Question

Use the stack-based algorithm for converting a postfix expression into an expression tree for the postfix expression: abc*+ghk+m*/* Illustrate each step.

Answer 1

The stack-based algorithm involves using a stack data structure to convert a postfix expression into an expression tree.

Step-by-step explanation:

The stack-based algorithm for converting a postfix expression into an expression tree involves using a stack data structure.

1. Start with an empty stack.
2. For each character in the postfix expression:
3. If it is an operand, create a new tree node with the operand as its value and push it onto the stack.
4. If it is an operator, pop two trees from the stack, with the top of the stack being the right child and the next element being the left child. Create a new tree node with the operator as its value and the two popped trees as its children. Push the new tree back onto the stack.
5. At the end, the entire expression tree will be on the stack. Pop it off and it will be the root of the expression tree.

For the postfix expression abc*+ghk+m*/*, the steps would be:

1. Create trees for operands a, b, c and push them onto the stack.
2. Encounter the operator *, pop trees b and c, create a new tree with * as the value and b and c as its children, push it back onto the stack.
3. Encounter the operator +, pop trees a and the result of the previous step, create a new tree with + as the value and a and the previous result as its children, push it back onto the stack.
4. Create trees for operands g, h, k and push them onto the stack.
5. Encounter the operator +, pop trees g and k, create a new tree with + as the value and g and k as its children, push it back onto the stack.
6. Encounter the operator *, pop trees the result of the previous step and m, create a new tree with * as the value and the previous result and m as its children, push it back onto the stack.
7. Encounter the operator /, pop trees the result of the previous step and the result of step 3, create a new tree with / as the value and the previous result and the previous previous result as its children, push it back onto the stack.
8. At this point, the entire expression tree is on the stack. Pop it off to get the root of the expression tree.