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一、高精度加法

#include<iostream>
#include<string>
using namespace std;
const int N = 1e6+10;
int a[N],b[N],c[N];
int la,lb,lc;
void add(int c[],int a[],int b[])
{for(int i = 0;i < lc;i++){c[i] += a[i] + b[i];c[i+1] = c[i] / 10;c[i] %= 10;}if(c[lc]) lc++;
}int main()
{string x,y;cin >> x >> y;la = x.size();lb = y.size();lc = max(la,lb);for(int i = 0;i < la;i++) a[la-i-1] = x[i]-'0';for(int i = 0;i < lb;i++) b[lb-i-1] = y[i]-'0';add(c,a,b);for(int i = lc-1;i >= 0;i--) cout << c[i];return 0;
} 

二、高精度减法

#include<iostream>
#include<string>
using namespace std;
const int N = 1e6+10;
int a[N],b[N],c[N];
int la,lb,lc;//比大小 
bool comp(string& x,string& y)//y>x返回true 
{if(x.size() != y.size()) return y.size() > x.size();//位数相等return y > x;
}
//高精度减法 
void sub(int c[],int a[],int b[])//a>b
{for(int i = 0;i < lc;i++){c[i] += a[i]-b[i];if(c[i] < 0){c[i+1]--;c[i] += 10;}	}while(lc > 1 && c[lc-1] == 0) lc--;
}
int main()
{string x,y;cin >> x >> y;if(comp(x,y)){swap(x,y);cout << "-";}la = x.size();lb = y.size();lc = max(la,lb);for(int i = 0;i < la;i++) a[la-i-1] = x[i]-'0';for(int i = 0;i < lb;i++) b[lb-i-1] = y[i]-'0';sub(c,a,b);for(int i = lc-1;i >= 0;i--) cout << c[i];return 0;
} 

三、高精度乘法

#include<iostream>
#include<string>
using namespace std;
const int N = 1e6+10;
int a[N],b[N],c[N];
int la,lb,lc;void mul(int c[],int a[],int b[])
{for(int i = 0;i < la;i++){for(int j = 0;j < lb;j++){c[i+j] += a[i]*b[j];}}for(int i = 0;i < lc;i++){c[i+1] += c[i]/10;c[i] %= 10;}while(lc > 1 && c[lc-1] == 0) lc--;
}int main()
{string x,y;cin >> x >> y;la = x.size();lb = y.size();lc = la+lb;for(int i = 0;i < la;i++) a[la-i-1] = x[i]-'0';for(int i = 0;i < lb;i++) b[lb-i-1] = y[i]-'0';mul(c,a,b);for(int i = lc-1;i >= 0;i--) cout << c[i];return 0;
} 

四、高精度除法（高精度除以低精度）

  由于高精度除以高精度的场景较为少见，算法竞赛中基本不会使用，所以这里并没有做整理。

#include<iostream>
#include<string>
using namespace std;
const int N = 1e6+10;
int a[N],b,c[N]; 
int la,lc;void div(int c[],int a[],int b)//高精度除以低精度
{long long tmp = 0;//余数 for(int i = la-1;i >= 0;i--){tmp = tmp*10 + a[i];c[i] = tmp / b;tmp %= b;}while(lc > 1 && c[lc-1] == 0) lc--;
} int main()
{string x;cin >> x >> b;la = x.size(); lc = la;for(int i = 0;i < la;i++) a[la-i-1] = x[i]-'0';div(c,a,b);for(int i = lc-1;i >= 0;i--) cout << c[i];return 0;}