3.20. Discussion Questions¶

1. Convert the following values to binary using “divide by 2.” Show the stack of remainders.
   • 17
   • 45
   • 96
2. Convert the following infix expressions to prefix (use full parentheses):
   • (A+B)*(C+D)*(E+F)
   • A+((B+C)*(D+E))
   • A*B*C*D+E+F
3. Convert the above infix expressions to postfix (use full parentheses).
4. Convert the above infix expressions to postfix using the direct conversion algorithm. Show the stack as the conversion takes place.
5. Evaluate the following postfix expressions. Show the stack as each operand and operator is processed.
   • 2 3 * 4 +
   • 1 2 + 3 + 4 + 5 +
   • 1 2 3 4 5 * + * +
6. The alternative implementation of the Queue ADT is to use a vector such that the rear of the queue is at the end of the vector. What would this mean for Big-O performance?