Given polynomial string str, the task is to differentiate the given string and print the string after differentiating it.
Note: The input format is such that there is a white space between a term and the ‘+’, ’-’ symbol
Examples:
Input: str = “4X3 + 3X1 + 2X2”
Output: “12X2 + 3X0 + 4X1”
Explanation:
The derivative of p(x) = A*XN is p'(x) = A * N * XN – 1
Input: str = “5X4 + 6X2 + 5X2”
Output: “20X3 + 12X1 + 10X1”
Approach: The idea is to observe that when the given equation consists of multiple polynomials
, the differentiation of the given polynomial
. And, it is known that the derivative of
is
Therefore, we split the given string and differentiate every term in it.
Below is the implementation of the above approach:
C++
// C++ program to differentiate the// given polynomial#include "bits/stdc++.h"#define MOD (1e9 + 7);using ll = int64_t;using ull = uint64_t;#define ll long longusing namespace std;// Function to differentiate the// given termstring diffTerm(string pTerm){ // Get the coefficient string coeffStr = "", S = ""; int i; // Loop to get the coefficient for (i = 0; pTerm[i] != 'x'; i++) coeffStr.push_back(pTerm[i]); long long coeff = atol(coeffStr.c_str()); // Loop to get the power of each term string powStr = ""; for (i = i + 2; i != pTerm.size(); i++) powStr.push_back(pTerm[i]); long long power = atol(powStr.c_str()); string a, b; // Converting the value // to the string ostringstream str1, str2; // For ax^n, we find (n)*a*x^(n-1) coeff = coeff * power; str1 << coeff; a = str1.str(); power--; str2 << power; b = str2.str(); S += a + "X^" + b; return S;}// Function to differentiate the// given polynomialstring diffstr(string& poly){ // We use istringstream to get // the input in tokens istringstream is(poly); string pTerm, S = ""; // For every token, compute the // differentiation while (is >> pTerm) { // If the token is equal to // '+', '-' then // continue with the string if (pTerm == "+") { S += " + "; continue; } if (pTerm == "-") { S += " - "; continue; } // Otherwise find the differentiation // of that particular term else S += diffTerm(pTerm); } return S;}// Driver codeint main(){ string str = "5x^4 + 6x^2 + 5x^2"; cout << diffstr(str); return 0;} |
Java
import java.util.Scanner;import java.util.StringTokenizer;public class DifferentiatePolynomial { static String diffTerm(String pTerm) { // Get the coefficient String coeffStr = "", S = ""; int i; // Loop to get the coefficient for (i = 0; pTerm.charAt(i) != 'x'; i++) { coeffStr = coeffStr + pTerm.charAt(i); } long coeff = Long.parseLong(coeffStr); // Loop to get the power of each term String powStr = ""; for (i = i + 2; i != pTerm.length(); i++) { powStr = powStr + pTerm.charAt(i); } long power = Long.parseLong(powStr); String a, b; // Converting the value // to the string StringBuilder str1 = new StringBuilder(); StringBuilder str2 = new StringBuilder(); // For ax^n, we find (n)*a*x^(n-1) coeff = coeff * power; str1.append(Long.toString(coeff)); a = str1.toString(); power--; str2.append(Long.toString(power)); b = str2.toString(); S = S + a + "X^" + b; return S; } static String diffstr(String poly) { String pTerm, S = ""; StringTokenizer st = new StringTokenizer(poly, " +"); // For every token, compute the differentiation while (st.hasMoreTokens()) { pTerm = st.nextToken(); // If the token is equal to '+', '-' then continue with the string if (pTerm.equals("+")) { S = S + " + "; continue; } if (pTerm.equals("-")) { S = S + " - "; continue; } // Otherwise find the differentiation of that particular term else { S = S + diffTerm(pTerm)+"+"; } } return S; } public static void main(String[] args) { String poly = "5x^4+6x^2+5x^2"; String ans = diffstr(poly); System.out.println(ans.substring(0,ans.length()-1)); }} |
Python3
# Python3 program to differentiate # the given polynomialMOD = (1e9 + 7)# Function to differentiate # the given termdef diffTerm(pTerm): # Get the coefficient coeffStr = "" S = "" # Loop to get the # coefficient i = 0 while (i < len(pTerm) and pTerm[i] != 'x'): coeffStr += (pTerm[i]) i += 1 coeff = int(coeffStr) # Loop to get the power # of each term powStr = "" j = i + 2 while j < len(pTerm): powStr += (pTerm[j]) j += 1 power = int(powStr) # For ax^n, we find # (n)*a*x^(n-1) coeff = coeff * power a = str(coeff) power -= 1 b = str(power) S += a + "X^" + b return S# Function to differentiate # the given polynomialdef diffstr(poly): pTerm = poly.split(" ") S = "" for i in range(len(pTerm)): # If the token is equal to # '+', '-' then # continue with the string if (pTerm[i] == "+"): S += " + " continue if (pTerm[i] == "-"): S += " - " continue # Otherwise find the differentiation # of that particular term else: S += diffTerm(pTerm[i]) return S# Driver codeif __name__ == "__main__": st = "5x^4 + 6x^2 + 5x^2" print(diffstr(st))# This code is contributed by Chitranayal |
C#
// C# program to differentiate the// given polynomialusing System;using System.Collections.Generic;class GFG { // Function to differentiate the // given term static string diffTerm(string pTerm) { // Get the coefficient string coeffStr = "", S = ""; int i; // Loop to get the coefficient for (i = 0; pTerm[i] != 'x'; i++) coeffStr += (pTerm[i]); long coeff = Convert.ToInt64(coeffStr); // Loop to get the power of each term string powStr = ""; for (i = i + 2; i != pTerm.Length; i++) powStr += (pTerm[i]); long power = Convert.ToInt64(powStr); string a, b; // For ax^n, we find (n)*a*x^(n-1) coeff = coeff * power; a = Convert.ToString(coeff); power--; b = Convert.ToString(power); S += a + "X^" + b; return S; } // Function to differentiate the // given polynomial static string diffstr(string poly) { // We use istringstream to get // the input in tokens string[] is1 = poly.Split(" "); string S = ""; // For every token, compute the // differentiation foreach(string pTerm in is1) { // If the token is equal to // '+', '-' then // continue with the string if (pTerm == "+") { S += " + "; continue; } if (pTerm == "-") { S += " - "; continue; } // Otherwise find the differentiation // of that particular term else S += diffTerm(pTerm); } return S; } // Driver code public static void Main(string[] args) { string str = "5x^4 + 6x^2 + 5x^2"; Console.WriteLine(diffstr(str)); }}// This code is contributed by phasing17. |
Javascript
// JS program to differentiate the// given polynomiallet MOD = (1e9 + 7);// Function to differentiate the// given termfunction diffTerm(pTerm){ // Get the coefficient let coeffStr = "", S = ""; let i; // Loop to get the coefficient for (i = 0; pTerm[i] != 'x'; i++) coeffStr += (pTerm[i]); let coeff = parseInt(coeffStr); // Loop to get the power of each term let powStr = ""; for (i = i + 2; i != pTerm.length; i++) powStr += (pTerm[i]); let power = parseInt(powStr); let a = ""; let b = ""; // Converting the value // to the string let str1, str2; // For ax^n, we find (n)*a*x^(n-1) coeff = coeff * power; str1 = coeff; a = str1; power--; str2 = power; b = str2; S += a + "X^" + b; return S;}// Function to differentiate the// given polynomialfunction diffstr( poly){ // We use istringstream to get // the input in tokens let is = poly.split(" "); let pTerm = "", S = ""; // For every token, compute the // differentiation for (pTerm of is) { // If the token is equal to // '+', '-' then // continue with the string if (pTerm == "+") { S += " + "; continue; } if (pTerm == "-") { S += " - "; continue; } // Otherwise find the differentiation // of that particular term else S += diffTerm(pTerm); } return S;}// Driver codelet str = "5x^4 + 6x^2 + 5x^2";console.log(diffstr(str));// This code is contributed by phasing17 |
Output:
20X^3 + 12X^1 + 10X^1
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