C++奥赛一本通刷题高精度题解

title: C++奥赛一本通刷题记录(高精度)
date: 2017-11-15
tags:

• 一本通
• openjudege
  categories: OI

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;
}

1. 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;
}

1. 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;
}

1. 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;
}

1. 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;
}

1. 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;
}

1. 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;
}

1. 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;
}