You manage to answer the child’s questions and they finish part 1 of their homework, but get stuck when they reach the next section: advanced math.

Now, addition and multiplication have different precedence levels, but they’re not the ones you’re familiar with. Instead, addition is evaluated before multiplication.

For example, the steps to evaluate the expression 1 + 2 * 3 + 4 * 5 + 6 are now as follows:

1 + 2 * 3 + 4 * 5 + 6
  3   * 3 + 4 * 5 + 6
  3   *   7   * 5 + 6
  3   *   7   *  11
     21       *  11
         231

Here are the other examples from above:

• 1 + (2 * 3) + (4 * (5 + 6)) still becomes 51.
• 2 * 3 + (4 * 5) becomes 46.
• 5 + (8 * 3 + 9 + 3 * 4 * 3) becomes 1445.
• 5 * 9 * (7 * 3 * 3 + 9 * 3 + (8 + 6 * 4)) becomes 669060.
• ((2 + 4 * 9) * (6 + 9 * 8 + 6) + 6) + 2 + 4 * 2 becomes 23340.

Assignment

What do you get if you add up the results of evaluating the homework problems using these new rules? This is done in the following way:

• Write a function evaluate that takes an expression (char*). The function must return the value (int) that results from evaluating the expression.
• Write a function homework that takes the pathname (char*) of a text file containing a series of expressions, one expression per line. The function must return the sum (int) of the values that result from evaluating each expression.

Example

In this interactive session we assume the text file homework.txt¹ to be located in the current directory.

> evaluate("1 + 2 * 3 + 4 * 5 + 6")
231
> evaluate("1 + (2 * 3) + (4 * (5 + 6))')
51
> evaluate("2 * 3 + (4 * 5)')
46
> evaluate("5 + (8 * 3 + 9 + 3 * 4 * 3)')
1445
> evaluate("5 * 9 * (7 * 3 * 3 + 9 * 3 + (8 + 6 * 4))')
669060
> evaluate("((2 + 4 * 9) * (6 + 9 * 8 + 6) + 6) + 2 + 4 * 2')
23340

> homework("homework.txt")
694173