What Is Prefix Expression in Data Structure?
In the field of data structure, a prefix expression, also known as Polish notation, is a way of representing arithmetic expressions. It was introduced by the Polish logician Jan Łukasiewicz in the 1920s.
Prefix Notation
In prefix notation, operators are written before their operands. This is in contrast to the more common infix notation, where operators are placed between operands. For example, in infix notation, the expression “3 + 4” would be written as “3 + 4”, while in prefix notation it would be written as “+ 3 4”.
This difference in notation may seem insignificant at first glance, but it has some important implications.
Evaluating Prefix Expressions
Evaluating a prefix expression involves scanning the expression from right to left. When an operator is encountered, it is applied to the immediately following operands. This process continues until all operators have been applied and a single value remains.
To illustrate this process, let’s consider the prefix expression “+ * 5 – 6 8 2”.
Step 1:
- Scan from right to left and encounter “*” operator.
- The next two values encountered are “5” and “-“.
- Multiply these two values: “5 * -” = “-5”.
- Replace these three values with their result: “+ -5 6 8 2”.
Step 2:
- The next operator encountered is “+”.
- The next value encountered is “-5”.
- Add these two values: “+ -5” = “-5”.
- Replace these three values with their result: “-5 6 8 2”.
Step 3:
- The next operator encountered is “-“.
- The next two values encountered are “6” and “8”.
- Subtract these two values: “6 – 8” = “-2”.
- Replace these three values with their result: “-5 -2 2”.
Step 4:
- The final operator encountered is “-“.
- The next two values encountered are “-5” and “2”.
- Subtract these two values: “-5 – 2” = “-7”.
- Replace these three values with their result: “-7 2”.
After evaluating all the operators, the final result of the prefix expression “+ * 5 – 6 8 2” is “-7”.
Advantages and Disadvantages of Prefix Notation
The use of prefix notation has both advantages and disadvantages.
Advantages:
- Simplicity: Prefix notation eliminates the need for parentheses or precedence rules, making expressions simpler to evaluate.
- Ease of Parsing: Scanning a prefix expression from right to left allows for straightforward parsing, especially in computer programs.
- No Ambiguity: Unlike infix notation, prefix notation avoids any ambiguity in the order of operations.
Disadvantages:
- Familiarity: Infix notation is more widely used and familiar, making prefix notation less intuitive to read for many people.
- Increased Length: Prefix notation can sometimes result in longer expressions compared to infix notation, which may reduce readability.
In conclusion, a prefix expression is a way of representing arithmetic expressions by placing operators before their operands. While it may have some disadvantages in terms of familiarity and increased length, it offers advantages such as simplicity, ease of parsing, and no ambiguity. Understanding prefix notation is essential for working with certain data structures and algorithms.