Program for Derivative of a Polynomial
Given a polynomial as a string and a value. Evaluate polynomial’s derivative for the given value.
Note: The input format is such that there is a white space between a term and the ‘+’ symbol
The derivative of p(x) = ax^n is p'(x) = a*n*x^(n-1)
Also, if p(x) = p1(x) + p2(x)
Here p1 and p2 are polynomials too
p'(x) = p1′(x) + p2′(x)
Input : 3x^3 + 4x^2 + 6x^1 + 89x^0 2 Output :58 Explanation : Derivative of given polynomial is : 9x^2 + 8x^1 + 6 Now put x = 2 9*4 + 8*2 + 6 = 36 + 16 + 6 = 58 Input : 1x^3 3 Output : 27
We split the input string into tokens and for each term calculate the derivative separately for each term and add them to get the result.
C++
// C++ program to find value of derivative of // a polynomial. #include <bits/stdc++.h> using namespace std; long long derivativeTerm(string pTerm, long long val) { // Get coefficient string coeffStr = "" ; int i; for (i = 0; pTerm[i] != 'x' ; i++) coeffStr.push_back(pTerm[i]); long long coeff = atol (coeffStr.c_str()); // Get Power (Skip 2 characters for x and ^) string powStr = "" ; for (i = i + 2; i != pTerm.size(); i++) powStr.push_back(pTerm[i]); long long power = atol (powStr.c_str()); // For ax^n, we return anx^(n-1) return coeff * power * pow (val, power - 1); } long long derivativeVal(string& poly, int val) { long long ans = 0; // We use istringstream to get input in tokens istringstream is(poly); string pTerm; while (is >> pTerm) { // If the token is equal to '+' then // continue with the string if (pTerm == "+" ) continue ; // Otherwise find the derivative of that // particular term else ans = (ans + derivativeTerm(pTerm, val)); } return ans; } // Driver code int main() { string str = "4x^3 + 3x^1 + 2x^2" ; int val = 2; cout << derivativeVal(str, val); return 0; } |
Java
// Java program to find value of derivative of // a polynomial import java.io.*; class GFG { static long derivativeTerm(String pTerm, long val) { // Get coefficient String coeffStr = "" ; int i; for (i = 0 ; pTerm.charAt(i) != 'x' ; i++) { if (pTerm.charAt(i)== ' ' ) continue ; coeffStr += (pTerm.charAt(i)); } long coeff = Long.parseLong(coeffStr); // Get Power (Skip 2 characters for x and ^) String powStr = "" ; for (i = i + 2 ; i != pTerm.length() && pTerm.charAt(i) != ' ' ; i++) { powStr += pTerm.charAt(i); } long power=Long.parseLong(powStr); // For ax^n, we return a(n)x^(n-1) return coeff * power * ( long )Math.pow(val, power - 1 ); } static long derivativeVal(String poly, int val) { long ans = 0 ; int i = 0 ; String[] stSplit = poly.split( "\\+" ); while (i<stSplit.length) { ans = (ans +derivativeTerm(stSplit[i], val)); i++; } return ans; } // Driver code public static void main (String[] args) { String str = "4x^3 + 3x^1 + 2x^2" ; int val = 2 ; System.out.println(derivativeVal(str, val)); } } // This code is contributed by avanitrachhadiya2155 |
Python3
# Python3 program to find # value of derivative of # a polynomial. def derivativeTerm(pTerm, val): # Get coefficient coeffStr = "" i = 0 while (i < len (pTerm) and pTerm[i] ! = 'x' ): coeffStr + = (pTerm[i]) i + = 1 coeff = int (coeffStr) # Get Power (Skip 2 characters # for x and ^) powStr = "" j = i + 2 while j < len (pTerm): powStr + = (pTerm[j]) j + = 1 power = int (powStr) # For ax^n, we return # a(n)x^(n-1) return (coeff * power * pow (val, power - 1 )) def derivativeVal(poly, val): ans = 0 i = 0 stSplit = poly.split( "+" ) while (i < len (stSplit)): ans = (ans + derivativeTerm(stSplit[i], val)) i + = 1 return ans # Driver code if __name__ = = "__main__" : st = "4x^3 + 3x^1 + 2x^2" val = 2 print (derivativeVal(st, val)) # This code is contributed by Chitranayal |
C#
// C# program to find value of derivative of // a polynomial using System; class GFG{ static long derivativeTerm( string pTerm, long val) { // Get coefficient string coeffStr = "" ; int i; for (i = 0; pTerm[i] != 'x' ; i++) { if (pTerm[i] == ' ' ) continue ; coeffStr += (pTerm[i]); } long coeff = long .Parse(coeffStr); // Get Power (Skip 2 characters for x and ^) string powStr = "" ; for (i = i + 2; i != pTerm.Length && pTerm[i] != ' ' ; i++) { powStr += pTerm[i]; } long power = long .Parse(powStr); // For ax^n, we return a(n)x^(n-1) return coeff * power * ( long )Math.Pow(val, power - 1); } static long derivativeVal( string poly, int val) { long ans = 0; int i = 0; String[] stSplit = poly.Split( "+" ); while (i < stSplit.Length) { ans = (ans +derivativeTerm(stSplit[i], val)); i++; } return ans; } // Driver code static public void Main() { String str = "4x^3 + 3x^1 + 2x^2" ; int val = 2; Console.WriteLine(derivativeVal(str, val)); } } // This code is contributed by rag2127 |
Javascript
<script> // Javascript program to find value of derivative of // a polynomial function derivativeTerm( pTerm,val) { // Get coefficient let coeffStr = "" ; let i; for (i = 0; pTerm[i] != 'x' ; i++) { if (pTerm[i]== ' ' ) continue ; coeffStr += (pTerm[i]); } let coeff = parseInt(coeffStr); // Get Power (Skip 2 characters for x and ^) let powStr = "" ; for (i = i + 2; i != pTerm.length && pTerm[i] != ' ' ; i++) { powStr += pTerm[i]; } let power=parseInt(powStr); // For ax^n, we return a(n)x^(n-1) return coeff * power * Math.pow(val, power - 1); } function derivativeVal(poly,val) { let ans = 0; let i = 0; let stSplit = poly.split( "+" ); while (i<stSplit.length) { ans = (ans +derivativeTerm(stSplit[i], val)); i++; } return ans; } // Driver code let str = "4x^3 + 3x^1 + 2x^2" ; let val = 2; document.write(derivativeVal(str, val)); // This code is contributed by ab2127 </script> |
Output
59
Time Complexity: O(n), where n is the number of terms in the polynomial.
Auxiliary Space: O(1)
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