高精度合集(vector,帶低精)
阿新 • • 發佈：2020-10-09
https://www.luogu.com.cn/problem/P1932
待補:壓位高精,多項式除法優化除法、取模
高精度除可以欽定選取前幾位後再進行除法（也許常數略小？）
Luogu1932 A+B A-B A*B A/B A%B Problem
高精度合集(vector,帶低精)
NTT優化乘法,vector,帶低精,無符號
#include<iostream> #include<cstdio> #include<algorithm> #include<cstring> #include<vector> #define N 20005 #define M 40005 #define ll long long #define ull unsigned long long #define a hz.w #define b kz.w #define c kzkz.w #define d kzzf.w #define P 998244353 #define inv(x) ksm(x,P-2) #define zero(x) (x.w[0]==1 && x.w[1]==0) #define IT vector<int> :: iterator using namespace std; const ll lim=922337203685477578; char orz[N]; int rev[M]; int G[2][25]; int e[M],f[M]; ll ten[25]; int ksm(int x,int y); void NTT(int *g,int t,int s); struct BigNumber { vector<int>w; void set0() { w.clear(); w.push_back(1),w.push_back(0); } void set1() { w.clear(); w.push_back(1),w.push_back(1); } void setNum(ll x) { if (!x) { set0(); return; } w.clear(); w.push_back(0); int g=0; while (x) { w.push_back(x%10); x/=10; g++; } w[0]=g; } void read() { scanf("%s",orz); w.clear(); w.push_back(strlen(orz)); for (int i=w[0]-1;i>=0;i--) w.push_back(orz[i]-'0'); } }s,t; BigNumber kz,kzkz,kzzf; void write(BigNumber kz) { for (int i=b[0];i>=1;i--) putchar(b[i]+'0'); putchar('\n'); } ll BigNumber_Turn_Number(BigNumber kz); bool operator < (BigNumber hz,ll x) { if (a[0]>19 || x<ten[a[0]]) return false; if (x>=ten[a[0]+1]) return true; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return a[i]<x/ten[i]%10; return false; } bool operator <= (BigNumber hz,ll x) { if (a[0]>19 || x<ten[a[0]]) return false; if (x>=ten[a[0]+1]) return true; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return a[i]<x/ten[i]%10; return true; } bool operator > (BigNumber hz,ll x) { if (a[0]>19 || x<ten[a[0]]) return true; if (x>=ten[a[0]+1]) return false; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return a[i]>x/ten[i]%10; return false; } bool operator >= (BigNumber hz,ll x) { if (a[0]>19 || x<ten[a[0]]) return true; if (x>=ten[a[0]+1]) return false; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return a[i]>x/ten[i]%10; return true; } bool operator == (BigNumber hz,ll x) { if (a[0]>19 || x<ten[a[0]]) return false; if (x>=ten[a[0]+1]) return false; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return false; return true; } bool operator != (BigNumber hz,ll x) { if (a[0]>19 || x<ten[a[0]]) return true; if (x>=ten[a[0]+1]) return true; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return true; return false; } bool operator < (ll x,BigNumber hz) { if (a[0]>19 || x<ten[a[0]]) return true; if (x>=ten[a[0]+1]) return false; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return a[i]>x/ten[i]%10; return false; } bool operator <= (ll x,BigNumber hz) { if (a[0]>19 || x<ten[a[0]]) return true; if (x>=ten[a[0]+1]) return false; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return a[i]>x/ten[i]%10; return true; } bool operator > (ll x,BigNumber hz) { if (a[0]>19 || x<ten[a[0]]) return false; if (x>=ten[a[0]+1]) return true; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return a[i]<x/ten[i]%10; return false; } bool operator >= (ll x,BigNumber hz) { if (a[0]>19 || x<ten[a[0]]) return false; if (x>=ten[a[0]+1]) return true; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return a[i]<x/ten[i]%10; return true; } bool operator == (ll x,BigNumber hz) { if (a[0]>19 || x<ten[a[0]]) return false; if (x>=ten[a[0]+1]) return false; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return false; return true; } bool operator != (ll x,BigNumber hz) { if (a[0]>19 || x<ten[a[0]]) return true; if (x>=ten[a[0]+1]) return true; for (int i=a[0];i>=1;i--) if (a[i]!=x/ten[i]%10) return true; return false; } bool operator < (BigNumber hz,BigNumber kz) { if (a[0]!=b[0]) return a[0]<b[0]; for (int i=a[0];i>=1;i--) if (a[i]!=b[i]) return a[i]<b[i]; return false; } bool operator <= (BigNumber hz,BigNumber kz) { if (a[0]!=b[0]) return a[0]<b[0]; for (int i=a[0];i>=1;i--) if (a[i]!=b[i]) return a[i]<b[i]; return true; } bool operator > (BigNumber hz,BigNumber kz) { if (a[0]!=b[0]) return a[0]>b[0]; for (int i=a[0];i>=1;i--) if (a[i]!=b[i]) return a[i]>b[i]; return false; } bool operator >= (BigNumber hz,BigNumber kz) { if (a[0]!=b[0]) return a[0]>b[0]; for (int i=a[0];i>=1;i--) if (a[i]!=b[i]) return a[i]>b[i]; return true; } bool operator == (BigNumber hz,BigNumber kz) { if (a[0]!=b[0]) return false; for (int i=a[0];i>=1;i--) if (a[i]!=b[i]) return false; return true; } bool operator != (BigNumber hz,BigNumber kz) { if (a[0]!=b[0]) return true; for (int i=a[0];i>=1;i--) if (a[i]!=b[i]) return true; return false; } BigNumber operator + (BigNumber hz,ll x) { for (int i=1;i<=a[0];i++) { x+=a[i]; a[i]=x%10; x/=10; } while (x) a[0]++,a.push_back(x%10),x/=10; return hz; } BigNumber operator - (BigNumber hz,ll x) { for (int i=1;i<=a[0];i++) { a[i]-=x%10; if (a[i]<0) a[i]+=10,a[i+1]--; x/=10; } IT it=a.end()-1; while (!(*it) && a[0]>1) { a[0]--; a.erase(it--); } return hz; } BigNumber operator * (BigNumber hz,ll x) { ll jw=0; if (x<=lim) { for (int i=1;i<=a[0];i++) { jw+=x*a[i]; a[i]=jw%10; jw/=10; } while (jw) a[0]++,a.push_back(jw%10),jw/=10; } else { ll rx=x/10; int tx=x%10,ri; for (int i=1;i<=a[0];i++) { ri=a[i]; a[i]=a[i]*tx+jw%10; jw=jw/10+rx*ri+a[i]/10; a[i]%=10; } while (jw) a[0]++,a.push_back(jw%10),jw/=10; } return hz; } BigNumber operator / (BigNumber hz,ll x) { e[0]=0; ll y=0; if (x<=lim) { for (int i=a[0];i;i--) { y=y*10+a[i]; if (e[0] || y>=x) e[++e[0]]=y/x,y%=x; } } else { ull s; int ct; for (int i=a[0];i;i--) { if (y<=lim) { y=y*10+a[i]; if (e[0] || y>=x) e[++e[0]]=y/x,y%=x; } else { s=a[i],ct=0; for (int j=1;j<=10;j++) { s+=y; if (s>=x) s-=x,ct++; } y=s; if (e[0] || ct) e[++e[0]]=ct; } } } if (!e[0]) e[0]++,e[1]=0; a.clear(); a.push_back(e[0]); for (int i=e[0];i;i--) a.push_back(e[i]); return hz; } BigNumber operator % (BigNumber hz,ll x) { ll y=0; if (x<=lim) { for (int i=a[0];i;i--) y=(y*10+a[i])%x; } else { ull s; for (int i=a[0];i;i--) { if (y<=lim) y=(y*10+a[i])%x; else { s=a[i]; for (int j=1;j<=10;j++) { s+=y; if (s>=x) s-=x; } y=s; } } } hz.setNum(y); return hz; } BigNumber operator + (ll x,BigNumber hz) { for (int i=1;i<=a[0];i++) { x+=a[i]; a[i]=x%10; x/=10; } while (x) a[0]++,a.push_back(x%10),x/=10; return hz; } BigNumber operator - (ll x,BigNumber hz) { x-=BigNumber_Turn_Number(hz); hz.setNum(x); return hz; } BigNumber operator * (ll x,BigNumber hz) { ll jw=0; if (x<=lim) { for (int i=1;i<=a[0];i++) { jw+=x*a[i]; a[i]=jw%10; jw/=10; } while (jw) a[0]++,a.push_back(jw%10),jw/=10; } else { ll rx=x/10; int tx=x%10,ri; for (int i=1;i<=a[0];i++) { ri=a[i]; a[i]=a[i]*tx+jw%10; jw=jw/10+rx*ri+a[i]/10; a[i]%=10; } while (jw) a[0]++,a.push_back(jw%10),jw/=10; } return hz; } BigNumber operator / (ll x,BigNumber hz) { if (x<hz) { hz.set0(); return hz; } x/=BigNumber_Turn_Number(hz); hz.setNum(x); return hz; } BigNumber operator % (ll x,BigNumber hz) { if (x<hz) { hz.setNum(x); return hz; } x%=BigNumber_Turn_Number(hz); hz.setNum(x); return hz; } BigNumber operator + (BigNumber hz,BigNumber kz) { int ws=max(a[0],b[0]); int jw=0; for (int i=1;i<=ws;i++) { if (b[0]<i) { b[0]++; b.push_back(0); } if (a[0]>=i) b[i]+=a[i]; b[i]+=jw; jw=b[i]/10; b[i]%=10; } while (jw) { b[0]++; b.push_back(jw%10); jw/=10; } return kz; } BigNumber operator - (BigNumber hz,BigNumber kz) { int ws=max(a[0],b[0]); for (int i=1;i<=ws;i++) { if (b[0]<i) b.push_back(a[i]); else b[i]=a[i]-b[i]; if (b[i]<0) { b[i]+=10; a[i+1]--; } } IT it=b.end()-1; while (!(*it) && ws>1) { ws--; b.erase(it--); } b[0]=ws; return kz; } BigNumber operator * (BigNumber hz,BigNumber kz) { if (zero(hz) || zero(kz)) { hz.set0(); return hz; } int la=a[0],lb=b[0]; int s=1,l=0; while (s<la+lb) { s <<=1; l++; } rev[0]=0; for (int i=1;i<s;i++) rev[i]=(rev[i >> 1] >> 1) | ((i & 1) << (l - 1)); e[0]=f[0]=0; for (int i=1;i<=la;i++) e[i-1]=a[i]; for (int i=1;i<=lb;i++) f[i-1]=b[i]; for (int i=la;i<s;i++) e[i]=0; for (int i=lb;i<s;i++) f[i]=0; NTT(e,0,s); NTT(f,0,s); for (int i=0;i<s;i++) e[i]=(ll)e[i]*f[i]%P; NTT(e,1,s); int invs=inv(s); for (int i=s;i>=1;i--) e[i]=(ll)e[i-1]*invs%P; e[0]=0; for (int i=1;i<=la+lb;i++) { e[i+1]+=e[i]/10; e[i]%=10; } a[0]=la+lb; while (!e[a[0]] && a[0]>1) a[0]--; for (int i=1;i<=a[0];i++) if (la<i) a.push_back(e[i]); else a[i]=e[i]; return hz; } BigNumber operator / (BigNumber hz,BigNumber kz) { c.clear(); c.push_back(0); for (int i=1;i<=a[0];i++) c.push_back(0); c[0]=a[0]; kzzf.set0(); for (int i=a[0];i>=1;i--) { if (!(d[0]==1 && d[1]==0)) { d.push_back(0); for (int i=d[0];i>=1;i--) d[i+1]=d[i]; d[1]=a[i]; d[0]++; } else d[1]=a[i]; while (kzzf>=kz) { kzzf=kzzf-kz; c[i]++; } } IT it=c.end()-1; while (!(*it) && c[0]>1) { c[0]--; c.erase(it--); } return kzkz; } BigNumber operator % (BigNumber hz,BigNumber kz) { kzzf.set0(); for (int i=a[0];i>=1;i--) { if (!(d[0]==1 && d[1]==0)) { d.push_back(0); for (int i=d[0];i>=1;i--) d[i+1]=d[i]; d[1]=a[i]; d[0]++; } else d[1]=a[i]; while (kzzf>=kz) kzzf=kzzf-kz; } return kzzf; } void operator += (BigNumber &kz,ll hz) { kz=kz+hz; } void operator -= (BigNumber &kz,ll hz) { kz=kz-hz; } void operator *= (BigNumber &kz,ll hz) { kz=kz*hz; } void operator /= (BigNumber &kz,ll hz) { kz=kz/hz; } void operator %= (BigNumber &kz,ll hz) { kz=kz%hz; } void operator += (BigNumber &kz,BigNumber hz) { kz=kz+hz; } void operator -= (BigNumber &kz,BigNumber hz) { kz=kz-hz; } void operator *= (BigNumber &kz,BigNumber hz) { kz=kz*hz; } void operator /= (BigNumber &kz,BigNumber hz) { kz=kz/hz; } void operator %= (BigNumber &kz,BigNumber hz) { kz=kz%hz; } BigNumber Number_Turn_BigNumber(ll x) { if (x==0) { kz.set0(); return kz; } b.clear(); b.push_back(0); while (x) { b[0]++; b.push_back(x%10); x/=10; } return kz; } ll BigNumber_Turn_Number(BigNumber kz) { ll y=0; for (int i=b[0];i>=1;i--) y=y*10+b[i]; return y; } void NTT(int *q,int t,int s) { for (int i=0;i<s;i++) if (i<rev[i]) swap(q[i],q[rev[i]]); for (int mid=1,o=1;mid<s;mid <<=1,o++) for (int j=0;j<s;j+=(mid << 1)) { int g=1; for (int k=0;k<mid;k++,g=(ll)g*G[t][o]%P) { int x=q[j+k],y=(ll)g*q[j+k+mid]%P; q[j+k]=(x+y)%P; q[j+k+mid]=(x-y+P)%P; } } } int ksm(int x,int y) { int ans=1; while (y) { if (y & 1) ans=(ll)ans*x%P; x=(ll)x*x%P; y >>=1; } return ans; } void Pre() { G[0][23]=ksm(3,(P-1)/(1 << 23)); G[1][23]=inv(G[0][23]); for (int i=22;i>=1;i--) { G[0][i]=(ll)G[0][i+1]*G[0][i+1]%P; G[1][i]=(ll)G[1][i+1]*G[1][i+1]%P; } ten[1]=1; for (int i=2;i<=19;i++) ten[i]=ten[i-1]*10; } int main() { Pre(); s.read(),t.read(); write(s+t); if (s<t) putchar('-'),write(t-s); else write(s-t); write(s*t); write(s/t); write(s%t); return 0; }