8.高精度减法

假定A和B都是正数，假定A这个数>=B这个数。

#include <bits/stdc++.h>
using namespace std;
bool cmp(vector<int> &A, vector<int> &B) { //判断是否A>=B，如果A>=B返回true，否则返回false 
    if (A.size() != B.size()) {
        return A.size() > B.size();
    }
    for (int i = A.size() - 1; i >= 0; i--) { //从高位开始比较 
        if (A[i] != B[i]) {
            return A[i] > B[i];
        }
    }
    return true; //A=B也成立 
}
vector<int> sub(vector<int> &A, vector<int> &B) {
    vector<int> C;
    int t = 0;
    //已经保证了A>=B 
    for (int i = 0; i < A.size(); i++) {
        //还是用t来表示当前这一位 
        t = A[i] - t;
        if (i < B.size()) {
            t -= B[i];
        }
        //若t>=0，就是t
        //若t<0，就是t+10 
        //t一定是个位数.-9 ~ 9
        C.push_back((t + 10) % 10);
        //t不是0就是1 
        //t=0表示没有借位
        //t=1表示借位了 
        if (t < 0) {
            t = 1;
        } else {
            t = 0;
        }
    }
    //去掉前导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.length() - 1; i >= 0; i--) {
        A.push_back(a[i] - '0');
    }
    for (int i = b.length() - 1; i >= 0; i--) {
        B.push_back(b[i] - '0');
    }
    vector<int> C;
    if (cmp(A, B)) { //如果A>=B的话，直接减。5-3 
        C = sub(A, B);
    } else { //否则：-(3 - 5) 
        cout << "-";
        C = sub(B, A);
    }
    for (int i = C.size() - 1; i >= 0; i--) {
        cout << C[i];
    }
    return 0;
}

 2020年9月29日更新：高精度压8位的做法

#include <bits/stdc++.h>
using namespace std;
const int base = 100000000;
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 + base) % base);
        if (t < 0) {
            t = 1;
        } else {
            t = 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, C;
    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 == 8 || i == 0) {
            A.push_back(s);
            s = 0;
            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 == 8 || i == 0) {
            B.push_back(s);
            s = 0;
            j = 0;
            t = 1;
        }
    }
    if (cmp(A, B)) {
        C = sub(A, B);
    } else {
        cout << "-";
        C = sub(B, A);
    }
    cout << C.back();
    for (int i = C.size() - 2; i >= 0; i--) {
        printf("%08d", C[i]);
    }
    return 0;
}