Write a class called RandomArithmeticExpression that forms a randomly generated expression that follows the rules listed in the grammar shown below. Your code will be tested by RandomArithmeticGenerator, which is available on Site to get you started.

  • To avoid the possibility of infinite recursion, limit the depth of recursion to 16 levels, where a level corresponds to any production involving at least one non-terminal on the right of the production.
  • When printed, there should be a single space between each of the non-blank characters in the expression.

Grammar:

The initial expression is S. The non-terminal expressions are S and E. The values x, y, and z are terminals, that is, they cannot be replaced by any other symbol. An expression appearing on the left of a --> may be replaced by any expression of the right of that arrow as shown below.

S --> E
E --> E + E
E --> E – E
E --> E * E
E --> E / E
E --> ( E )
E --> x | y | z

For example, a derivation might be:

S --> E --> E + E --> E + ( E ) --> E * E + ( E ) --> x * E +( E ) --> x * E – E +( E ) --> x * E – E +( z ) --> x * E – z +( z ) --> x * y – z +( z )

Here are four randomly generated expressions:

( x + ( x + z / y + z / x * z / y * z / y ) - y - y / x ) x * ( ( y * ( x * y * y * y ) * y / z * z + x ) / x ) ( z ) y / y * y - x * z / ( x ) + x - z - z

Here is the test driver code: See image.

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