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que2.cpp
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1029 lines (1011 loc) · 16.2 KB
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//Representation:
//For writing product of 2 functions please use brackets and * or / symbols
//For power format I have used something like x^(n)
#include <string>
#include <cstring>
#include <iostream>
#include <fstream>
using namespace std;
string differentiate(string);
int universal=0;
int getcoef(string a)
{
char sign='+';
int i=0;
if(a[0]=='-')
{
sign='-';
i=1;
}
int coef=0;
//cout<<i<<endl;
while(a[i]<58 && a[i]>47) //Returns coefficient of a term
{
int c=a[i]-'0';
//cout<<c;
coef=coef*10+c;
i++;
}
if(coef==0)
coef=1;
if(sign=='-')
coef*=-1;
return coef;
}
string numtostr(int a)
{
string res;
if(a<0)
{
a=a*(-1);
res="-";
}
int arr[10],l=0;
while(a!=0)
{
int num=a%10; //returns integer as string with sign
arr[l]=num;
l++;
a/=10;
}
l--;
while(l>=0)
{
char c=arr[l]+48;
res.push_back(c);
l--;
}
return res;
}
string multiply(string a,string b)
{
int coef=getcoef(a)*getcoef(b),st=0,i=0,j=0;
string c,d,res;
if(a[0]=='-')
st=1;
for(i=st;i<a.length();i++)
{
if(a[i]<58 && a[i]>47)
continue;
break;
}
while(i<a.length())
{
c.push_back(a[i]);
i++;
}
st=0;
if(b[0]=='-')
st=1;
for(j=st;j<b.length();j++)
{
if(b[j]<58 && b[j]>47)
continue;
break;
}
while(j<b.length())
{
d.push_back(b[j]);
j++;
}
if(coef!=1 && coef!=-1)
res=numtostr(coef);
else
{
if(coef==-1)
res+='-';
}
res+=c;res+=d;
return res;
}
string diff(string a)
{
int coef=getcoef(a); //Function returns derivative of a term
string inp;
int j=0;
for(int i=0;i<a.length();i++)
{
if(a[i]=='-')
continue;
if(a[i]<58 && a[i]>47)
continue;
if(a[i]=='(')
{
j=i;
break;
}
inp.push_back(a[i]);
}
//cout<<a[j]<<endl;
string inp2;
int pow=0;
if(j==0)
{
if(inp!="x")
return "0";
else
return numtostr(coef);
}
else
{
if(a[j-1]=='^' && a[j-2]!='e')
{
j++;
int multi=1;
if(a[j]=='-')
{
multi=-1;
j++;
}
while(a[j]!=')')
{
int digit=a[j]-'0';
pow=pow*10+digit;
j++;
}
pow*=multi;
j++;
}
int brackt=1;
j++;
while(j<a.length())
{
if(a[j]=='(')
brackt++;
if(a[j]==')')
brackt--;
if(brackt==0)
break;
inp2.push_back(a[j]);
j++;
}
//cout<<inp2<<endl;
}
int isx=0;
if(inp2=="x" || inp=="x^")
{
isx=1;
}
//CASES FOR DERIVATIVE
string derivative,res;
if(inp=="sin" || inp=="sin^")
derivative="cos";
if(inp=="cos" || inp=="cos^")
derivative="-sin";
if(inp=="tan" || inp=="tan^")
derivative="sec^(2)";
if(inp=="cot" || inp=="cot^")
derivative="-cosec^(2)";
if(inp=="sinh" || inp=="sinh^")
derivative="cosh";
if(inp=="cosh" || inp=="cosh^")
derivative="sinh";
if(inp=="e^")
derivative="e^";
//int len=inp.length();
//int index=0;
if(pow)
{
coef*=pow;
pow-=1;
string power=numtostr(pow);
//res=numtostr(coef);
if(inp=="x^")
{
res=numtostr(coef);
if(pow==1)
res+="x";
else
{
res+=inp;
res+="(";
res+=power;
res+=")";
}
return res;
}
}
if(isx)
{
if(inp=="cosec") //If function is of the form f(x) we can directly return the answer
{
coef*=-1;
res=numtostr(coef);
res+="cosec(x)cot(x)";
return res;
}
if(inp=="sec")
{
res=numtostr(coef);
res+="sec(x)tan(x)";
return res;
}
if(inp=="arcsin")
{
res=numtostr(coef);
res+="(1-x^(2))^(-1/2)";
return res;
}
if(inp=="arccos")
{
coef*=-1;
res=numtostr(coef);
res+="(1-x^(2))^(-1/2)";
return res;
}
if(inp=="arctan")
{
res=numtostr(coef);
res+="(1+x^(2))^(-1)";
return res;
}
if(inp=="arccot")
{
coef*=-1;
res=numtostr(coef);
res+="(1+x^(2))^(-1)";
return res;
}
if(inp=="arccosec")
{
coef*=-1;
res=numtostr(coef);
res+="(x^(2)-1)^(-1/2)/x";
return res;
}
if(inp=="arcsec")
{
res=numtostr(coef);
res+="(x^(2)-1)^(-1/2)/x";
return res;
}
if(inp=="tanh")
{
res=numtostr(coef);
res+="(1-tanh^(2)(x))";
return res;
}
if(inp=="coth")
{
res=numtostr(coef);
res+="(1-coth^(2)(x))";
return res;
}
if(inp=="cosech")
{
coef*=-1;
res=numtostr(coef);
res+="cosech(x)coth(x)";
return res;
}
if(inp=="sech")
{
coef*=-1;
res=numtostr(coef);
res+="sech(x)tanh(x)";
return res;
}
if(inp=="ln")
{
res=numtostr(coef);
res+="x^(-1)";
return res;
}
if(inp=="sin^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="sin(x)";
res+=derivative;
res+="(x)";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="sin^(";
res+=numtostr(pow);
res+=")";
res+="(x)";
res+=derivative;
res+="(x)";
}
return res;
}
if(inp=="cos^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="cos(x)";
res+="sin(x)";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="cos^(";
res+=numtostr(pow);
res+=")";
res+="(x)";
res+="sin(x)";
}
return res;
}
if(inp=="tan^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="tan(x)";
res+=derivative;
res+="(x)";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="tan^(";
res+=numtostr(pow);
res+=")";
res+="(x)";
res+=derivative;
res+="(x)";
}
return res;
}
if(inp=="cot^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="cot(x)";
res+="cosec^(2)(x)";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="cot^(";
res+=numtostr(pow);
res+=")";
res+="(x)";
res+="cosec^(2)(x)";
}
return res;
}
if(inp=="cosh^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="cosh(x)";
res+="sinh(x)";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="cosh^(";
res+=numtostr(pow);
res+=")";
res+="(x)";
res+="sinh(x)";
}
return res;
}
if(inp=="sinh^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="sinh(x)";
res+="cosh(x)";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
res+="sinh^(";
res+=numtostr(pow);
res+=")";
res+="(x)";
res+="cosh(x)";
}
return res;
}
if(inp=="e^")
{
res=numtostr(coef);
res+="e^(x)";
return res;
}
coef*=getcoef(derivative);
string der;
if(derivative[0]=='-')
{
for(int size=1;size<derivative.length();size++)
der.push_back(derivative[size]);
}
else
der=derivative;
res=numtostr(coef);
res+=der;
res+="(x)";
return res;
}
else //If function is of type f(g(x)) to implement chain rule we have this part
{
string der1=diff(inp2),res1;
//cout<<der1<<endl;
int start=0;
if(der1[0]=='-')
start=1;
int sz;
for(sz=start;sz<der1.length();sz++)
{
if(der1[sz]<58 && der1[sz]>47)
continue;
else break;
}
int ck=1; //variable ck is used to check if we need to print g'(x)
coef*=getcoef(der1);
if(sz==der1.length())
{
ck=0;
}
else
{
while(sz<der1.length())
{
res1.push_back(der1[sz]);
sz++;
}
}
//cout<<coef<<endl;
if(inp=="cosec")
{
coef*=-1;
res=numtostr(coef);
if(ck)
res+=res1;
res+="cosec(";res+=inp2;res+=")cot(";res+=inp2;res+=")";
return res;
}
if(inp=="sec")
{
res=numtostr(coef);
if(ck)
res+=res1;
res+="sec(";res+=inp2;res+=")tan(";res+=inp2;res+=")";
return res;
}
if(inp=="arcsin")
{
res=numtostr(coef);
if(ck)
res+=res1;
res+="(1-(";res+=inp2;res+=")^(2))";res+="^(-1/2)";
return res;
}
if(inp=="arccos")
{
coef*=-1;
res=numtostr(coef);
if(ck)
res+=res1;
res+="(1-(";res+=inp2;res+=")^(2))";res+="^(-1/2)";
return res;
}
if(inp=="arctan")
{
res=numtostr(coef);
if(ck)
res+=res1;
res+="(1+(";res+=inp2;res+=")^(2))";res+="^(-1)";
return res;
}
if(inp=="arccot")
{
coef*=-1;
res=numtostr(coef);
if(ck)
res+=res1;
res+="(1+(";res+=inp2;res+=")^(2))";res+="^(-1)";
return res;
}
if(inp=="arccosec")
{
coef*=-1;
res=numtostr(coef);
if(ck)
res+=res1;
res+="((";res+=inp2;res+=")^(2)-1)^(-1/2)/(";res+=inp2;res+=")";
return res;
}
if(inp=="arcsec")
{
res=numtostr(coef);
if(ck)
res+=res1;
res+="((";res+=inp2;res+=")^(2)-1)^(-1/2)/(";res+=inp2;res+=")";
return res;
}
if(inp=="tanh")
{
res=numtostr(coef);
if(ck)
res+=res1;
res+="(1-tanh^(2)(";res+=inp2;res+="))";
return res;
}
if(inp=="coth")
{
res=numtostr(coef);
if(ck)
res+=res1;
res+="(1-coth^(2)(";res+=inp2;res+="))";
return res;
}
if(inp=="cosech")
{
coef*=-1;
res=numtostr(coef);
if(ck)
res+=res1;
res+="cosech(";res+=inp2;res+=")coth(";res+=inp2;res+=")";
return res;
}
if(inp=="sech")
{
coef*=-1;
res=numtostr(coef);
if(ck)
res+=res1;
res+="sech(";res+=inp2;res+=")tanh(";res+=inp2;res+=")";
return res;
}
if(inp=="ln")
{
res=numtostr(coef);
if(ck)
res+=res1;
res+="(";res+=inp2;res+=")^(-1)";
return res;
}
if(inp=="sin^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="sin(";res+=inp2;res+=")";
res+=derivative;
res+="(";res+=inp2;res+=")";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="sin^(";
res+=numtostr(pow);
res+=")";
res+="(";res+=inp2;res+=")";
res+=derivative;
res+="(";res+=inp2;res+=")";
}
return res;
}
if(inp=="cos^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="cos(";res+=inp2;res+=")";
res+="sin(";res+=inp2;res+=")";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="cos^(";
res+=numtostr(pow);
res+=")(";
res+=inp2;res+=")";
res+="sin(";res+=inp2;res+=")";
}
return res;
}
if(inp=="tan^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="tan(";res+=inp2;res+=")";
res+=derivative;
res+="(";res+=inp2;res+=")";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="tan^(";
res+=numtostr(pow);
res+=")(";
res+=inp2;res+=")";
res+=derivative;
res+="(";res+=inp2;res+=")";
}
return res;
}
if(inp=="cot^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="cot(";res+=inp2;res+=")";
res+="cosec^(2)(";res+=inp2;res+=")";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="cot^(";
res+=numtostr(pow);
res+=")(";
res+=inp2;res+=")";
res+="cosec^(2)(";res+=inp2;res+=")";
}
return res;
}
if(inp=="cosh^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="cosh(";res+=inp2;res+=")";
res+="sinh(";res+=inp2;res+=")";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="cosh^(";
res+=numtostr(pow);
res+=")";
res+="(";res+=inp2;res+=")";
res+="sinh(";res+=inp2;res+=")";
}
return res;
}
if(inp=="sinh^")
{
if(pow==1)
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="sinh(";res+=inp2;res+=")";
res+="cosh(";res+=inp2;res+=")";
}
else
{
coef*=getcoef(derivative);
res=numtostr(coef);
if(ck)
res+=res1;
res+="sinh^(";
res+=numtostr(pow);
res+=")";
res+="(";res+=inp2;res+=")";
res+="cosh(";res+=inp2;res+=")";
}
return res;
}
if(inp=="e^")
{
res=numtostr(coef);
if(ck)
res+=res1;
res+="e^(";res+=inp2;res+=")";
return res;
}
coef*=getcoef(derivative);
string der;
if(derivative[0]=='-')
{
for(int size=1;size<derivative.length();size++)
der.push_back(derivative[size]);
}
else
der=derivative;
res=numtostr(coef);
if(ck)
res+=res1;
res+=der;res+="(";res+=inp2;res+=")";
return res;
}
}
string differentiate(string a) //Differentiates any expression implementing u*v,u/v,u+v,u-v and chain rules
{
universal++;
string inp1,inp2,inp,res;
if(a[0]=='(') //cases for product,division or powers of complex functions
{
//cout<<"False"<<endl;
int brackt=1,j=1;
while(j<a.length())
{
if(a[j]=='(')
brackt++;
if(a[j]==')')
brackt--;
if(brackt==0)
break;
inp1.push_back(a[j]);
j++;
}
//cout<<'\n'<<inp1<<endl;
j++;
if(j==a.length())
res=diff(inp1);
else
{
//cout<<"Maybe"<<endl;
string der1,der2;
int l=j;
j+=2;
int b1=1;
while(j<a.length())
{
if(a[j]=='(')
b1++;
if(a[j]==')')
b1--;
if(b1==0)
break;
inp2.push_back(a[j]);
j++;
}
der1=diff(inp1),der2=diff(inp2);
if(a[l]=='*') //case for product rule
{
res+=multiply(inp1,der2);
string check=multiply(inp2,der1);
if(check[0]!='-')
res+="+";
res+=check;
}
else //case for quotient rule
{
res+="(";
res+=multiply(der1,inp2);
string check=multiply(inp1,der2);
string add;
if(check[0]=='-')
{
res+="+";
for(int index=1;index<check.length();index++)
add.push_back(check[index]);
}
else
{
res+="-";
add=check;
}
res+=add;res+=")/(";res+=inp2;res+=")^(2)";
}
}
j++;
if(j!=a.length())
{
if(a[j]=='+')
j++;
string restof;
while(j<a.length())
{
restof.push_back(a[j]);
j++;
}
string remadd=diff(restof);
if(remadd[0]!='-')
res+='+';
res+=remadd;
}
}
else //cases for simpler functions
{
//cout<<"True"<<endl;
string terms[100];
int ind=0,simple=1,start,done=0;
char prev='+';
if(a[0]=='-')
{
prev='-';
start=1;
}
for(int i=start;i<a.length();i++)
{
cout<<"Yes "<<endl;
if(a[i]=='^')
{
//cout<<"1"<<endl;
while(a[i]!=')')
{
terms[ind].push_back(a[i]);
i++;
}
terms[ind].push_back(a[i]);
i++;
}
if(a[i]=='(')
{
//cout<<"2 "<<endl;
int brackt=0;
while(i<a.length())
{
if(a[i]=='*' || a[i]=='/')
simple=0;
if(a[i]=='(')
brackt++;
if(a[i]==')')
brackt--;
terms[ind].push_back(a[i]);
if(brackt==0)
break;
i++;
}
}
if(a[i]=='-' || a[i]=='+')
{
done=1; //remember to write done=1 later
//cout<<"3 "<<endl;
string resi,resf;
if(simple)
{
//cout<<"4 "<<endl;
resi=diff(terms[ind]);
if(resi[0]=='-')
{
if(prev=='+')
resf=resi;
else
{
resf+='+';
for(int k=1;k<resi.length();k++)
resf.push_back(resi[k]);
}
}
else
{
res+=prev;
resf=resi;
}
res+=resf;
ind++;
prev=a[i];
i++;
}
else
{
resi=diff(terms[ind]);
if(resi[0]=='-')
{
if(prev=='+')
resf=resi;
else
{
resf+='+';
for(int k=1;k<resi.length();k++)
resf.push_back(resi[k]);
}
}
else
{
res+=prev;
resf=resi;
}
res+=resf;
ind++;
}
}
terms[ind].push_back(a[i]);
}
string resi,resf;
if(simple)
{
resi=diff(terms[ind]);
//cout<<resi<<endl;
if(resi[0]=='-')
{
if(prev=='+')
resf=resi;
else
{
resf+='+';
for(int k=1;k<resi.length();k++)
resf.push_back(resi[k]);
}
}
else
{
res+=prev;
resf=resi;
}
res+=resf;
ind++;
}
else
{
resi=diff(terms[ind]);
if(resi[0]=='-')
{
if(prev=='+')
resf=resi;
else
{
resf+='+';
for(int k=1;k<resi.length();k++)
resf.push_back(resi[k]);
}