Given a polynomial string str, the task is to integrate the given string and print the string after integrating it. Note: The input format is such that there is a whitespace between a term and the ‘+’ symbol. Examples:
Input: str = “4X3 + 3X1 + 2X2” Output: X4 + (3/2)X2 + (2/3)X3 + C Input: str = “5X3 + 7X1 + 2X2 + 1X0” Output: (5/4)X4 + (7/2)X2 + (2/3)X3 + Xq + C
Approach: The idea is to observe that when the given equation consists of multiple polynomials
// C++ program to find the indefinite // integral of 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 perform the integral // of each term string inteTerm(string pTerm) { // Get the coefficient
string coeffStr = "" , S = "" ;
int i;
// Loop to iterate and get the
// Coefficient
for (i = 0; pTerm[i] != 'x' ; i++)
coeffStr.push_back(pTerm[i]);
long long coeff
= atol (coeffStr.c_str());
string powStr = "" ;
// Loop to find the power
// of the term
for (i = i + 2; i != pTerm.size(); i++)
powStr.push_back(pTerm[i]);
long long power
= atol (powStr.c_str());
string a, b;
ostringstream str1, str2;
// For ax^n, we find a*x^(n+1)/(n+1)
str1 << coeff;
a = str1.str();
power++;
str2 << power;
b = str2.str();
S += "(" + a + "/" + b + ")X^" + b;
return S;
} // Function to find the indefinite // integral of the given polynomial string integrationVal(string& poly) { // We use istringstream to get the
// input in tokens
istringstream is(poly);
string pTerm, S = "" ;
// Loop to iterate through
// every term
while (is >> pTerm) {
// If the token = '+' then
// continue with the string
if (pTerm == "+" ) {
S += " + " ;
continue ;
}
if (pTerm == "-" ) {
S += " - " ;
continue ;
}
// Otherwise find
// the integration of
// that particular term
else
S += inteTerm(pTerm);
}
return S;
} // Driver code int main()
{ string str
= "5x^3 + 7x^1 + 2x^2 + 1x^0" ;
cout << integrationVal(str)
<< " + C " ;
return 0;
} |
// Java program to find the indefinite // integral of the given polynomial import java.util.*;
class GFG {
// Function to perform the integral
// of each term
static String inteTerm(String pTerm)
{
// Get the coefficient
String coeffStr = "" , S = "" ;
int i;
// Loop to iterate and get the
// Coefficient
for (i = 0 ; pTerm.charAt(i) != 'x' ; i++)
coeffStr += (pTerm.charAt(i));
long coeff = Long.valueOf(coeffStr);
String powStr = "" ;
// Loop to find the power
// of the term
for (i = i + 2 ; i != pTerm.length(); i++)
powStr += (pTerm.charAt(i));
long power = Long.valueOf(powStr);
String a, b;
// For ax^n, we find a*x^(n+1)/(n+1)
a = String.valueOf(coeff);
power++;
b = String.valueOf(power);
S += "(" + String.valueOf(a) + "/"
+ String.valueOf(b) + ")X^"
+ String.valueOf(b);
return S;
}
// Function to find the indefinite
// integral of the given polynomial
static String integrationVal(String poly)
{
// We use iStringstream to get the
// input in tokens
String[] is1 = poly.split( " " );
String S = "" ;
// Loop to iterate through
// every term
for (String pTerm : is1) {
// If the token = '+' then
// continue with the String
if (pTerm.equals( "+" )) {
S += " + " ;
continue ;
}
if (pTerm.equals( "-" )) {
S += " - " ;
continue ;
}
// Otherwise find
// the integration of
// that particular term
else
S += inteTerm(pTerm);
}
return S;
}
// Driver code
public static void main(String[] args)
{
String str = "5x^3 + 7x^1 + 2x^2 + 1x^0" ;
System.out.println(integrationVal(str) + " + C " );
}
} // This code is contributed by phasing17 |
# Python3 program to find the indefinite # integral of the given polynomial MOD = 1000000007
# Function to perform the integral # of each term def inteTerm( pTerm):
# Get the coefficient
coeffStr = ""
S = "";
# Loop to iterate and get the
# Coefficient
i = 0
while pTerm[i] ! = 'x' :
coeffStr + = (pTerm[i]);
i + = 1
coeff = int (coeffStr)
powStr = "";
# Loop to find the power
# of the term
for j in range (i + 2 , len (pTerm)):
powStr + = (pTerm[j]);
power = int (powStr)
a = ""
b = "";
# For ax^n, we find a*x^(n+1)/(n+1)
str1 = coeff;
a = str1
power + = 1
str2 = power;
b = str2
S + = "(" + str (a) + "/" + str (b) + ")X^" + str (b);
return S;
# Function to find the indefinite # integral of the given polynomial def integrationVal(poly):
# We use istringstream to get the
# input in tokens
is1 = poly.split();
S = "";
# Loop to iterate through
# every term
for pTerm in is1:
# If the token = '+' then
# continue with the string
if (pTerm = = "+" ) :
S + = " + " ;
continue ;
if (pTerm = = "-" ):
S + = " - " ;
continue ;
# Otherwise find
# the integration of
# that particular term
else :
S + = inteTerm(pTerm);
return S;
# Driver code str1 = "5x^3 + 7x^1 + 2x^2 + 1x^0" ;
print (integrationVal(str1) + " + C " );
# This code is contributed by phasing17 |
// C# program to find the indefinite // integral of the given polynomial using System;
using System.Collections.Generic;
class GFG {
// Function to perform the integral
// of each term
static string inteTerm( string pTerm)
{
// Get the coefficient
string coeffStr = "" , S = "" ;
int i;
// Loop to iterate and get the
// Coefficient
for (i = 0; pTerm[i] != 'x' ; i++)
coeffStr += (pTerm[i]);
long coeff = Convert.ToInt64(coeffStr);
string powStr = "" ;
// Loop to find the power
// of the term
for (i = i + 2; i != pTerm.Length; i++)
powStr += (pTerm[i]);
long power = Convert.ToInt64(powStr);
string a, b;
// For ax^n, we find a*x^(n+1)/(n+1)
a = Convert.ToString(coeff);
power++;
b = Convert.ToString(power);
S += "(" + Convert.ToString(a) + "/"
+ Convert.ToString(b) + ")X^"
+ Convert.ToString(b);
return S;
}
// Function to find the indefinite
// integral of the given polynomial
static string integrationVal( string poly)
{
// We use istringstream to get the
// input in tokens
string [] is1 = poly.Split( " " );
string S = "" ;
// Loop to iterate through
// every term
foreach ( string pTerm in is1)
{
// If the token = '+' then
// continue with the string
if (pTerm == "+" ) {
S += " + " ;
continue ;
}
if (pTerm == "-" ) {
S += " - " ;
continue ;
}
// Otherwise find
// the integration of
// that particular term
else
S += inteTerm(pTerm);
}
return S;
}
// Driver code
public static void Main( string [] args)
{
string str = "5x^3 + 7x^1 + 2x^2 + 1x^0" ;
Console.WriteLine(integrationVal(str) + " + C " );
}
} // This code is contributed by phasing17 |
// JavaScript program to find the indefinite // integral of the given polynomial let MOD = (1e9 + 7); // Function to perform the integral // of each term function inteTerm( pTerm)
{ // Get the coefficient
let coeffStr = "" , S = "" ;
let i;
// Loop to iterate and get the
// Coefficient
for (i = 0; pTerm[i] != 'x' ; i++)
coeffStr += (pTerm[i]);
let coeff
= parseInt(coeffStr)
let powStr = "" ;
// Loop to find the power
// of the term
for (i = i + 2; i != pTerm.length; i++)
powStr += (pTerm[i]);
let power
= parseInt(powStr)
let a = "" , b = "" ;
let str1, str2;
// For ax^n, we find a*x^(n+1)/(n+1)
str1 = coeff;
a = str1
power++;
str2 = power;
b = str2
S += "(" + a + "/" + b + ")X^" + b;
return S;
} // Function to find the indefinite // integral of the given polynomial function integrationVal(poly)
{ // We use istringstream to get the
// input in tokens
let is = poly.split( " " );
let pTerm, S = "" ;
// Loop to iterate through
// every term
for (pTerm of is)
{
// If the token = '+' then
// continue with the string
if (pTerm == "+" ) {
S += " + " ;
continue ;
}
if (pTerm == "-" ) {
S += " - " ;
continue ;
}
// Otherwise find
// the integration of
// that particular term
else
S += inteTerm(pTerm);
}
return S;
} // Driver code let str = "5x^3 + 7x^1 + 2x^2 + 1x^0" ;
console.log(integrationVal(str) + " + C " );
// This code is contributed by phasing17 |
(5/4)X^4 + (7/2)X^2 + (2/3)X^3 + (1/1)X^1 + C