The task in this problem is to evaluate a sequence of simple C expressions, but you need not know C to solve the problem! Each of the expressions will appear on a line by itself and will contain no more than 80 characters. The expressions to be evaluated will contain only simple integer variables and a limited set of operators; there will be no constants in the expressions. There are 26 variables which may appear in our simple expressions, namely those with the names a through z (lower-case letters only). At the beginning of evaluation of each expression, these 26 variables will have the integer values 1 through 26, respectively (that is, a = 1, b = 2, ...). Each variable will appear at most once in an expression and many variables may not be used at all.
The operators that may appear in expressions include the binary (two-operand) + and -, with the usual interpretation. Thus the expression a + c - d + b has the value 2 (computed as 1 + 3 - 4 + 2). The only other operators that may appear in expressions are ++ and --. These are unary (one-operand) operators, and may appear before or after any variable. When the ++ operator appears before a variable, that variable's value is incremented (by one) before the variable's value is used in determining the value of the entire expression. Thus the value of the expression ++ c - b is 2, with c being incremented to 4 prior to evaluation the entire expression. When the ++ operator appears after a variable, that variable is incremented (again, by one) after its value is used to determine the value of the entire expression. Thus the value of the expression c ++ - b is 1, but c is incremented after the complete expression is evaluated; its value will still be 4. The -- operator can also be used before or after a variable to decrement (by one) the variable; its placement before or after the variable has the same significance as for the ++ operator. Thus the value of the expression -- c + b -- has the value 4, with variables b and c having the values 1 and 2 following the evaluation of the expression.
Here's another, more algorithmic, approach to explaining the ++ and -- operators. We'll consider only the ++ operator, for brevity:
- Identify each variable that has a ++ operator before it. Write a simple assignment statement that increments the value of each such variable, and remove the ++ from before that variable in the expression.
- In a similar manner, identify each variable that has a ++ operator after it. Write a simple assignment statement that increments the value of each of these, and remove the ++ operator from after that variable in the expression.
- Now the expression has no ++ operators before or after any variables. Write the statement that evaluates the remaining expression after those statements written in step 1, and before those written in step 2.
- Execute the statements generated in step 1, then those generated in step 3, and finally the one generated in step 2, in that order.
Using this approach, evaluating the expression ++ a + b ++ is equivalent to computing a = a + 1 (from step 1 of the algorithm) expression = a + b (from step 3) b = b + 1 (from step 2) where expression would receive the value of the complete expression.