从多项式函数字符串动态分配数组

Question

So I have a polynomial addition problem like the one below:

(1*x+2*x^3-1*x+7)+(1+1*x^2-1*x+1*x^4)

I need to figure out how to extract the numbers for the coefficients and exponents and enter them into a dynamically allocated 2D array (from here I can sort them and add them together before outputting the answer).

I am pretty lost on how to do this because the polynomials can be in any order of degrees and include any amount of terms. I can dynamically allocate them after I extract all of the numbers. The part I need help on is:

• Extracting all of the numbers
• Differentiating between them to see if it is a coefficient or an exponent
• Allowing this to happen for any number of terms

If anyone could answer this or at least point me in the right direction it would be appreciated.

Answer 1

Your problem looks like its parsing and evaluation.

• Step1: You need to parse the string assuming an infix expression, so that you can pull out the coefficient

• Step2: push those coefficients into a vector/deque etc to perform the polynomial calculation.

Here are some good examples:

Evaluating arithmetic expressions from string in C++

What is the best way to evaluate mathematical expressions in C++?

Answer 2

To extract coefficients from a string you need to create a parser. You can use special library like boost.spirit , you can use special tool which builds parsers like Flex , or you can make your own manually using regular expressions or not.

To store coeficients you can use std::vector<int> using indexes as power of x, so for 1*x+2*x^3-1*x+7 your vector would have data:

{ 7, -1, 0, 2 } // 7*x^0 + -1*x^1 + 0*x^2 + 2*x^3 

then you do not need to sort them to add coefficients. To store all polynoms you would use std::vector<std::vector<int>> accordingly.