A The Power Of Fobonacci
B Quadratic equation
参考代码：
#include<bits/stdc++.h> using namespace std; const int mod=1e9+7; typedef long long LL; #define int long long int quick_pow(int a,int b,int p=mod) { int ans=1; while(b) { if(b&1) ans=1LL*ans*a%mod; a=1LL*a*a%mod; b>>=1; } return ans; } namespace Cipolla{ LL w,P; struct E{ LL x,y; E(LL _x,LL _y):x(_x),y(_y){} friend E operator *(E a,E b){ return E((a.x*b.x%P+a.y*b.y%P*w)%P,(a.x*b.y%P+a.y*b.x%P)%P); } }; inline E Pow(E x,int y){ E ret=E(1,0); for(;y;y>>=1,x=x*x) if(y&1) ret=ret*x; return ret; } LL calc(LL x,LL p){ P=p; x%=P; if(x==0) return 0; LL tmp=quick_pow(x,(p-1)/2,p); if(tmp!=1) return -1; while(1){ tmp=rand()%p; LL cur=(tmp*tmp%P+P-x)%P; if(quick_pow(cur,(p-1)/2,p)==p-1) break; } w=(tmp*tmp%P+P-x)%P; E A=E(tmp,1); return Pow(A,(p+1)/2).x; } } int32_t main() { int t; scanf("%lld",&t); int b,c; int inv2=(mod+1)/2; while(t--) { scanf("%lld%lld",&b,&c); int delta=Cipolla::calc(b*b-4LL*c+mod,mod)%mod; if(delta==-1) puts("-1 -1"); else { int y=(1LL*(b+delta)*inv2%mod+mod)%mod; int x=(1LL*(b-delta)*inv2%mod+mod)%mod; if(x>y) swap(x,y); printf("%lld %lld\n",x,y); } } }
C Inversions of all permutations
D Knapsack Cryptosystem
#include<bits/stdc++.h> #define maxl 20 using namespace std; int n,m,tot,cnt; int dy[(1<<maxl)]; long long ss,ans; long long a[maxl],b[maxl]; long long suma[1<<maxl],sumb[1<<maxl]; struct node { long long num; long long val; bool operator < (const node &b)const { return val<b.val; } }c[1<<maxl]; inline void prework() { n=tot/2;m=tot-n; for(int i=n;i>=1;i--) scanf("%lld",&a[i]); for(int i=m;i>=1;i--) scanf("%lld",&b[i]); } inline bool cmp(const node &x,const node &y) { return x.val<y.val; } inline void mainwork() { if(ss==0) { ans=0; return; } suma[0]=0;sumb[0]=0; cnt=0; c[++cnt]=node{0,0}; int up=1<<n,t; for(int s=1;s<up;s++) { t=s-(s&-s); suma[s]=suma[t]+a[dy[s&-s]+1]; c[++cnt]=node{s,suma[s]}; } sort(c+1,c+1+cnt,cmp); up=1<<m;int id; for(int s=1;s<up;s++) { t=s-(s&-s); sumb[s]=sumb[t]+b[dy[s&-s]+1]; id=lower_bound(c+1,c+1+cnt,node{s,ss-sumb[s]})-c; if(id<=cnt && c[id].val==ss-sumb[s]) { ans=c[id].num*(1<<m)+s; break; } } } inline void print() { for(int i=tot-1;i>=0;i--) printf("%lld",((ans>>i)&1)); puts(""); } int main() { for(int i=0;i<=19;i++) dy[1<<i]=i; while(~scanf("%d%lld",&tot,&ss)) { prework(); mainwork(); print(); } return 0; }
E All men are brothers
#include<bits/stdc++.h> #define maxl 100010 using namespace std; int n,m,top; int f[maxl],tot,s[maxl]; __int128 t[maxl],one=1; __int128 sum[5]; inline void prework() { tot=n; for(int i=1;i<=n;i++) f[i]=i,t[i]=one; sum[1]=one*n; sum[2]=one*n*(n-1)/2; sum[3]=one*n*(n-1)*(n-2)/6; sum[4]=one*n*(n-1)*(n-2)*(n-3)/24; } inline void print(__int128 x) { top=0; if(x==0) s[++top]=0; while(x>0) { s[++top]=x%10; x/=10; } for(int i=top;i>=1;i--) printf("%d",s[i]); puts(""); } inline int find(int x) { if(f[x]!=x) f[x]=find(f[x]); return f[x]; } inline void mainwork() { print(sum[4]); int u,v,x,y; for(int i=1;i<=m;i++) { scanf("%d%d",&u,&v); x=find(u);y=find(v); if(x!=y) { tot--; if(tot>=4) { sum[1]-=t[x]+t[y]; sum[2]-=t[x]*sum[1]+t[y]*sum[1]+t[x]*t[y]; sum[3]-=t[x]*sum[2]+t[y]*sum[2]+t[x]*t[y]*sum[1]; sum[4]-=t[x]*sum[3]+t[y]*sum[3]+t[x]*t[y]*sum[2]; t[x]+=t[y];f[y]=x; sum[4]+=t[x]*sum[3]; sum[3]+=t[x]*sum[2]; sum[2]+=t[x]*sum[1]; sum[1]+=t[x]; } else sum[4]=0; } print(sum[4]); } } int main() { while(~scanf("%d%d",&n,&m)) { prework(); mainwork(); } return 0; }
F Birthday Reminders
G Checkers
H Cutting Bamboos
#include<bits/stdc++.h> using namespace std; typedef long long ll; #define eps 1e-8 const int maxn=1e5+10; const int maxm=2e5+10; int n,q,rt[maxn*40],tot; ll a[maxm],pre[maxm]; struct Node{ int ls,rs; ll sum,cnt; } tr[maxn*40]; inline void Insert(int y,int &x,int l,int r,int val) { tr[++tot]=tr[y];tr[tot].sum+=val;++tr[tot].cnt; x=tot; if(l==r) return ; int mid=l+r>>1; if(val<=mid) Insert(tr[y].ls,tr[x].ls,l,mid,val); else Insert(tr[y].rs,tr[x].rs,mid+1,r,val); } inline double Query(int x,int y,int l,int r,int L,int R,double val) { //cout<<"Q"<<endl; double res=0; if(l==L&&r==R) { res=(tr[y].sum-tr[x].sum)-(tr[y].cnt-tr[x].cnt)*val; return res; } int mid=l+r>>1; if(R<=mid) res=Query(tr[x].ls,tr[y].ls,l,mid,L,R,val); else if(L>mid) res=Query(tr[x].rs,tr[y].rs,mid+1,r,L,R,val); else { res+=Query(tr[x].ls,tr[y].ls,l,mid,L,mid,val); res+=Query(tr[x].rs,tr[y].rs,mid+1,r,mid+1,R,val); } return res; } int main() { scanf("%d%d",&n,&q); tot=0; for(int i=1;i<=n;++i) scanf("%lld",a+i),pre[i]=pre[i-1]+a[i]; tr[rt[0]].sum=tr[rt[0]].cnt=0;tr[rt[0]].ls=0;tr[rt[0]].ls=0; for(int i=1;i<=n;++i) Insert(rt[i-1],rt[i],1,maxn,a[i]); while(q--) { int l,r,x,y; scanf("%d%d%d%d",&l,&r,&x,&y); double L=0,R=1.0*maxn,mid,res; double ans=1.0*(pre[r]-pre[l-1])*x/y; while(R-L>eps) { //cout<<"erfen"<<endl; mid=(R+L)/2; int num=(int)mid; if(mid>1.0*num) ++num; res=Query(rt[l-1],rt[r],1,maxn,num,maxn,mid); if(res<ans) R=mid; else L=mid; } printf("%.8lf\n",L); } return 0; }
I KM and M
J Symmetrical Painting
#include<bits/stdc++.h> using namespace std; typedef long long LL; const int size=3e5+5; const int lens=1e6+5; int sum,tot; int L[size],R[size]; int idl[size],idr[size],idmid[size]; int cnt[lens][3]; int v[lens]; int main() { int n; scanf("%d",&n); int l,r; for(int i=1;i<=n;i++) { scanf("%d%d",&L[i],&R[i]); L[i]=L[i]*2; R[i]=R[i]*2; } sum=0; for(int i=1;i<=n;i++) { v[++sum]=L[i]; v[++sum]=R[i]; v[++sum]=(int)((1ll*L[i]+1ll*R[i])/2); } sort(v+1,v+1+sum); tot=unique(v+1,v+1+sum)-v-1; int sz=tot,d; for(int i=1;i<=n;i++) { idl[i]=lower_bound(v+1,v+1+tot,L[i])-v; idr[i]=lower_bound(v+1,v+1+tot,R[i])-v; d=(int)((1ll*L[i]+1ll*R[i])/2); idmid[i]=lower_bound(v+1,v+1+tot,d)-v; } for(int i=1;i<=n;i++) { cnt[idl[i]][0]++;cnt[idr[i]][1]++;cnt[idmid[i]][2]++; } LL ty0=cnt[1][0],ty1=cnt[1][1],ty2=cnt[1][2]; LL ans=0; LL tmp=ans; for(int i=2;i<=sz;i++) { LL r=v[i],l=v[i-1]; tmp=tmp+1LL*(r-l)*(ty0-2*ty2+ty1); ty0+=cnt[i][0],ty1+=cnt[i][1],ty2+=cnt[i][2]; // cout<<ty0<<' '<<ty1<<' '<<ty2<<endl; // cout<<tmp<<endl; ans=max(ans,tmp); } printf("%lld\n",ans); return 0; }