BigInt (BIG INTEGERS) in C++ with Example (original) (raw)

`#include <bits/stdc++.h> using namespace std;

class BigInt{ string digits; public:

//Constructors:
BigInt(unsigned long long n = 0);
BigInt(string &);
BigInt(const char *);
BigInt(BigInt &);

//Helper Functions:
friend void divide_by_2(BigInt &a);
friend bool Null(const BigInt &);
friend int Length(const BigInt &);
int operator[](const int)const;

           /* * * * Operator Overloading * * * */

//Direct assignment
BigInt &operator=(const BigInt &);

//Post/Pre - Incrementation
BigInt &operator++();
BigInt operator++(int temp);
BigInt &operator--();
BigInt operator--(int temp);

//Addition and Subtraction
friend BigInt &operator+=(BigInt &, const BigInt &);
friend BigInt operator+(const BigInt &, const BigInt &);
friend BigInt operator-(const BigInt &, const BigInt &);
friend BigInt &operator-=(BigInt &, const BigInt &);

//Comparison operators
friend bool operator==(const BigInt &, const BigInt &);
friend bool operator!=(const BigInt &, const BigInt &);

friend bool operator>(const BigInt &, const BigInt &);
friend bool operator>=(const BigInt &, const BigInt &);
friend bool operator<(const BigInt &, const BigInt &);
friend bool operator<=(const BigInt &, const BigInt &);

//Multiplication and Division
friend BigInt &operator*=(BigInt &, const BigInt &);
friend BigInt operator*(const BigInt &, const BigInt &);
friend BigInt &operator/=(BigInt &, const BigInt &);
friend BigInt operator/(const BigInt &, const BigInt &);

//Modulo
friend BigInt operator%(const BigInt &, const BigInt &);
friend BigInt &operator%=(BigInt &, const BigInt &);

//Power Function
friend BigInt &operator^=(BigInt &,const BigInt &);
friend BigInt operator^(BigInt &, const BigInt &);

//Square Root Function
friend BigInt sqrt(BigInt &a);

//Read and Write
friend ostream &operator<<(ostream &,const BigInt &);
friend istream &operator>>(istream &, BigInt &);

//Others
friend BigInt NthCatalan(int n);
friend BigInt NthFibonacci(int n);
friend BigInt Factorial(int n);

};

BigInt::BigInt(string & s){ digits = ""; int n = s.size(); for (int i = n - 1; i >= 0;i--){ if(!isdigit(s[i])) throw("ERROR"); digits.push_back(s[i] - '0'); } } BigInt::BigInt(unsigned long long nr){ do{ digits.push_back(nr % 10); nr /= 10; } while (nr); } BigInt::BigInt(const char *s){ digits = ""; for (int i = strlen(s) - 1; i >= 0;i--) { if(!isdigit(s[i])) throw("ERROR"); digits.push_back(s[i] - '0'); } } BigInt::BigInt(BigInt & a){ digits = a.digits; }

bool Null(const BigInt& a){ if(a.digits.size() == 1 && a.digits[0] == 0) return true; return false; } int Length(const BigInt & a){ return a.digits.size(); } int BigInt::operator[](const int index)const{ if(digits.size() <= index || index < 0) throw("ERROR"); return digits[index]; } bool operator==(const BigInt &a, const BigInt &b){ return a.digits == b.digits; } bool operator!=(const BigInt & a,const BigInt &b){ return !(a == b); } bool operator<(const BigInt&a,const BigInt&b){ int n = Length(a), m = Length(b); if(n != m) return n < m; while(n--) if(a.digits[n] != b.digits[n]) return a.digits[n] < b.digits[n]; return false; } bool operator>(const BigInt&a,const BigInt&b){ return b < a; } bool operator>=(const BigInt&a,const BigInt&b){ return !(a < b); } bool operator<=(const BigInt&a,const BigInt&b){ return !(a > b); }

BigInt &BigInt::operator=(const BigInt &a){ digits = a.digits; return *this; }

BigInt &BigInt::operator++(){ int i, n = digits.size(); for (i = 0; i < n && digits[i] == 9;i++) digits[i] = 0; if(i == n) digits.push_back(1); else digits[i]++; return *this; } BigInt BigInt::operator++(int temp){ BigInt aux; aux = *this; ++(*this); return aux; }

BigInt &BigInt::operator--(){ if(digits[0] == 0 && digits.size() == 1) throw("UNDERFLOW"); int i, n = digits.size(); for (i = 0; digits[i] == 0 && i < n;i++) digits[i] = 9; digits[i]--; if(n > 1 && digits[n - 1] == 0) digits.pop_back(); return *this; } BigInt BigInt::operator--(int temp){ BigInt aux; aux = *this; --(*this); return aux; }

BigInt &operator+=(BigInt &a,const BigInt& b){ int t = 0, s, i; int n = Length(a), m = Length(b); if(m > n) a.digits.append(m - n, 0); n = Length(a); for (i = 0; i < n;i++){ if(i < m) s = (a.digits[i] + b.digits[i]) + t; else s = a.digits[i] + t; t = s / 10; a.digits[i] = (s % 10); } if(t) a.digits.push_back(t); return a; } BigInt operator+(const BigInt &a, const BigInt &b){ BigInt temp; temp = a; temp += b; return temp; }

BigInt &operator-=(BigInt&a,const BigInt &b){ if(a < b) throw("UNDERFLOW"); int n = Length(a), m = Length(b); int i, t = 0, s; for (i = 0; i < n;i++){ if(i < m) s = a.digits[i] - b.digits[i]+ t; else s = a.digits[i]+ t; if(s < 0) s += 10, t = -1; else t = 0; a.digits[i] = s; } while(n > 1 && a.digits[n - 1] == 0) a.digits.pop_back(), n--; return a; } BigInt operator-(const BigInt& a,const BigInt&b){ BigInt temp; temp = a; temp -= b; return temp; }

BigInt &operator*=(BigInt &a, const BigInt &b) { if(Null(a) || Null(b)){ a = BigInt(); return a; } int n = a.digits.size(), m = b.digits.size(); vector v(n + m, 0); for (int i = 0; i < n;i++) for (int j = 0; j < m;j++){ v[i + j] += (a.digits[i] ) * (b.digits[j]); } n += m; a.digits.resize(v.size()); for (int s, i = 0, t = 0; i < n; i++) { s = t + v[i]; v[i] = s % 10; t = s / 10; a.digits[i] = v[i] ; } for (int i = n - 1; i >= 1 && !v[i];i--) a.digits.pop_back(); return a; } BigInt operator*(const BigInt&a,const BigInt&b){ BigInt temp; temp = a; temp *= b; return temp; }

BigInt &operator/=(BigInt& a,const BigInt &b){ if(Null(b)) throw("Arithmetic Error: Division By 0"); if(a < b){ a = BigInt(); return a; } if(a == b){ a = BigInt(1); return a; } int i, lgcat = 0, cc; int n = Length(a), m = Length(b); vector cat(n, 0); BigInt t; for (i = n - 1; t * 10 + a.digits[i] < b;i--){ t *= 10; t += a.digits[i] ; } for (; i >= 0; i--){ t = t * 10 + a.digits[i]; for (cc = 9; cc * b > t;cc--); t -= cc * b; cat[lgcat++] = cc; } a.digits.resize(cat.size()); for (i = 0; i < lgcat;i++) a.digits[i] = cat[lgcat - i - 1]; a.digits.resize(lgcat); return a; } BigInt operator/(const BigInt &a,const BigInt &b){ BigInt temp; temp = a; temp /= b; return temp; }

BigInt &operator%=(BigInt& a,const BigInt &b){ if(Null(b)) throw("Arithmetic Error: Division By 0"); if(a < b){ return a; } if(a == b){ a = BigInt(); return a; } int i, lgcat = 0, cc; int n = Length(a), m = Length(b); vector cat(n, 0); BigInt t; for (i = n - 1; t * 10 + a.digits[i] < b;i--){ t *= 10; t += a.digits[i]; } for (; i >= 0; i--){ t = t * 10 + a.digits[i]; for (cc = 9; cc * b > t;cc--); t -= cc * b; cat[lgcat++] = cc; } a = t; return a; } BigInt operator%(const BigInt &a,const BigInt &b){ BigInt temp; temp = a; temp %= b; return temp; }

BigInt &operator^=(BigInt & a,const BigInt & b){ BigInt Exponent, Base(a); Exponent = b; a = 1; while(!Null(Exponent)){ if(Exponent[0] & 1) a *= Base; Base *= Base; divide_by_2(Exponent); } return a; } BigInt operator^(BigInt & a,BigInt & b){ BigInt temp(a); temp ^= b; return temp; }

void divide_by_2(BigInt & a){ int add = 0; for (int i = a.digits.size() - 1; i >= 0;i--){ int digit = (a.digits[i] >> 1) + add; add = ((a.digits[i] & 1) * 5); a.digits[i] = digit; } while(a.digits.size() > 1 && !a.digits.back()) a.digits.pop_back(); }

BigInt sqrt(BigInt & a){ BigInt left(1), right(a), v(1), mid, prod; divide_by_2(right); while(left <= right){ mid += left; mid += right; divide_by_2(mid); prod = (mid * mid); if(prod <= a){ v = mid; ++mid; left = mid; } else{ --mid; right = mid; } mid = BigInt(); } return v; }

BigInt NthCatalan(int n){ BigInt a(1),b; for (int i = 2; i <= n;i++) a *= i; b = a; for (int i = n + 1; i <= 2 * n;i++) b *= i; a *= a; a *= (n + 1); b /= a; return b; }

BigInt NthFibonacci(int n){ BigInt a(1), b(1), c; if(!n) return c; n--; while(n--){ c = a + b; b = a; a = c; } return b; }

BigInt Factorial(int n){ BigInt f(1); for (int i = 2; i <= n;i++) f *= i; return f; }

istream &operator>>(istream &in, BigInt& a) { string s; if (!(in >> s)) return in;

a.digits.clear();
int n = s.size();

for (int i = n - 1; i >= 0; i--) {
    if (!isdigit(s[i])) {
        throw runtime_error("INVALID NUMBER");
    }
    a.digits.push_back(s[i] - '0');
}

// Remove leading zeros which 
// are at the BACK of the digits string
while (a.digits.size() > 1 && a.digits.back() == 0) {
    a.digits.pop_back();
}

return in;

}

ostream &operator<<(ostream &out,const BigInt &a){ for (int i = a.digits.size() - 1; i >= 0;i--) cout << (short)a.digits[i]; return cout; }

//Driver code with some examples int main() { BigInt first("12345"); cout << "The number of digits" << " in first big integer = " << Length(first) << '\n'; BigInt second(12345); if (first == second) { cout << "first and second are equal!\n"; } else cout << "Not equal!\n"; BigInt third("10000"); BigInt fourth("100000"); if (third < fourth) { cout << "third is smaller than fourth!\n"; } BigInt fifth("10000000"); if (fifth > fourth) { cout << "fifth is larger than fourth!\n"; }

// Printing all the numbers
cout << "first = " << first << '\n';
cout << "second = " << second << '\n';
cout << "third = " << third << '\n';
cout << "fourth = " << fourth<< '\n';
cout << "fifth = " << fifth<< '\n';

// Incrementing the value of first
first++;
cout << "After incrementing the"
     << " value of first is : ";
cout << first << '\n';
BigInt sum;
sum = (fourth + fifth);
cout << "Sum of fourth and fifth = "
     << sum << '\n';
BigInt product;
product = second * third;
cout << "Product of second and third = "
     << product << '\n';

// Print the fibonacci number from 1 to 100
cout << "-------------------------Fibonacci"
     << "------------------------------\n";
for (int i = 0; i <= 100; i++) {
    BigInt Fib;
    Fib = NthFibonacci(i);
    cout << "Fibonacci " << i << " = " << Fib<<'\n';
}
cout << "-------------------------Catalan"
     << "------------------------------\n";
for (int i = 0; i <= 100; i++) {
    BigInt Cat;
    Cat = NthCatalan(i);
    cout << "Catalan " << i << " = " << Cat<<'\n';
}

// Calculating factorial of from 1 to 100
cout << "-------------------------Factorial"
     << "------------------------------\n";
for (int i = 0; i <= 100; i++) {
    BigInt fact;
    fact = Factorial(i);
    cout << "Factorial of "
         << i << " = ";
    cout << fact << '\n';
}

// This code is contributed // by Gatea David }

`