Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
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
#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
Updated on: 20-Dec-2019
4K+ Views
Advertisements