C++奥赛一本通刷题记录(高精度)

2017.11.15 By gwj1139177410

1. 大整数加法 openjudge10

   //Add Template
   #include<iostream>
   #include<algorithm>
   #include<string>
   using namespace std;
   const int maxn = 220;
   int a[maxn], b[maxn], c[maxn];
   int main(){
      string s1, s2;  cin>>s1>>s2;
      a[0] = s1.size();  b[0] = s2.size();
      for(int i = 1; i <= a[0]; i++)a[i]=s1[a[0]-i]-'0';
      for(int i = 1; i <= b[0]; i++)b[i]=s2[b[0]-i]-'0';
      c[0] = max(a[0],b[0])+1;
      for(int i = 1; i <= c[0]; i++){
          c[i] += a[i]+b[i];
          if(c[i] >= 10){
              c[i] %= 10;
              c[i+1]++;
          }
      }
      while(c[0]>1 && c[c[0]]==0)c[0]--;
      for(int i = c[0]; i >= 1; i--)cout<<c[i];
      return 0;
   }
   

2. 大整数减法 openjudge11

   //Sub Template
   #include<iostream>
   #include<algorithm>
   #include<string>
   using namespace std;
   const int maxn = 220;
   int a[maxn], b[maxn], c[maxn];
   int main(){
      string s1, s2;  cin>>s1>>s2;
      if(s1.size()<s2.size()||(s1.size()==s2.size()&&s1<s2)){
          cout<<"-";  swap(s1,s2);
      }
      a[0] = s1.size();  b[0] = s2.size();
      for(int i = 1; i <= a[0]; i++)a[i]=s1[a[0]-i]-'0';
      for(int i = 1; i <= b[0]; i++)b[i]=s2[b[0]-i]-'0';
      c[0] = max(a[0],b[0])+1;
      for(int i = 1; i <= c[0]; i++){
          if(a[i]<b[i]){ a[i+1]--; a[i]+=10; }
          c[i] = a[i]-b[i];
      }
      while(c[0]>1 && c[c[0]]==0)c[0]--;
      for(int i = c[0]; i >= 1; i--)cout<<c[i];
      return 0;
   }
   

3. 计算2的N次方 openjudge12

   //大数计算本质, 模拟即可
   #include<iostream>
   using namespace std;
   const int maxn = 110;
   int a[maxn];
   int main(){
      int n;  cin>>n;  a[0]=n+1;//可能进位
      a[1] = 1;
      for(int i = 1; i <= n; i++){
          for(int j = 1; j <= a[0]; j++)a[j]=a[j]+a[j];//每次乘以2
          for(int j = 1; j <= a[0]; j++){//单独处理进位避免覆盖
              if(a[j]>=10){
                  a[j+1] += a[j]/10;
                  a[j] %= 10;
              }
          }
      }
      while(a[0]>1 && a[a[0]]==0)a[0]--;
      for(int i = a[0]; i >= 1; i--)cout<<a[i];
      return 0;
   }
   

4. 大整数因子 openjudge13

   //高精除低精,模板
   #include<iostream>
   #include<string>
   using namespace std;
   const int maxn = 40;
   int a[maxn], flag=1;
   int mod(int a[], int b){//return a%b;
      int x = 0;
      for(int i = a[0]; i >= 1; i--){
       //c[i] = (a[i]+x*10)/b;
       x = (a[i]+x*10)%b;
   }
      return x;
   }
   int main(){
      string s;  cin>>s;  a[0]=s.size();
      for(int i = 1; i <= a[0]; i++)a[i]=s[a[0]-i]-'0';
      for(int i = 2; i <= 9; i++){
          if(mod(a,i)==0){
              cout<<i<<" ";
              flag = 0;
          }
      }
      if(flag)cout<<"none\n";
      return 0;
   }
   

5. 求10000以内n的阶乘 openjudge14

   //高精乘低精,模板
   #include<iostream>
   #include<string>
   using namespace std;
   const int maxn = 50010;//bugs:10000!得50000位啊
   int a[maxn];
   void mul(int a[], int b){ //a=a*b
      int x = 0; //进位位
      for(int i = 1; i <= a[0]; i++){
          a[i] = a[i]*b+x;  x = 0;
          if(a[i]>=10){
              x = a[i]/10;
              a[i] %= 10;
              if(i == a[0])a[0]++;
          }
      }
   }
   int main(){
      int n;  cin>>n;  a[0]=1; a[1]=1;
      for(int i = 2; i <= n; i++)mul(a,i);
      for(int i = a[0]; i >= 1; i--)cout<<a[i];
      return 0;
   }
   

6. 阶乘和 openjudge15

   //高精乘低精,高精加法,模板
   #include<iostream>
   #include<algorithm>
   #include<string>
   #include<cstring>
   using namespace std;
   const int maxn = 50010;
   int a[maxn], b[maxn], c[maxn];
   void mul(int a[], int b){ //a=a*b
      int x = 0; //进位位
      for(int i = 1; i <= a[0]; i++){
          a[i] = a[i]*b+x;  x = 0;
          if(a[i]>=10){
              x = a[i]/10;
              a[i] %= 10;
              if(i == a[0])a[0]++;
          }
      }
   }
   void add(int a[], int b[]){ //a=a+b
      for(int i = 0; i <= a[0]; i++){ c[i]=a[i]; a[i]=0;}//copy
      a[0]=max(b[0],c[0])+1;
      for(int i = 1; i <= a[0]; i++){
          a[i] += b[i]+c[i];
          if(a[i]>=10){
              a[i+1]++;
              a[i] %= 10;
          }
      }
      while(a[a[0]]==0 && a[0]>1)a[0]--;
   }
   int main(){
      int n;  cin>>n;  a[0]=b[0]=1; a[1]=b[1]=1;
      for(int i = 2; i <= n; i++){
          mul(b,i);  add(a,b);
      }
      for(int i = a[0]; i >= 1; i--)cout<<a[i];
      return 0;
   }
   

7. 大整数除法 openjudge09

   //高精除高精,模板
   #include<iostream>
   #include<algorithm>
   #include<string>
   #include<cstring>
   using namespace std;
   const int maxn = 220;
   int a[maxn], b[maxn], c[maxn], t[maxn];
   int compare(int x[], int y[]){
   if(x[0] < y[0])return -1;
   if(x[0] > y[0])return 1;
   for(int i = x[0]; i > 0; i--){ //越后面的位越大啊
       if(x[i] < y[i])return -1;
       if(x[i] > y[i])return 1;
   }
   return 0;
   }
   void times(int x[], int y[], int k){
   for(int i = 1; i <= x[0]; i++)y[i+k-1] = x[i];
   y[0] = x[0]+k-1;
   }
   int main(){
   string s1, s2;  cin>>s1>>s2;
   a[0] = s1.size();  b[0] = s2.size();
   //bugs:a比b小的情况,就是...如果只剩0的话这个商的长度的也会变成0 错误数据:0 100
   if(a[0]<b[0]||(a[0]==b[0]&&s1<s2)){ cout<<"0\n"; return 0; }
   for(int i = 1; i <= a[0]; i++)a[i] = s1[a[0]-i]-'0';
   for(int i = 1; i <= b[0]; i++)b[i] = s2[b[0]-i]-'0';
   c[0] = a[0]-b[0]+1;
   for(int i = c[0]; i > 0; i--){
       memset(t,0,sizeof(t));
       times(b,t,i);
       while(compare(a,t)>=0){
           c[i]++;
           for(int j = 1; j <= a[0]; j++){
               if(a[j] < t[j]){
                   a[j+1]--;
                   a[j] += 10;
               }
               a[j] -= t[j];
           }
           while(!a[a[0]] && a[0]>1)a[0]--;
       }
   }
   while(!c[c[0]] && c[0]>1)c[0]--;
   for(int i = c[0]; i > 0; i--)cout<<c[i];
   return 0;
   }
   

8. 除以13 openjudge27

   //高精除低精,模板
   #include<iostream>
   #include<string>
   using namespace std;
   const int maxn = 110;
   int a[maxn], c[maxn];
   int main(){
      string s;  cin>>s;  c[0]=a[0]=s.size();
      for(int i = 1; i <= a[0]; i++)a[i]=s[a[0]-i]-'0';
      int x = 0;
      for(int i = a[0]; i >= 1; i--){
       c[i] = (a[i]+x*10)/13;
       x = (a[i]+x*10)%13;
   }
      while(!c[c[0]] && c[0]>1)c[0]--;
      for(int i = c[0]; i >= 1; i--)cout<<c[i];
      cout<<"\n"<<x<<"\n";
      return 0;
   }
   

   ​