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rings.cpp
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rings.cpp
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//
// Created by euler.lee on 20. 8. 18..
//
#include "rings.h"
long long Long::BASE = 10000000, Long::Digits = 7;
void Long::unique() { // V >= 0
while (V.size()>1 && V.back()==0) V.pop_back(); // 1) V.back() != 0 : remove Leading Zero
long long carry = 0;
for (unsigned int i=0; i<V.size(); i++) {
carry += V[i];
V[i] = carry % BASE;
carry /= BASE;
}
while (carry > 0) {
V.push_back(carry%BASE);
carry /= BASE;
}
if (V.size()==1 && V[0] == 0) sign=0; // when Zero
}
const Long Long::mag() const {
Long mag = *this;
if (mag.sign==-1) mag.sign=1;
return mag;
}
const Long abs(const Long & x) {
return x.mag();
}
Long Long::addV(const Long& A, const Long& B){ // return A+B for A,B>0
Long sum = (A.V.size()>=B.V.size() ? A : B);
const Long *small = (A.V.size()>=B.V.size() ? &B : &A);
for (unsigned int i = 0; i < small->V.size(); i++) sum.V[i] += small->V[i];
sum.unique();
return sum;
}
Long Long::subV(const Long& A, const Long& B){ // return A-B for A>B>0
Long dif;
unsigned int md = A.V.size(); // md = argmax_d A.V[d-1]!=B.V[d-1]
if (A.V.size()==B.V.size()) { // md < A.V.size --> md==0 || A.V[md-1] > B.V[md-1]
while (md>0 && A.V[md-1] == B.V[md-1]) md--;
} // else --> md == A.V.size
// if (md==0) return Long();
dif.V.resize(md);
for (unsigned int j=0; j<md; j++) dif.V[j] = A.V[j]+BASE-1;
dif.V[0] += 1;
dif.V[md-1] -= BASE;
for (unsigned int j=0; j<(md==A.V.size() ? B.V.size() : md); j++)
dif.V[j] -= B.V[j];
dif.unique();
return dif;
}
Long& Long::operator+= (const Long& A) {
Long sum = *this;
if (sign * A.sign >= 0) { // 1:(+,+) 2:(-,-), 3:(+,0), 4:(-,0), 5:(0,0)
sum = addV(mag(), A.mag());
sum.sign = sign + A.sign;
if (sum.sign>1) sum.sign = 1;
else if(sum.sign< -1) sum.sign = -1;
} else { // 5+(-3), 3+(-5)
if (mag() == A.mag()) sum = Long(0);
else if (mag() > A.mag()) {
sum = subV(mag(), A.mag());
sum.sign = sign;
} else {
sum = subV(A.mag(), mag());
sum.sign = A.sign;
}
}
return *this = sum;
}
Long& Long::operator-= (const Long& A) {
return *this += (-A);
}
Long& Long::operator<<= (const unsigned int& s) {
if (*this != Long()) {
vector<int> padZero(s, 0);
V.insert(V.begin(), padZero.begin(), padZero.end() );
}
return *this;
}
Long& Long::operator>>= (const unsigned int& s) {
if (s<V.size()) {
V.erase(V.begin(), V.begin()+s);
} else *this=Long();
return *this;
}
Long& Long::operator^= (const unsigned int& s) {
Long mul = Long(1);
Long base = *this;
unsigned int p = s;
while (p > 0) {
if (p & 1) mul *= base;
base *= base;
p >>= 1;
}
return *this = mul;
}
Long& Long::operator*= (const Long& A) {
sign *= A.sign;
if (sign==0) {*this=Long(); return *this;}
Long sum = Long(0);
for (unsigned int i = 0; i < A.V.size(); i++) {
if (A.V[i]==0) continue;
Long mul = *this;
for (unsigned int j = 0; j < mul.V.size(); j++)
mul.V[j] *= A.V[i];
//mul.unique();
mul <<= i;
sum += mul; // with unique();
}
sum.sign = sign;
return *this = sum;
}
Long& Long::operator/= (const Long& C) {
if (C==Long()) return *this; // Error: divided by zero
Long Q, sum = Long();
Long R = mag(), A = C.mag();
long long q = 1, a = A.V.back(), dig = 1;
// b = log10 BASE, lB = log10 *this = b*nB+rB, lA = log10 A = b*nA+rA,
// if nA >0 : la = log10 a = b, ld = log10 dig = b-rA;
// if nA==0 : la = rA, ld = 0
// lq = log10 q = b+rB-la+ld = b+rB-rA
// lQ = log10 Q = lq+b*(nB-1-nA)
// log10 A*Q = lA+lQ = b*nB+rB
if (A.V.size()>1) {
a *= BASE;
a += A.V[A.V.size() - 2];
dig = BASE;
while (a >= BASE) {
a /= 10;
dig /= 10;
}
a += 1;
} // BASE/10 + 1 <= a <= BASE
while (R.V.size()>A.V.size() && q>0) {
q = (R.V.back() * BASE + R.V[R.V.size() - 2]) / a * dig;
Q = Long(q)<<(R.V.size()-1-A.V.size());
sum+=Q;
Q *= A;
R -= Q;
} // --> R.V.size()==A.V.size() || q==0
if (R >= A) {
q = R.V.back() / a * dig;
Q = Long(q)<<(R.V.size()-A.V.size());
sum+=Q;
Q *= A;
R -= Q;
}
while ( R >= A ) {
sum += 1;
R -= A;
}
if (sum.sign != 0) sum.sign = sign * C.sign; // if sum is not zero
return *this = sum;
}
Long& Long::operator%= (const Long& A) {
if (A==Long()) return *this; // Error: divided by zero
if (A==Long(1)) return *this = Long(0); // Simple & avoid infinte loops
Long B = (*this / A) * A;
*this -= B;
return *this;
}
bool Long::operator==(const Long& A) const {
if (sign!=A.sign || V.size()!=A.V.size()) return false;
for (unsigned int i=0; i<V.size(); i++) if (V[i]!=A.V[i]) return false;
return true;
}
bool Long::operator<(const Long& A) const {
// 1:(1,-1), 2:(1,0), 3:(-1,0), 4:(11,1), 5:(-11,-1), 6:(2,1), 7:(-2,-1), 8:(1,1), 9:(-1,-1), 10:(0,0)
if (*this == A) return false; // Done 8,9,10
if (sign != A.sign) return (sign<A.sign); // Done 1,2,3
if (V.size() != A.V.size()) return (V.size() < A.V.size() ? sign==1 : sign==-1); // Done 4,5
unsigned int i=V.size();
while (i>0 && V[i-1]==A.V[i-1]) i--;
return (V[i-1]<A.V[i-1] ? sign==1 : sign==-1); // Done 6,7
}
// Print types of numbers
ostream& operator<< (ostream& os, Long p) {
if (p.sign == 0) os<<"0";
else {
os << (p.sign == -1 ? "-":"") << p.V.back();
for (unsigned int i = p.V.size()-1; i > 0; i--)
os << setfill('0') << setw(p.Digits) << p.V[i-1];
}
return os;
}