Expression Compiler

The instructions of a stack based virtual machine use a stack from which their arguments are fetched, and they replace the arguments with the result of the operation. Consider a stack based virtual machine which supports the following instructions:

• PUSH <n> - push the number <n> on to the stack.
• ADD - pops the top two elements of the stack, adds them and pushes the result back on to the stack.
• SUB - pops the top two elements, subtracts the top most element from the second element and pushes the result back on to the stack.
• MUL - pops the top two elements, multiplies them and pushes them back on to the stack.
• DIV - pops the top two elements, divides the second element by the top most element, and pushes the result back on to the stack.

Write a program which accepts an arithmetic expression, and generates as output, the instructions needed by this virtual machine to evaluate the expression.

Notes

• The arithmetic expression will be provided as a command line parameter to the program.
• The program's output should consist of one instruction per line.
• The expression string will only have the following characters: 0-9,+,-,*,/,(,). No other characters such as space characters will appear in the expression string.
• All numbers present in the expression will be single digit integers.
• Only binary addition(+), subtruction(-), multiplication(*) and division(/) operations are supported. Multiplication and division operations take precedence over addition and subtraction.
• Unary negative and unary positive operators are not supported.
• The expression can be arbitrarily nested using parentheses.
• There are many different valid instruction sequences for a given expression. The program can produce any valid output.

Examples