Since the question asks us to find all of the valid expressions, we need a way to iterate over all of them. (Hint: Recursion!)
提示 3
We can keep track of the expression string and evaluate it at the very end. But that would take a lot of time. Can we keep track of the expression's value as well so as to avoid the evaluation at the very end of recursion?
提示 4
Think carefully about the multiply operator. It has a higher precedence than the addition and subtraction operators.
1 + 2 = 3
1 + 2 - 4 --> 3 - 4 --> -1
1 + 2 - 4 * 12 --> -1 * 12 --> -12 (WRONG!)
1 + 2 - 4 * 12 --> -1 - (-4) + (-4 * 12) --> 3 + (-48) --> -45 (CORRECT!)
提示 5
We simply need to keep track of the last operand in our expression and reverse it's effect on the expression's value while considering the multiply operator.
