高精度减法

Point:

1、计算减法先比较大小

2、公式

$$ tmp = a[i] - tmp - (i < b.size() \; ? \; b[i] \; : \; 0)$$

3、注意前导零

#include <iostream>
#include <vector>

using namespace std;

// >= or <
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;
}
// 减法
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; // 注意
        if(i < b.size()) t -= b[i];
        c.push_back((t + 10) % 10);
        if(t < 0) t = 1;
        else t = 0;
    }
    while(c.size() > 1 && c.back() == 0) c.pop_back();
    return c;
}
int main()
{
    string x, y;
    cin >> x >> y;
    vector<int> a, b;
    for(int i = x.size() - 1; i >= 0; -- i) a.push_back(x[i] - '0');
    for(int i = y.size() - 1; i >= 0; -- i) b.push_back(y[i] - '0');
    if(cmp(a, b))
    {
        a = sub(a, b);
        for(int i = a.size() - 1; i >= 0; -- i) cout << a[i];
    }
    else
    {
        a = sub(b, a);
        cout << "-";
        for(int i = a.size() - 1; i >= 0; -- i) cout << a[i];
    }

    return 0;
}