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APPLICATION: AN RPN CALCULATOR Although the stack data structure is one of the simplest, it is essential in certain important applications. Some of these are illustrated in the following examples. An arithmetic expression is said to be in postfix notation (also called reverse Polish notation, or RPN) if each operator is placed after its operands. For example, the postfix expression for 3*(4 + 5) is 3 4 5 + *. [The expression 3*(4 + 5) is called an infix expression.] Postfix expressions are easier to process by machine than are infix expressions. Calculators that process postfix expressions are called RPN calculators. EXAMPLE 5.6 An RPN Calculator
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This program parses postfix expressions, performing the indicated arithmetic. It uses a stack to accumulate the operands.
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public class Calculator { public static void main(String[] args) { Deque<String> stack = new ArrayDeque<String>(); Scanner in = new Scanner(System.in); while (true) { String input = in.nextLine(); char ch = input.charAt(0); if (ch == '+' || ch == '-' || ch == '*' || ch == '/') { double y = Double.parseDouble(stack.pop()); double x = Double.parseDouble(stack.pop()); double z = 0; switch (ch) { case '+': z = x + y; break; case '-': z = x - y; break; case '*': z = x * y; break; case '/': z = x / y; } System.out.printf("\t%.2f %c %.2f = %.2f%n", x, ch, y, z); stack.push(new Double(z).toString()); } else if (ch == 'q' || ch == 'Q') { return; } else { stack.push(input); } } } }
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3 4 5 + 4.00 + 5.00 = 9.00 * 3.00 * 9.00 = 27.00 10 / 27.00 / 10.00 = 2.70 1 2.70 1.00 = 1.70 Q
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At line 3, the program instantiates a stack of strings, like the one in Example 5.1 on page 103. Then it goes into an infinite while loop at line 5, interactively reading a string on each iteration at line 6. If the user inputs anything other than +, -, *, /, q, or Q, the program assumes it is a number and pushes it onto the stack at line 23. If it is one of the four arithmetic operations, then the top two numbers are popped off the stack at lines 9 10 and the operation is applied to them. The result is printed at line 18 and then pushed onto the stack at line 19. The program ends when the user enters q or Q (for quit ).
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Human readers tend to prefer infix to postfix notation for arithmetic expressions. The following example converts a given infix expression to postfix. EXAMPLE 5.7 Converting Infix to Postfix
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public class TestScanner { public static void main(String[] args) { Deque<String> stack = new ArrayDeque<String>(); String line = new Scanner(System.in).nextLine(); System.out.println(line); Scanner scanner = new Scanner(line); while (scanner.hasNext()) { if (scanner.hasNextInt()) { System.out.print(scanner.nextInt() + " "); } else { String str = scanner. next(); if ("+-*/".indexOf(str) >= 0) { stack.push(str); } else if (str.equals(")")) { System.out.print(stack.pop() + " "); } } } while (!stack.isEmpty()) { System.out.print(stack.pop() + " "); } System.out.println(); } }
The output is:
( 80 30 ) * ( 40 + 50 / 10 ) 80 30 40 50 10 / + *
The output shows that the program parsed the infix expression ( 80 30 ) * ( 40 + 50 / 10 ) to generate its postfix equivalent 80 30 40 50 10 / + *. The program uses a stack, declared at line 3, and a scanner, declared at line 6. The scanner extracts integer and string tokens from the input line. If the token is an integer, it is printed immediately, at line 9. If it is one of the four strings "+", "-", "*", or "/", it is pushed onto the stack at line 13. If it is the strings ")", then the top element of the stack is popped off and printed at line 15. After the input line has been completely parsed, the remaining elements are popped from the stack and printed at lines 19 21.
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