C++奥赛一本通刷题记录(高精度)

2017.11.15 By gwj1139177410

//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;
}

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;
}

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;
}

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
";
   return 0;
}

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;
}

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;
}

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
"; 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;
}

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<<"
"<<x<<"
";
   return 0;
}