Program to differentiate the given Polynomial

Last Updated : 17 Feb, 2023

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*X^N is p'(x) = A * N * X^{N - 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

p(x) = p1(x) + p2(x)

, the differentiation of the given polynomial

p'(x) = p1'(x) + p2'(x)

. And, it is known that the derivative of

p(x) = AX^N

p'(x) = A*N*X^{N - 1}

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 long
using namespace std;

// Function to differentiate the
// given term
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.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 polynomial
string 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 code
int 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 polynomial
MOD = (1e9 + 7)

# Function to differentiate 
# the given term
def 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 polynomial
def 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 code
if __name__ == "__main__":

    st = "5x^4 + 6x^2 + 5x^2"
    print(diffstr(st))

# This code is contributed by Chitranayal

// C# program to differentiate the
// given polynomial

using 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 polynomial

let MOD = (1e9 + 7);

// Function to differentiate the
// given term
function 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 polynomial
function 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 code
let str = "5x^4 + 6x^2 + 5x^2";
console.log(diffstr(str));


// This code is contributed by phasing17