Editorial for Xử lý số nguyên lớn


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Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

Code mẫu của flashmt

const base=100000000;
      digit=8;
      maxk=130000;
type bignum=array[0..maxk] of int64;
var a,b,c,d,re:bignum;
    e:array[1..1000] of char;
    bg:boolean;


procedure rf(var a:bignum);
var s:string; i,m,j:longint; c:char; code:integer; t:int64;
begin
     fillchar(a,sizeof(a),0);
     while not eoln do
     begin
          inc(a[0]);
          read(e[a[0]]);
     end;
     m:=a[0] mod digit;
     if m=0 then m:=digit;
     a[0]:=(a[0]+digit-1) div digit;
     s:='';
     for i:=1 to m do s:=s+e[i];
     val(s,t,code);
     a[a[0]]:=t;
     for i:=0 to a[0]-2 do
     begin
          s:='';
          for j:=1 to digit do s:=s+e[m+j+i*digit];
          val(s,t,code);
          a[a[0]-i-1]:=t;
     end;
end;

function big:boolean;
var i:longint;
begin
     big:=a[0]>b[0];
     if a[0]=b[0] then
     begin
          big:=true;
          for i:=a[0] downto 1 do
              if a[i]>b[i] then break
              else
              begin
                   if a[i]<b[i] then
                   begin
                        big:=false;
                        break;
                   end;
              end;
     end;
end;

procedure wr(var k:bignum);
var s:string; t,j,i:longint;
begin
     for i:=k[0] downto 1 do
     begin
          if i<k[0] then
          begin
               str(k[i],s);
               t:=length(s);
               for j:=t+1 to digit do write(0);
          end;
          write(k[i]);
     end;
     writeln;
end;

procedure plus;
var i,max:longint; mem:int64;
begin
     fillchar(c,sizeof(c),0);
     mem:=0;
     if a[0]>b[0] then max:=a[0] else max:=b[0];
     for i:=1 to max do
     begin
          c[i]:=(a[i]+b[i]+mem) mod base;
          mem:=(a[i]+b[i]+mem) div base;
     end;
     if mem>0 then
     begin
          inc(max);
          c[max]:=mem;
     end;
     c[0]:=max;
     wr(c);
end;

procedure minus;
var i,max:longint; mem:int64;
begin
     fillchar(c,sizeof(c),0);
     mem:=0;
     if not bg then
     begin
          write('-');
          d:=a; a:=b; b:=d;
     end;
     max:=a[0];
     for i:=1 to a[0] do
     begin
          if a[i]<b[i]+mem then
          begin
               c[i]:=a[i]+base-b[i]-mem;
               mem:=1;
          end
          else
          begin
               c[i]:=a[i]-b[i]-mem;
               mem:=0;
          end;
     end;
     while (c[max]=0) and (max>1) do dec(max);
     c[0]:=max;
     wr(c);
end;

procedure multi;
var i,j,max,maxr:longint; mem,t:int64;
begin
     fillchar(re,sizeof(re),0);
     maxr:=a[0];
     for i:=1 to b[0] do
     begin
          mem:=0;
          fillchar(c,sizeof(c),0);
          c[0]:=a[0];
          for j:=1 to a[0] do
          begin
               c[j]:=(a[j]*b[i]+mem) mod base;
               mem:=(a[j]*b[i]+mem) div base;
          end;
          if mem>0 then
          begin
               inc(c[0]);
               c[c[0]]:=mem;
          end;
          mem:=0;
          for j:=1 to c[0] do
          begin
               t:=c[j]+re[j+i-1]+mem;
               re[j+i-1]:=t mod base;
               mem:=t div base;
          end;
          j:=c[0]+i-1;
          if j>maxr then maxr:=j;
          while mem>0 do
          begin
               inc(j);
               if j>maxr then maxr:=j;
               t:=mem+re[j];
               re[j]:=t mod base;
               mem:=t div base;
          end;
     end;
     re[0]:=maxr;
     wr(re);
end;

begin
     rf(a);
     readln;
     rf(b);
     bg:=big;
     plus;
     minus;
     multi;
end.

Code mẫu của happyboy99x

a=int(input())
b=int(input())
print(a+b)
print(a-b)
print(a*b)

Code mẫu của ladpro98

#include <bits/stdc++.h>

using namespace std;

// * BIG INTEGER

typedef vector<int> bigInt;
const int BASE = 1000;
const int LENGTH = 3;

// * Refine function
bigInt& fix(bigInt &a) {
  a.push_back(0);
  for (int i = 0; i + 1 < a.size(); ++i) {
    a[i + 1] += a[i] / BASE; a[i] %= BASE;
    if (a[i] < 0) a[i] += BASE, --a[i + 1];
  }
  while (a.size() > 1 && a.back() == 0) a.pop_back();
  return a;
}

// * Constructors
bigInt big(int x) {
  bigInt result;
  while (x > 0) {
    result.push_back(x % BASE);
    x /= BASE;
  }
  return result;
}

bigInt big(string s) {
  bigInt result(s.size() / LENGTH + 1);
  for (int i = 0; i < s.size(); ++i) {
    int pos = (s.size() - i - 1) / LENGTH;
    result[pos] = result[pos] * 10 + s[i] - '0';
  }
  return fix(result), result;
}

// * Compare operators

int compare(bigInt &a, bigInt &b) {
  if (a.size() != b.size()) return (int)a.size() - (int)b.size();
  for (int i = 0; i < a.size(); ++i)
    if (a[i] != b[i]) return a[i] - b[i];
  return 0;
}

#define DEFINE_OPERATOR(x) bool operator x (bigInt &a, bigInt &b) { return compare(a, b) x 0; }
DEFINE_OPERATOR(==)
DEFINE_OPERATOR(!=)
DEFINE_OPERATOR(>)
DEFINE_OPERATOR(<)
DEFINE_OPERATOR(>=)
DEFINE_OPERATOR(<=)
#undef DEFINE_OPERATOR

// * Arithmetic operators

void operator += (bigInt &a, bigInt b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < b.size(); ++i)
    a[i] += b[i];
  fix(a);
}

void operator -= (bigInt &a, bigInt b) {
  for (int i = 0; i < b.size(); ++i)
    a[i] -= b[i];
  fix(a);
}

void operator *= (bigInt &a, int b) {
  for (int i = 0; i < a.size(); ++i)
    a[i] *= b;
  fix(a);
}

void divide(bigInt a, int b, bigInt &q, int &r) {
  for (int i = int(a.size()) - 1; i >= 0; --i) {
    r = r * BASE + a[i];
    q.push_back(r / b); r %= b;
  }
  reverse(q.begin(), q.end());
  fix(q);
}

bigInt operator + (bigInt a, bigInt b) { a += b; return a; }
bigInt operator - (bigInt a, bigInt b) { a -= b; return a; }
bigInt operator * (bigInt a, int b) { a *= b; return a; }

bigInt operator / (bigInt a, int b) {
  bigInt q; int r = 0;
  divide(a, b, q, r);
  return q;
}
int operator % (bigInt a, int b) {
  bigInt q; int r = 0;
  divide(a, b, q, r);
  return r;
}

bigInt operator * (bigInt a, bigInt b) {
  bigInt result (a.size() + b.size());
  for (int i = 0; i < a.size(); ++i)
    for (int j = 0; j < b.size(); ++j)
      result[i + j] += a[i] * b[j];
  return fix(result);
}

// * I/O routines

istream& operator >> (istream& cin, bigInt &a) {
  string s; cin >> s;
  a = big(s);
  return cin;
}

ostream& operator << (ostream& cout, const bigInt &a) {
  cout << a.back();
  for (int i = (int)a.size() - 2; i >= 0; --i)
    cout << setw(LENGTH) << setfill('0') << a[i];
  return cout;
}

int main() {
  bigInt a, b;
  cin >> a >> b;
  cout << a + b << endl;
  if (a < b)
    cout << '-' << b - a << endl;
  else
    cout << a - b << endl;
  cout << a * b << endl;
  return 0;
}

Code mẫu của RR

#include <vector>
#include <cstdlib>
#include <iostream>
#include <iomanip>
#include <string>
#include <ctime>
using namespace std;

// base and base_digits must be consistent
const int base = 1000000000;
const int base_digits = 9;

struct bigint {
    vector<int> a;
    int sign;

    bigint() :
        sign(1) {
    }

    bigint(long long v) {
        *this = v;
    }

    bigint(const string &s) {
        read(s);
    }

    void operator=(const bigint &v) {
        sign = v.sign;
        a = v.a;
    }

    void operator=(long long v) {
        sign = 1;
        if (v < 0)
            sign = -1, v = -v;
        for (; v > 0; v = v / base)
            a.push_back(v % base);
    }

    bigint operator+(const bigint &v) const {
        if (sign == v.sign) {
            bigint res = v;

            for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
                if (i == (int) res.a.size())
                    res.a.push_back(0);
                res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
                carry = res.a[i] >= base;
                if (carry)
                    res.a[i] -= base;
            }
            return res;
        }
        return *this - (-v);
    }

    bigint operator-(const bigint &v) const {
        if (sign == v.sign) {
            if (abs() >= v.abs()) {
                bigint res = *this;
                for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
                    res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
                    carry = res.a[i] < 0;
                    if (carry)
                        res.a[i] += base;
                }
                res.trim();
                return res;
            }
            return -(v - *this);
        }
        return *this + (-v);
    }

    void operator*=(int v) {
        if (v < 0)
            sign = -sign, v = -v;
        for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
            if (i == (int) a.size())
                a.push_back(0);
            long long cur = a[i] * (long long) v + carry;
            carry = (int) (cur / base);
            a[i] = (int) (cur % base);
            //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
        }
        trim();
    }

    bigint operator*(int v) const {
        bigint res = *this;
        res *= v;
        return res;
    }

    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
        int norm = base / (b1.a.back() + 1);
        bigint a = a1.abs() * norm;
        bigint b = b1.abs() * norm;
        bigint q, r;
        q.a.resize(a.a.size());

        for (int i = a.a.size() - 1; i >= 0; i--) {
            r *= base;
            r += a.a[i];
            int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
            int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
            int d = ((long long) base * s1 + s2) / b.a.back();
            r -= b * d;
            while (r < 0)
                r += b, --d;
            q.a[i] = d;
        }

        q.sign = a1.sign * b1.sign;
        r.sign = a1.sign;
        q.trim();
        r.trim();
        return make_pair(q, r / norm);
    }

    bigint operator/(const bigint &v) const {
        return divmod(*this, v).first;
    }

    bigint operator%(const bigint &v) const {
        return divmod(*this, v).second;
    }

    void operator/=(int v) {
        if (v < 0)
            sign = -sign, v = -v;
        for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
            long long cur = a[i] + rem * (long long) base;
            a[i] = (int) (cur / v);
            rem = (int) (cur % v);
        }
        trim();
    }

    bigint operator/(int v) const {
        bigint res = *this;
        res /= v;
        return res;
    }

    int operator%(int v) const {
        if (v < 0)
            v = -v;
        int m = 0;
        for (int i = a.size() - 1; i >= 0; --i)
            m = (a[i] + m * (long long) base) % v;
        return m * sign;
    }

    void operator+=(const bigint &v) {
        *this = *this + v;
    }
    void operator-=(const bigint &v) {
        *this = *this - v;
    }
    void operator*=(const bigint &v) {
        *this = *this * v;
    }
    void operator/=(const bigint &v) {
        *this = *this / v;
    }

    bool operator<(const bigint &v) const {
        if (sign != v.sign)
            return sign < v.sign;
        if (a.size() != v.a.size())
            return a.size() * sign < v.a.size() * v.sign;
        for (int i = a.size() - 1; i >= 0; i--)
            if (a[i] != v.a[i])
                return a[i] * sign < v.a[i] * sign;
        return false;
    }

    bool operator>(const bigint &v) const {
        return v < *this;
    }
    bool operator<=(const bigint &v) const {
        return !(v < *this);
    }
    bool operator>=(const bigint &v) const {
        return !(*this < v);
    }
    bool operator==(const bigint &v) const {
        return !(*this < v) && !(v < *this);
    }
    bool operator!=(const bigint &v) const {
        return *this < v || v < *this;
    }

    void trim() {
        while (!a.empty() && !a.back())
            a.pop_back();
        if (a.empty())
            sign = 1;
    }

    bool isZero() const {
        return a.empty() || (a.size() == 1 && !a[0]);
    }

    bigint operator-() const {
        bigint res = *this;
        res.sign = -sign;
        return res;
    }

    bigint abs() const {
        bigint res = *this;
        res.sign *= res.sign;
        return res;
    }

    long long longValue() const {
        long long res = 0;
        for (int i = a.size() - 1; i >= 0; i--)
            res = res * base + a[i];
        return res * sign;
    }

    friend bigint gcd(const bigint &a, const bigint &b) {
        return b.isZero() ? a : gcd(b, a % b);
    }
    friend bigint lcm(const bigint &a, const bigint &b) {
        return a / gcd(a, b) * b;
    }

    void read(const string &s) {
        sign = 1;
        a.clear();
        int pos = 0;
        while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
            if (s[pos] == '-')
                sign = -sign;
            ++pos;
        }
        for (int i = s.size() - 1; i >= pos; i -= base_digits) {
            int x = 0;
            for (int j = max(pos, i - base_digits + 1); j <= i; j++)
                x = x * 10 + s[j] - '0';
            a.push_back(x);
        }
        trim();
    }

    friend istream& operator>>(istream &stream, bigint &v) {
        string s;
        stream >> s;
        v.read(s);
        return stream;
    }

    friend ostream& operator<<(ostream &stream, const bigint &v) {
        if (v.sign == -1)
            stream << '-';
        stream << (v.a.empty() ? 0 : v.a.back());
        for (int i = (int) v.a.size() - 2; i >= 0; --i)
            stream << setw(base_digits) << setfill('0') << v.a[i];
        return stream;
    }

    static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
        vector<long long> p(max(old_digits, new_digits) + 1);
        p[0] = 1;
        for (int i = 1; i < (int) p.size(); i++)
            p[i] = p[i - 1] * 10;
        vector<int> res;
        long long cur = 0;
        int cur_digits = 0;
        for (int i = 0; i < (int) a.size(); i++) {
            cur += a[i] * p[cur_digits];
            cur_digits += old_digits;
            while (cur_digits >= new_digits) {
                res.push_back(int(cur % p[new_digits]));
                cur /= p[new_digits];
                cur_digits -= new_digits;
            }
        }
        res.push_back((int) cur);
        while (!res.empty() && !res.back())
            res.pop_back();
        return res;
    }

    typedef vector<long long> vll;

    static vll karatsubaMultiply(const vll &a, const vll &b) {
        int n = a.size();
        vll res(n + n);
        if (n <= 32) {
            for (int i = 0; i < n; i++)
                for (int j = 0; j < n; j++)
                    res[i + j] += a[i] * b[j];
            return res;
        }

        int k = n >> 1;
        vll a1(a.begin(), a.begin() + k);
        vll a2(a.begin() + k, a.end());
        vll b1(b.begin(), b.begin() + k);
        vll b2(b.begin() + k, b.end());

        vll a1b1 = karatsubaMultiply(a1, b1);
        vll a2b2 = karatsubaMultiply(a2, b2);

        for (int i = 0; i < k; i++)
            a2[i] += a1[i];
        for (int i = 0; i < k; i++)
            b2[i] += b1[i];

        vll r = karatsubaMultiply(a2, b2);
        for (int i = 0; i < (int) a1b1.size(); i++)
            r[i] -= a1b1[i];
        for (int i = 0; i < (int) a2b2.size(); i++)
            r[i] -= a2b2[i];

        for (int i = 0; i < (int) r.size(); i++)
            res[i + k] += r[i];
        for (int i = 0; i < (int) a1b1.size(); i++)
            res[i] += a1b1[i];
        for (int i = 0; i < (int) a2b2.size(); i++)
            res[i + n] += a2b2[i];
        return res;
    }

    bigint operator*(const bigint &v) const {
        vector<int> a6 = convert_base(this->a, base_digits, 6);
        vector<int> b6 = convert_base(v.a, base_digits, 6);
        vll a(a6.begin(), a6.end());
        vll b(b6.begin(), b6.end());
        while (a.size() < b.size())
            a.push_back(0);
        while (b.size() < a.size())
            b.push_back(0);
        while (a.size() & (a.size() - 1))
            a.push_back(0), b.push_back(0);
        vll c = karatsubaMultiply(a, b);
        bigint res;
        res.sign = sign * v.sign;
        for (int i = 0, carry = 0; i < (int) c.size(); i++) {
            long long cur = c[i] + carry;
            res.a.push_back((int) (cur % 1000000));
            carry = (int) (cur / 1000000);
        }
        res.a = convert_base(res.a, 6, base_digits);
        res.trim();
        return res;
    }
};

int main() {
    ios :: sync_with_stdio(false);
    string A, B; cin >> A >> B;
    bigint a(A);
    bigint b(B);

    cout << a + b << endl;
    cout << a - b << endl;
    cout << a * b << endl;
}

Code mẫu của hieult

#include <cstdlib>
#include <iostream>
using namespace std;
int a[3000],b[3000],c[3000],_a[3000],_b[3000],_c[3000],ti[3000],hi[3000],to[3000];
int a1,b1,c1,i,_a1,_b1,_c1;
int tong()
{
long tong,nho=0;
int i,j;
//int a[1000], b[1000], c[1000],a1, b1, c1;
a1=_a1;
b1=_b1;
for (i=1; i<=a1; i++) a[i]=_a[i];
for (i=1; i<=b1; i++) b[i]=_b[i];
for (i=1; i<=a1; i++) c[i]=a[i];
for (i=1; i<=a1; i++) a[i]=c[a1-i+1];
for (i=1; i<=b1; i++) c[i]=b[i];
for (i=1; i<=b1; i++) b[i]=c[b1-i+1];
if (a1>b1) c1=a1; else c1=b1;
for (i=a1+1; i<=c1; i++)a[i]=0;
for (i=b1+1; i<=c1; i++)b[i]=0;
for (i=1; i<=c1; i++)
  {
  tong=nho+a[i]+b[i];
  c[i]=tong%10;
  nho=tong/10;
  }
if (nho>0) c1++, c[c1]=nho;
for (i=1; i<=c1; i++) a[i]=c[i];
for (i=1; i<=c1; i++) c[i]=a[c1-i+1];
for (i=1; i<=c1; i++) to[i]=c[i];
to[0]=c1;
}
int _hieu()
{
//int a[1000], b[1000], c[1000], a1, b1, c1;
long tong,nho=0,dau=1;
int i,j,tg;
a1=_a1;
b1=_b1;
for (i=1; i<=a1; i++) a[i]=_a[i];
for (i=1; i<=b1; i++) b[i]=_b[i];
for (i=1; i<=a1; i++) c[i]=a[i];
for (i=1; i<=a1; i++) a[i]=c[a1-i+1];
for (i=1; i<=b1; i++) c[i]=b[i];
for (i=1; i<=b1; i++) b[i]=c[b1-i+1];
if (a1>b1) c1=a1; else c1=b1;
for (i=a1+1; i<=c1; i++)a[i]=0;
for (i=b1+1; i<=c1; i++)b[i]=0;
for (i=c1; i>=1; i--)
if (a[i]!=b[i]){
if (a[i]<b[i])dau=-1; else dau=1;
break;
}
if (dau==-1){
for (i=1; i<=c1; i++){
tg=a[i];
a[i]=b[i];
b[i]=tg;
}
}
for (i=1; i<=c1; i++){
tong=10+nho+a[i]-b[i];
c[i]=tong%10;
if (tong/10>0) nho=0; else nho=-1;
}
while (c[c1]==0& c1>1)c1--;
for (i=1; i<=c1; i++) a[i]=c[i];
for (i=1; i<=c1; i++) c[i]=a[c1-i+1];
hi[c1+1]=dau;
hi[0]=c1;
for (i=1; i<=c1; i++) hi[i]=c[i];
}
int tich(){
//int a[1000], b[1000], c[1000], a1, b1, c1;
long tong=0,nho=0;
int i,j;
a1=0;b1=0;c1=0;
a1=_a1;
b1=_b1;
tong=0; nho=0;
for (i=1; i<=a1; i++) a[i]=_a[i];
for (i=1; i<=b1; i++) b[i]=_b[i];
for (i=1; i<=a1; i++) c[i]=a[i];
for (i=1; i<=a1; i++) a[i]=c[a1-i+1];
for (i=1; i<=b1; i++) c[i]=b[i];
for (i=1; i<=b1; i++) b[i]=c[b1-i+1];
c1=a1+b1;
for (i=1; i<=c1; i++) c[i]=0;
for (i=1; i<=c1; i++){
tong=nho;
for (j=1; j<=i; j++)
tong = tong + a[j]*b[i+1-j];
c[i]=tong%10;
nho=tong/10; 
}
if (nho>0) c[c1]=nho;
if (c[c1]==0) c1--;
for (i=1; i<=c1; i++) a[i]=c[i];
for (i=1; i<=c1; i++) c[i]=a[c1-i+1];
ti[0]=c1;
for (i=1; i<=c1; i++) ti[i]=c[i];
}
int nhap(){
string st1,st2;
char ch='a';
cin>>st1;
cin>>st2;
a1=st1.length();
b1=st2.length();
for (i=0; i<a1; i++) a[i+1]=short(st1[i])-48;
for (i=0; i<b1; i++) b[i+1]=short(st2[i])-48;
for (i=1; i<=a1; i++) _a[i]=a[i];
for (i=1; i<=b1; i++) _b[i]=b[i];
_a1=a1;
_b1=b1;
}
int thu(){
tich();
tong(); 
_hieu();
for(i=1; i<=to[0]; i++) cout<<to[i]; cout<<endl;
if (hi[hi[0]+1]==-1) cout<<"-";
for(i=1; i<=hi[0]; i++) cout<<hi[i]; cout<<endl;
for(i=1; i<=ti[0]; i++) cout<<ti[i]; 
}
int main(int argc, char *argv[])
{
nhap();
thu();
//system("PAUSE");
return(0);
}

Code mẫu của ll931110

Program BIGNUM;
        Const
                input  = '';
                output = '';
        Type
                arr = array[1..2000] of longint;
        Var
                a,b,c: arr;
                k,m,n: integer;
                   fa: text;
                   ch: char;
                    i: integer;

Procedure init;
          Var
                f: text;
                i: integer;
          Begin
                m:= 0;
                n:= 0;

                Assign(f, input);
                       Reset(f);
                       While not eoln(f) do
                                Begin
                                        inc(m);
                                        Read(f, ch);
                                        a[m]:= ord(ch) - 48;
                                End;
                       For i:= 1 to m do a[2000 - m + i]:= a[i];
                       m:= 2001 - m;

                       Readln(f);
                       While not eoln(f) do
                                Begin
                                        inc(n);
                                        Read(f, ch);
                                        b[n]:= ord(ch) - 48;
                                End;
                       For i:= 1 to n do b[2000 - n + i]:= b[i];
                       n:= 2001 - n;
                Close(f);

                If m > n then k:= n else k:= m;
          End;

Procedure printresult(p: integer);
          Var
                i: integer;
          Begin
                For i:= p to 2000 do write(fa, c[i]);
                Writeln(fa);
          End;

Procedure add;
          Var
                i: integer;
          Begin
                Fillchar(c, sizeof(c), 0);

                For i:= 2000 downto k do
                        Begin
                                c[i]:= c[i] + (a[i] + b[i]);
                                If c[i] > 9 then
                                        Begin
                                                inc(c[i - 1]);
                                                c[i]:= c[i] - 10;
                                        End;
                        End;

                If c[k - 1] <> 0 then printresult(k - 1)
                                 else printresult(k);
          End;

Procedure subtract(x,y: arr);
          Var
                s,i: integer;
          Begin
                Fillchar(c, sizeof(c), 0);

                For i:= 2000 downto k do
                        Begin
                                c[i]:= c[i] + (x[i] - y[i]);
                                If c[i] < 0 then
                                        Begin
                                                dec(c[i - 1]);
                                                c[i]:= c[i] + 10;
                                        End;
                        End;

                 s:= k;
                 While c[s] = 0 do inc(s);
                 printresult(s);
          End;

Procedure minus;
          Var
                d: integer;
          Begin
                d:= k;
                While (d <= 2000) and (a[d] = b[d]) do inc(d);

                If d > 2000 then writeln(fa, 0) else
                        If a[d] > b[d] then subtract(a,b)
                                       else begin
                                                  write(fa, '-');
                                                  subtract(b,a);
                                            end;
          End;


Procedure multiply;
          Var
                i,j,t: integer;
          Begin
                Fillchar(c, sizeof(c), 0);

                For i:= 2000 downto m do
                        For j:= 2000 downto n do
                                Begin
                                        t:= i + j - 2000;
                                        c[t]:= c[t] + a[i] * b[j];
                                        If c[t] > 9 then
                                                Begin
                                                        c[t - 1]:= c[t - 1] + c[t] div 10;
                                                        c[t]:= c[t] mod 10;
                                                End;
                                End;

                t:= 1;
                While c[t] = 0 do inc(t);
                printresult(t);
          End;

Begin
        init;
        Assign(fa, output);
                Rewrite(fa);
                        add;
                        minus;
                        multiply;
                Close(fa);
End.

Code mẫu của skyvn97

#include<stdio.h>
#include<string.h>
#include<algorithm>
#define MAX   2611
using namespace std;
struct bignum
{
       int nd;
       int sb;
       int d[MAX];
       bignum()
       {
        nd=0;
       }     
       bignum(int x)
       {
        if (x==0)
           {
            nd=1;
            sb=1;
            d[1]=0;
           }
        if (x>0)
           {
            nd=0;
            sb=1;
            while (x>0)
                  {
                   nd++;
                   d[nd]=x%10;
                   x=x/10;
                  }            
           }
        if (x<0)
           {
            nd=0;
            sb=-1;
            x=-x;
            while (x>0)
                  {
                   nd++;
                   d[nd]=x%10;
                   x=x/10;
                  }
           }
       }
       bignum(const bignum &x)
       {
        nd=x.nd;
        sb=x.sb;
        int i;
        for (i=1;i<=nd;i=i+1) d[i]=x.d[i];
       }
       void input(void)
       {
        char s[MAX];
        scanf("%s",s);
        sb=1;
        nd=0;
        int i;
        for (i=strlen(s)-1;i>=0;i=i-1)
            {
             nd++;
             d[nd]=s[i]-48;
            } 
       }
       void print(void)
       {
        if (sb<0) printf("-");
        int i;
        for (i=nd;i>=1;i=i-1) printf("%d",d[i]);        
       }              
       bignum abs()
       {
        bignum r=bignum(*this);
        r.sb=1;
        return (r);
       }
       int cmp(const bignum&x)
       {
        if (sb>x.sb) return (1);        
        if (sb<x.sb) return (-1);
        if (nd>x.nd) return (sb);
        if (nd<x.nd) return (-sb);
        int i;
        for (i=nd;i>=1;i=i-1)
            {
             if (d[i]>x.d[i]) return (sb);
             if (d[i]<x.d[i]) return (-sb);
            }
        return (0);
       }
       bignum operator + (const bignum &x) // only compatible for non-negative integer
       {
        int n=max(nd,x.nd);
        int i,s,c;
        bignum res (*this);
        res=bignum();
        res.sb=1;;
        s=0;c=0;
        for (i=nd+1;i<=n;i=i+1) d[i]=0;
        //for (i=x.nd+1;i<=n;i=i+1) x.d[i]=0;
        for (i=1;i<=n;i=i+1)
            {
             s=d[i]+x.d[i]+c;
             if (s>9) c=1;
             else c=0;
             res.nd++;
             res.d[res.nd]=s%10;
            }
        if (c>0)
           {
            res.nd++;
            res.d[res.nd]=1;
           }
        return (res);
       }
       bignum operator - (const bignum &x) // only compatible for non-negative integer
       {
        int tmp=cmp(x);
        if (tmp>0)
           {
            bignum res;
            res=bignum();
            res.sb=1;
            int i,s,c;
            //for (i=x.nd+1;i<=nd;i=i+1) x.d[i]=0;
            s=0;
            c=0;                
            for (i=1;i<=nd;i=i+1)
                {
                 s=d[i]-x.d[i]-c;
                 if (s<0)
                    {
                     s=s+10;
                     c=1;
                    }
                 else c=0;
                 res.nd++;
                 res.d[res.nd]=s%10;                 
                }
            while (res.d[res.nd]==0) res.nd--;            
            return (res);
           }       
        if (tmp==0) return (bignum(0));
        if (tmp<0)
           {
            bignum res;
            res=bignum();
            int i,s,c;
            res.sb=-1;
            s=0;c=0;
            for (i=nd+1;i<=x.nd;i=i+1) d[i]=0;
            for (i=1;i<=x.nd;i=i+1)
                {
                 s=x.d[i]-d[i]-c;
                 if (s<0)
                    {
                     s=s+10;
                     c=1;
                    }
                 else c=0;
                 res.nd++;
                 res.d[res.nd]=s%10;
                }                
            while (res.d[res.nd]==0) res.nd--;
            return (res);
           }     
       }
       bignum operator * (const bignum &x) //compatible for all numbers
       {
        if ((nd==1) && (d[1]==0)) return (bignum(0));
        if ((x.nd==1) && (x.d[1]==0)) return (bignum(0));
        bignum res;
        res=bignum();
        res.sb=sb*x.sb;
        int i,j,s,c;
        for (i=1;i<=x.nd;i=i+1)
            {
             bignum tmp=bignum();
             for (j=1;j<i;j=j+1)
                 {
                  tmp.nd++;
                  tmp.d[tmp.nd]=0;                  
                 }
             s=0;c=0;
             for (j=1;j<=nd;j=j+1)
                 {
                  s=d[j]*x.d[i]+c;
                  c=s/10;
                  tmp.nd++;
                  tmp.d[tmp.nd]=s%10;                  
                 }
             while (c>0)
                   {
                    tmp.nd++;
                    tmp.d[tmp.nd]=c%10;
                    c=c/10;
                   }
             res=res+tmp;
            }
        return (res);
       }
};
bignum a,b,c;
int main(void)
{
    a.input();
    b.input();
    c=a+b;
    c.print();
    printf("\n");
    c=a-b;
    c.print();
    printf("\n");
    c=a*b;
    c.print();
    printf("\n");   
}

Code mẫu của khuc_tuan

import java.math.BigInteger;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        BigInteger a = new BigInteger(sc.next());
        BigInteger b = new BigInteger(sc.next());
        System.out.println(a.add(b));
        System.out.println(a.subtract(b));
        System.out.println(a.multiply(b));
    }
}

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