高精度计算时要把数据存入数组，先存低位，因为当发生进位时，向数组最后一个元素后增加元素是非常容易的。

高精度加法模板：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
#include <iostream>
#include <vector>

using namespace std;

vector<int> add(vector<int>& A, vector<int>& B) {
    vector<int> C;
    int t = 0;
    for(int i=0; i<A.size() || i<B.size();i++) {
        if(i<A.size()) t+=A[i];
        if(i<B.size()) t+=B[i];

        C.push_back(t%10);
        t/=10;
    }
    if(t) C.push_back(1);
    return C;
}

int main() {
    string a, b;
    cin >> a >> b;
    vector<int> A, B;
    for(int i=a.size()-1;i>=0;i--) A.push_back(a[i]-'0');
    for(int i=b.size()-1;i>=0;i--) B.push_back(b[i]-'0');
    auto C = add(A,B);
    for(int i=C.size()-1;i>=0;i--) cout << C[i];
    return 0;
}

高精度加法 + 压位：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
#include <iostream>
#include <vector>

using namespace std;
const int base = 1e9;
vector<int> add(vector<int>& A, vector<int>& B) {
  vector<int> C;
  int t = 0;
  for (int i = 0; i < A.size() || i < B.size(); i++) {
    if (i < A.size()) t += A[i];
    if (i < B.size()) t += B[i];

    C.push_back(t % base);
    t /= base;
  }
  if (t) C.push_back(1);
  return C;
}

int main() {
  string a, b;
  vector<int> A, B;
  cin >> a >> b;
  for (int i = a.size() - 1, s = 0, j = 0, t = 1; i >= 0; i--) {
    s += (a[i] - '0') * t;
    j++, t *= 10;
    if (j == 9 || i == 0) {
      A.push_back(s);
      s = j = 0;
      t = 1;
    }
  }
  for (int i = b.size() - 1, s = 0, j = 0, t = 1; i >= 0; i--) {
    s += (b[i] - '0') * t;
    j++, t *= 10;
    if (j == 9 || i == 0) {
      B.push_back(s);
      s = j = 0;
      t = 1;
    }
  }
  auto C = add(A, B);
  cout << C.back();
  for (int i = C.size() - 2; i >= 0; i--) printf("%09d", C[i]);
  cout << endl;
  return 0;
}

高精度减法模板：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
#include <iostream>
#include <vector>

using namespace std;
bool cmp(vector<int>& A, vector<int>& B) {
    if(A.size()!=B.size()) {
        return A.size() > B.size();
    }
    for(int i=A.size()-1;i>=0;i--) {
        if(A[i]!=B[i]) return A[i] > B[i];
    }
    return true;
}
vector<int> sub(vector<int>& A, vector<int>& B) {
    vector<int> C;
    int t = 0;
    for(int i=0; i<A.size();i++) {
        t = A[i]-t;
        if(i<B.size()) t-=B[i];

        C.push_back((t+10)%10);
        if (t<0) t=1;
        else t=0;
    }
    // 干掉前导 0，当结果是 0 的时候，保留一个 0
    while(C.size()>1 && C.back() == 0) C.pop_back();
    return C;
}

int main() {
    string a, b;
    cin >> a >> b;
    vector<int> A, B;
    for(int i=a.size()-1;i>=0;i--) A.push_back(a[i]-'0');
    for(int i=b.size()-1;i>=0;i--) B.push_back(b[i]-'0');

    if(cmp(A, B)) {
        auto C = sub(A,B);
        for(int i=C.size()-1;i>=0;i--) cout << C[i];
    } else {
        auto C = sub(B,A);
        cout << "-";
        for(int i=C.size()-1;i>=0;i--) cout << C[i];
    }

    return 0;
}

高精度乘法模板：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
#include <iostream>
#include <vector>
using namespace std;

vector<int> mul(vector<int>& A, int B) {
    vector<int> C;
    for(int i=0,t =0;i<A.size()||t;i++) {
        if(i<A.size()) t+=A[i]*B;
        C.push_back(t%10);
        t/=10;
    }
    while(C.size()>1&&C.back() == 0) C.pop_back();
    return C;
}
int main() {
    string a;
    int b;
    cin >> a >> b;
    vector<int> A;
    for(int i=a.size()-1;i>=0;i--) A.push_back(a[i]-'0');
    auto C = mul(A, b);
    for(int i=C.size()-1;i>=0;i--) cout << C[i];
    return 0;
}