Infix And Prefix Conversion Questions

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infix, prefix based stack question



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What Is Infix and Prefix Conversion in DSA?

In DSA, expressions can be represented in different notations, mainly infix, prefix, and postfix. Each notation has unique advantages and purposes, especially when handling expressions in compilers and evaluating arithmetic operations. Here, we discuss infix and prefix conversion, the need for these conversions, and methods to perform them.

What is Infix and Prefix Notation?

  • Infix Notation: Operators are placed between operands. For example, A + B.
  • Prefix Notation: Operators are placed before the operands. For example, +AB.

Advantages and Disadvantages of Infix and Prefix Notations

  • Infix Notation:
    • Advantages: Easy for humans to read and understand, as it aligns with typical arithmetic expressions.
    • Disadvantages: Requires complex parsing logic due to operator precedence and associativity rules.
  • Prefix Notation:
    • Advantages: No need for operator precedence or parentheses; easier for computers to evaluate.
    • Disadvantages: Less intuitive for humans and can be difficult to interpret without understanding the notation.

Why is there a Need to Convert Between Notations?

Conversion between notations (infix, prefix, and postfix) is essential because different situations require different forms of expression. For instance:

  • Computers efficiently evaluate prefix and postfix expressions without needing parentheses or operator precedence.
  • Compilers convert infix expressions to prefix or postfix during expression evaluation to simplify the process and improve performance.
  • Infix notation is more intuitive for users, while prefix and postfix are preferred for computation and stack-based evaluation.

Method to Convert Infix to Prefix

  • Step 1: Reverse the infix expression.
  • Step 2: Replace opening parentheses with closing ones and vice versa.
  • Step 3: Convert the modified expression to postfix notation using stack-based methods.
  • Step 4: Reverse the postfix expression to get the prefix expression.

Method to Convert Prefix to Infix

  • Step 1: Read the prefix expression from right to left.
  • Step 2: If an operand is found, push it to the stack.
  • Step 3: If an operator is found, pop two operands from the stack, apply the operator between them, and push the resulting expression back to the stack.
  • Step 4: Continue until the expression is fully processed, with the final result as the infix expression.

21. Convert the infix expression (A+B)*(C-D) to prefix expression.

Answer:

To convert the infix expression (A+B)*(C-D) to prefix expression, we need to follow the operator precedence and associativity rules.
The steps are as follows:
1. First, convert (A+B) and (C-D) to prefix.
2. (A+B) becomes +AB and (C-D) becomes -CD.
3. Now, multiply these two sub-expressions.
4. The final prefix expression is *+AB-CD.

22. Convert the prefix expression *+AB-CD to infix expression.

Answer:

The given prefix expression is *+AB-CD.
1. Start from the rightmost operator and process each one sequentially.
2. First, we identify * as the operator. So, the infix form would be (A+B)*(C-D).
3. Therefore, the infix expression is (A+B)*(C-D).

23. Convert the infix expression A*(B+C/D) to prefix expression.

Answer:

To convert the infix expression A*(B+C/D) to prefix, follow these steps:
1. First, deal with the sub-expression inside parentheses (B+C/D).
2. C/D becomes /CD, and then (B+C/D) becomes +B/CD.
3. Finally, multiply this sub-expression with A, which gives us *A+B/CD.

24. Convert the prefix expression -+ABC to infix expression.

Answer:

The given prefix expression is -+ABC.
1. Start from the leftmost operator and process each one sequentially.
2. First, apply +AB, which becomes (A+B).
3. Next, apply the operator -, which gives us (A+B)-C.
4. Therefore, the infix expression is (A+B)-C.

25. Convert the infix expression (X+Y)/(Z-W) to prefix expression.

Answer:

To convert the infix expression (X+Y)/(Z-W) to prefix, follow these steps:
1. First, convert (X+Y) and (Z-W) to prefix.
2. (X+Y) becomes +XY and (Z-W) becomes -ZW.
3. Now divide these two sub-expressions.
4. The final prefix expression is /+XY-ZW.

27. Convert the infix expression (P/Q)+(R-S) to prefix expression.

Answer:

To convert the infix expression (P/Q)+(R-S) to prefix, follow these steps:
1. First, convert (P/Q) and (R-S) to prefix.
2. (P/Q) becomes /PQ and (R-S) becomes -RS.
3. Now add these two sub-expressions.
4. The final prefix expression is +/PQ-RS.

28. Convert the prefix expression +*AB/CD to infix expression.

Answer:

The given prefix expression is +*AB/CD.
1. Start from the leftmost operator and process each one sequentially.
2. First, apply *AB, which becomes (A*B).
3. Then, apply /CD, which becomes (C/D).
4. Finally, apply +, giving the infix expression as ((A*B)+(C/D)).

29. Convert the infix expression A/(B*C+D) to prefix expression.

Answer:

To convert the infix expression A/(B*C+D) to prefix, follow these steps:
1. First, deal with the sub-expression inside parentheses (B*C+D).
2. B*C becomes *BC, and then (B*C+D) becomes +*BCD.
3. Finally, divide this sub-expression by A, which gives us /A+*BCD.

30. Convert the prefix expression -*AB/CD to infix expression.

Answer:

The given prefix expression is -*AB/CD.
1. Start from the leftmost operator and process each one sequentially.
2. First, apply *AB, which becomes (A*B).
3. Then, apply /CD, which becomes (C/D).
4. Finally, apply -, giving the infix expression as ((A*B)-(C/D)).

31. Convert the infix expression (X-Y)*(Z+W) to prefix expression.

Answer:

To convert the infix expression (X-Y)*(Z+W) to prefix, follow these steps:
1. First, convert (X-Y) and (Z+W) to prefix.
2. (X-Y) becomes -XY and (Z+W) becomes +ZW.
3. Now multiply these two sub-expressions.
4. The final prefix expression is *-XY+ZW.

32. Convert the prefix expression /-AB*CD to infix expression.

Answer:

The given prefix expression is /-AB*CD.
1. Start from the leftmost operator and process each one sequentially.
2. First, apply -AB, which becomes (A-B).
3. Then, apply *CD, which becomes (C*D).
4. Finally, apply /, giving the infix expression as ((A-B)/(C*D)).

33. Convert the infix expression A+B*C-D to prefix expression.

Answer:

To convert the infix expression A+B*C-D to prefix, follow these steps:
1. First, multiply B and C to get *BC.
2. Then, add A to *BC to get +A*BC.
3. Finally, subtract D from +A*BC, which gives -+A*BCD.

35. Convert the infix expression (M+N)*(P-Q)/R to prefix expression.

Answer:

To convert the infix expression (M+N)*(P-Q)/R to prefix, follow these steps:
1. First, convert (M+N) and (P-Q) to prefix.
2. (M+N) becomes +MN and (P-Q) becomes -PQ.
3. Multiply +MN and -PQ, which gives *+MN-PQ.
4. Finally, divide by R to get / *+MN-PQ R.