Given the expression, (x+y)*w+u/(v+x*w)+z, Please show the content in the stack after the operand vis read...
Given the expression, (x+y)*w+u/(v+x*w)+z, Please show the content in the stack after the operand vis read in postfix transformation.
Homework Answers
I have made a table which involves the operations and the following are the things which need to take into consideration while reading the table.
- the stack column contains the stack at each operation and left is the bottom-most element and right is the topmost element of the stack.
- Operation column contains the description of the operation performed upon reading the new character which can be read from the character column.
- Postfix is the string which is generated until now.
Following is the table.
| Sno | Character | Post-fix | stack(bottom…..top) | operation |
| 1 | ( | ( | Put the bracket opening to the stack | |
| 2 | x | x | ( | append the character to postfix |
| 3 | + | x | (+ | add to the stack |
| 4 | y | xy | (+ | append the character to postfix |
| 5 | ) | xy+ | - | pop out of the stack until first ( |
| 6 | * | xy+ | * | push to the stack |
| 7 | w | xy+w | * | append the character to postfix |
| 8 | + | xy+w* | + | Popped out until the operations having greater precedence than + |
| 9 | u | xy+w*u | + | append the character to postfix |
| 10 | / | xy+w*u | +/ | push to the stack |
| 11 | ( | xy+w*u | +/( | push to the stack |
| 12 | v | xy+w*uv | +/( | append the character to postfix |
| 13 | + | xy+w*uv | +/(+ | push to the stack |
| 14 | x | xy+w*uvx | +/(+ | append the character to postfix |
| 15 | * | xy+w*uvx | +/(+* | push to the stack |
| 16 | w | xy+w*uvxw | +/(+* | append the character to postfix |
| 17 | ) | xy+w*uvxw*+ | +/ | Pop until the ( |
| 18 | + | xy+w*uvxw*+/+ | + | Popped out until the operations having greater precedence than + |
| 19 | z | xy+w*uvxw*+/+z | + | append the character to postfix |
| 20 | xy+w*uvxw*+/+z+ | - | popped the remaining operations |
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