C++ Program for Derivative of a Polynomial

Given a string containing the polynomial term, the task is to evaluate the derivative of that polynomial.

What is a Polynomial?

Polynomial comes from two words: - “Poly” which means “many” and “nomial” means “terms”, which comprises many terms. Polynomial expression is an expression containing variables, coefficients and exponents, which only involves operations such as, addition, multiplication and subtraction of variable(s).

Example of polynomial

x2+x+1

Derivative of the polynomial p(x) = mx^n  will be −

m * n * x^(n-1)

Example

Input: str = "2x^3 +1x^1 + 3x^2"
   val = 2
Output: 37
Explanation: 6x^2 + 1x^0 + 6x^1
   Putting x = 2
   6*4 + 1 + 6*2 = 24 + 1 + 12 = 37

Input: str = “1x^3”
   val = 2
Output: 12
Explanation: 1 * 3 *x^2
   Putting x = 2
   3 * 4 = 12

Approach we will be using to solve the above problem −

• Take the input  as a string and a value of x
• Now traverse the string and check for the digits, and variables.
• Keep adding and traversing the string till we find ‘+’.
• Then m * n * x^(n-1).
• Return the result.

Algorithm

Start
Step 1-> In function long long term(string polyterm, long long val)
   Declare and initialize coeffStr = "”
   Declare i
   Loop For i = 0 and polyterm[i] != 'x' and i++
      Call coeffStr.push_back(polyterm[i])
      Set coeff = atol(coeffStr.c_str()
      Declare and initialize powStr = ""
      Loop For i = i + 2 and i != polyterm.size() and i++ powStr.push_back(polyterm[i])
         Set power = atol(powStr.c_str());
   Return coeff * power * pow(val, power - 1)
Step 2-> In function long long value(string& str, int val)
   Set ans = 0
   Call istringstream is(str)
   Declare string polyterm
   Loop While is >> polyterm
      If polyterm == "+” then,
         Continue
      Else
         Set ans = (ans + term(polyterm, val))
   Return ans
Step 3-> In function int main()
   Declare and initialize str = "2x^3 + 1x^1 + 3x^2"
   Declare and initialize val = 2
   Print the value received by value(str, val)
Stop

Example

 Live Demo

#include
using namespace std;
long long term(string polyterm, long long val) {
   //to find the coefficient
   string coeffStr = "";
   int i;
   for (i = 0; polyterm[i] != 'x'; i++)
      coeffStr.push_back(polyterm[i]);
   long long coeff = atol(coeffStr.c_str());
   // to get the power value
   string powStr = "";
   for (i = i + 2; i != polyterm.size(); i++)
      powStr.push_back(polyterm[i]);
   long long power = atol(powStr.c_str());
   // For ax^n, we return a(n-1)x^(n-1)
   return coeff * power * pow(val, power - 1);
}
long long value(string& str, int val) {
   long long ans = 0;
   // using istringstream to get input in tokens
   istringstream is(str);
   string polyterm;
   while (is >> polyterm) {
      // check if the token is equal to '+' then
      // continue with the string
      if (polyterm == "+")
         continue;
         // Otherwise find the derivative of that
         // particular term
      else
         ans = (ans + term(polyterm, val));
   }
   return ans;
}
// main function
int main() {
   string str = "2x^3 + 1x^1 + 3x^2";
   int val = 2;
   cout << value(str, val);
   return 0;
}

Output

37