高精度 加减乘除

• add：

 1 #include <iostream>
 2 #include <vector>
 3 #include <string>
 4 #include <algorithm>
 5 
 6 using namespace std;
 7 
 8 vector<int> a, b, c;//c = a + b
 9 
10 void add(){
11     int t = 0;//代表进位
12     for(int i = 0;i < a.size() || i < b.size();++i){
13         if(i < a.size()) t += a[i];        
14         if(i < b.size()) t += b[i];
15         c.push_back(t%10);
16         t /= 10;
17     }    
18     if(t)c.push_back(t);
19 }
20 
21 int main(){
22     string s1,s2;    
23     cin >> s1 >> s2;
24     
25     for(int i = s1.size()-1;i >= 0;--i)a.push_back(s1[i] - '0');
26     for(int i = s2.size()-1;i >= 0;--i)b.push_back(s2[i] - '0');
27     
28     add();
29     
30     for(int i = c.size()-1;i >= 0;--i)cout << c[i];      
31 }

• mul：

 1 #include <iostream>
 2 #include <vector>
 3 
 4 using namespace std;
 5 
 6 //a*b = c
 7 void mul(vector<int>& a,int b,vector<int>& c){
 8     int t = 0;
 9     for(int i = 0;i < a.size();++i){
10         c.push_back((a[i]*b + t) % 10);
11         t = (a[i]*b + t) / 10; 
12     }    
13     if(t)c.push_back(t);
14 }
15 
16 int main(){
17     string s;
18     int b;
19     cin >> s >> b;
20     vector<int> a;
21     for(int i = s.size()-1;i >= 0;--i)a.push_back(s[i] - '0');
22     
23     vector<int> c;
24     mul(a,b,c);
25     for(int i = c.size()-1;i >= 0;--i)cout << c[i];
26     
27     return 0;
28 }

• div：

 1 #include <iostream>
 2 #include <vector>
 3 #include <string>
 4 
 5 using namespace std;
 6 
 7 void div(vector<int>& a,int b,vector<int>& c,int& r){
 8     for(int i = 0;i < a.size();++i){
 9         r = r * 10 + a[i];
10         c.push_back(r/b);
11         r %= b;
12     }
13 }
14 
15 int main(){
16     string s;
17     cin >> s;
18     vector<int> a;
19     for(int i = 0;i < s.size();++i)a.push_back(s[i] - '0');
20     int b;
21     cin>>b;
22     
23     int r = 0;
24     vector<int> c;
25     div(a,b,c,r);
26     bool flag = true;
27     for(int i = 0;i < c.size();++i){
28         if(c[i] != 0)flag = false;
29         if(flag == false)cout << c[i];
30     }
31     cout << endl << r;
32     return 0;
33 }

• sub：

 1 #include <iostream>
 2 #include <vector>
 3 #include <string>
 4 
 5 using namespace std;
 6 
 7 //a >= b return true else return false
 8 bool cmp(vector<int>& a,vector<int>& b){
 9     if(a.size() != b.size()) return a.size() > b.size();
10     for(int i = a.size()-1;i >= 0;--i)
11         if(a[i] != b[i]) return a[i] > b[i];
12     return true;
13 }
14 
15 //a >= b
16 void sub(vector<int>& a, vector<int>& b, vector<int>& c){
17     int t = 0;//代表借位
18     for(int i = 0;i < a.size();++i){
19         t = a[i] - t;
20         if(i < b.size())
21             t -= b[i];
22         //这句包含了t > 0 and t < 0，结果都是t+10 % 10
23         c.push_back((t+10)%10);
24         if(t >= 0)t = 0;//代表不需要借位
25         else t = 1;//借位
26     }
27     //去掉前面的0
28     while(c.size() > 1 && c.back() == 0)c.pop_back();
29 }
30 
31 int main(){
32     string s1, s2;
33     cin >> s1 >> s2;
34     vector<int> a, b, c;
35     
36     for(int i = s1.size()-1;i >= 0;--i)a.push_back(s1[i]-'0');
37     for(int i = s2.size()-1;i >= 0;--i)b.push_back(s2[i]-'0');
38     
39     if(cmp(a,b)){
40         sub(a, b, c);
41         for(int i = c.size()-1;i >= 0;--i)cout << c[i];
42     }
43     else{
44         sub(b, a, c);
45         cout << '-';
46         for(int i = c.size()-1;i >= 0;--i)cout << c[i];
47     } 
48     
49     return 0;
50 }