Postfix Stack Operator Stack
- 3. Keep reading
until ‘)’ -> 2.
- r end of string -> 4.
- 4. Move operators to
Postfix Stack
2 3 4 *
+
Postfix Stack Operator Stack
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Infix: (2 * 3 )+ 4 Postfix: 2 3 *4 +
2 3 4 *
+
- 4. Move operators to
Postfix Stack
Postfix Stack Operator Stack Postfix Stack Operator Stack
- 5. Pop and push onto empty
stack to invert, then print
2 3 4 *
+
SLIDE 86
Search a Flight Map
Fly from Origin to Destination following map
- 1. Reach destination
- 2. Reach city with no departing flights (dead end)
- 3. Go in circles forever
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z R C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z R X C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z R X C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z R X C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z R X C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z R X W C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z R X W S C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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P Origin = P , Destination = Z R X W S T C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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Origin = P , Destination = Z R X W S T P C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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Origin = P , Destination = Z R X W S T P C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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Origin = P , Destination = Z R X W S T P C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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Origin = P , Destination = Z R X W S T Y P C = visited C = backtracked
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Backtracking
Avoid dead end by backtracking Avoid traveling in circles by marking visited cities
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Origin = P , Destination = Z R X W S T Y Z P C = visited C = backtracked
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Backtracking
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Origin = P , Destination = Z
P
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P
Backtracking
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Origin = P , Destination = Z
R
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P
Backtracking
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Origin = P , Destination = Z
R X
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P
Backtracking
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Origin = P , Destination = Z
R
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Backtracking
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Origin = P , Destination = Z
P
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P W
Backtracking
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Origin = P , Destination = Z
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P W
Backtracking
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Origin = P , Destination = Z
S
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P W
Backtracking
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Origin = P , Destination = Z
S T
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Backtracking
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Origin = P , Destination = Z
P W S
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Backtracking
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Origin = P , Destination = Z
P W
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P W
Backtracking
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Origin = P , Destination = Z
Y
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P W Y
Backtracking
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Origin = P , Destination = Z
Z
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Backtracking
while(not found flights from origin to destination) { if no flight exists from city on top of stack to unvisited destination pop the stack //BACKTRACK else { select an unvisited city C accessible from city currently at top of stack push C on stack mark C as visited } }
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Program Stack and Recursion
Recursion works because function waiting for result/ return from recursive call are on program stack Order of execution determined by stack
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More Applications
Balancing anything!
- html tags (e.g <p> matches </p>
Reverse characters in a word or words in a sentence Undo mechanism for editors or backups Traversals (graphs / trees) . . .
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Stack ADT
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#ifndef STACK_H_ #define STACK_H_ template<<typename ItemType> class Stack { public: Stack(); void push(const ItemType& new_entry); //adds an element to top of stack void pop(); // removes element from top of stack ItemType top() const; // returns a copy of element at top of stack int size() const; // returns the number of elements in the stack bool isEmpty() const;//returns true if no elements on stack, else false private: //implementation details here }; //end Stack #include "Stack.cpp" #endif // STACK_H_`