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Stacks have numerous applications in computer science, and two common ones are the conversion of infix expressions to postfix and prefix notations, as well as the evaluation of postfix expressions. Let’s delve into each of these applications:

1. Conversion of Infix to Postfix and Prefix Expressions:

Infix notation is the common way we write expressions, where operators are written between the operands, such as 2 + 3 * 4. However, for evaluation by computers, postfix (also known as Reverse Polish Notation) and prefix (also known as Polish Notation) notations are often preferred because they don’t require parentheses to denote precedence.

  • Infix to Postfix Conversion:
    • We can use stacks to convert infix expressions to postfix expressions. The algorithm involves scanning the infix expression from left to right and using a stack to keep track of operators. The resulting postfix expression is obtained by popping the operators from the stack based on their precedence.
  • Infix to Prefix Conversion:
    • Similar to infix to postfix conversion, but the operators are placed before their operands. The algorithm is slightly different but follows the same principle of using a stack.

2. Evaluation of Postfix Expressions using Stack:

Postfix notation is more suitable for evaluation by computers because it doesn’t require parentheses to denote precedence. In postfix notation, the operator comes after the operands, such as 23 4 * + which is equivalent to 2 + 3 * 4.

  • Algorithm for Postfix Evaluation:
    • Start scanning the expression from left to right.
    • If an operand is encountered, push it onto the stack.
    • If an operator is encountered, pop the top two operands from the stack, perform the operation, and push the result back onto the stack.
    • Repeat until the entire expression is scanned.
    • At the end, the result will be the only element left on the stack.

Example:

Let’s evaluate the postfix expression 23 4 * +:

  1. Scan the expression from left to right.
  2. Push operands onto the stack: Stack: [2, 3]
  3. Encounter *: Pop 3 and 2, perform 3 * 2, push 6 onto the stack: Stack: [6]
  4. Encounter +: Pop 6 and 4, perform 6 + 4, push 10 onto the stack: Stack: [10]
  5. The result 10 is the final answer.

These applications illustrate how stacks are utilized in converting infix expressions to postfix and prefix notations and in evaluating postfix expressions efficiently.