T1 导弹袭击
每个型号看成点 ((frac{1}{a_i},frac{1}{b_i}))，维护下凸壳。
#include<bits/stdc++.h> #define ld long double using namespace std; const int N=310000; int q[N],n,fry,frx,top,nxt[N]; ld k[N]; bool ans[N]; struct dian { int id,x,y; // bool operator<(const dian & a)const{ // return x>a.x||(x==a.x&&y>a.y); // } }d[N]; bool operator <(const dian &a,const dian &b) { return a.x>b.x||(a.x==b.x&&a.y>b.y); } ld K(dian i,dian j) { return (ld)i.x*j.x*(j.y-i.y)/((ld)i.y*j.y*(j.x-i.x)); } int main() { scanf("%d",&n); for(int i=1;i<=n;i++) { d[i].id=i; scanf("%d%d",&d[i].x,&d[i].y); if(fry<d[i].y||(d[i].y==fry&&frx<d[i].x)) { fry=d[i].y; frx=d[i].x; } } // sort(d+1,d+1+n,cmp); sort(d+1,d+1+n); q[++top]=1; for(int i=2;i<=n&&frx<=d[i].x;i++) { if(d[q[top]].x==d[i].x) { if(d[q[top]].y==d[i].y) { nxt[d[i].id]=nxt[d[q[top]].id]; nxt[d[q[top]].id]=d[i].id; } continue; } while(top>1&&k[top]>K(d[q[top]],d[i])) top--; q[++top]=i; k[top]=K(d[q[top-1]],d[i]); } for(;top;top--) { for(int i=d[q[top]].id;i;i=nxt[i]) ans[i]=1; } for(int i=1;i<=n;i++) if(ans[i]) printf("%d ",i); printf(" "); return 0; }
T2 炼金术士的疑惑
高斯消元裸题，读入略烦。
#include<bits/stdc++.h> using namespace std; const int N=210; const long double x=0.000001; inline int read() { int s=0,w=1;char ch=getchar(); while(!isdigit(ch)){if(ch=='-')w=-1;ch=getchar();} while(isdigit(ch)){s=s*10+ch-'0';ch=getchar();} return s*w; } inline long double _fabs(long double x) { if(x<0) return -x; else return x; } int n,m; char opt[10]; long double a[N][N],d[N],num; bool vis[N]; map<string,int> hah; string s; int main() { n=read(); int w; for(int i=1;i<=n+1;i++) { w=1; for(int j=1;j<=200;j++) { cin>>num>>s;num*=w; if(hah.find(s)==hah.end()) { hah[s]=++m; } a[i][hah[s]]=num; scanf("%s",opt+1); if(opt[1]=='=') { w=-1; } else if(opt[1]=='H') { if(i<=n) { scanf("%Lf",&d[i]); } break; } } } for(int i=1;i<=n;i++) a[i][m+1]=d[i]; for(int i=1;i<=n;i++) { int maxx=i; for(int j=i+1;j<=n;j++) { if(_fabs(a[j][i])>_fabs(a[maxx][i])) maxx=j; } if(maxx!=i) for(int j=1;j<=m+1;j++) { swap(a[i][j],a[maxx][j]); } if(_fabs(a[i][i])<1e-8) continue; long double chu=a[i][i]; for(int j=i;j<=m+1;j++) a[i][j]/=chu; for(int j=1;j<=n+1;j++) { if(j==i) continue; long double chu=a[j][i]; for(int k=i;k<=m+1;k++) { a[j][k]-=a[i][k]*chu; } } } if(a[n+1][m+1]-x<0&&a[n+1][m+1]+x>0) printf("0.0 "); else printf("%.1Lf ",-a[n+1][m+1]); return 0; } /* 2 1 C + 1 O2 = 1 CO2 H= -393.5 1 CO + 0.5 O2 = 1 CO2 H= -283.0 2 C + 1 O2 = 2 CO H= ? */
T3
老司机的狂欢。
二分答案做第一问。
#include<bits/stdc++.h> #define int long long #define lowbit(x) (x&(-x)) using namespace std; const int N=110000; int n,k,l,r,mid,goa[N],ygoa[N],minn[N][23],ans,b[N],tot,sta[N],fa[N][23],tp; double tree[N]; bool flag; inline int _max(int a,int b) { return a>b?a:b; } void plu(int cur,int v) { while(cur<=n) { tree[cur]=_max(tree[cur],v); cur+=lowbit(cur); } return; } int find(int cur) { int res=0; while(cur>0) { res=_max(res,tree[cur]); cur-=lowbit(cur); } return res; } struct peopl { int x,a,id; }p[N]; inline int read() { int s=0,w=1;char ch=getchar(); while(!isdigit(ch)){if(ch=='-')w=-1;ch=getchar();} while(isdigit(ch)){s=s*10+ch-'0';ch=getchar();} return s*w; } bool cmp(const peopl &a,peopl &b) { return a.x<b.x; } bool check(int x) { memset(tree,0,sizeof(tree)); for(int i=n;i>=1;i--) { ygoa[i]=goa[i]=2.0*p[i].x+1.0*p[i].a*x*x; } sort(goa+1,goa+1+n); for(int i=1;i<=n;i++) { ygoa[i]=lower_bound(goa+1,goa+1+n,ygoa[i]) - goa; plu(ygoa[i],find(ygoa[i]-1)+1); } if(find(n)>=k) { if(find(n)>k) { flag=1; } else flag=0; return 1; } return 0; } struct node { int dis,id; }c[N]; bool operator < (const node &aa,const node &bb){ if(aa.dis!=bb.dis)return aa.dis<bb.dis; int xx=aa.id; int yy=bb.id; int mina=aa.id,minb=bb.id; for(int i=20;i>=0;i--){ if(fa[xx][i]!=fa[yy][i]){ mina=min(mina,minn[xx][i]); minb=min(minb,minn[yy][i]); xx=fa[xx][i]; yy=fa[yy][i]; } } return mina>minb; } node ask(int x){ node anss=node{0,0}; for(;x;x-=x&-x)anss=max(anss,c[x]); return anss; } void add(int x,node w){ for(;x<=tot;x+=x&-x) c[x]=max(c[x],w); return ; } void slove(int x) { for(int i=n;i>=1;i--) { b[i]=ygoa[i]=goa[i]=2.0*p[i].x+1.0*p[i].a*x*x; } sort(goa+1,goa+1+n); tot=unique(goa+1,goa+1+n)- goa -1; for(int i=1;i<=n;i++) { b[i]=lower_bound(goa+1,goa+1+tot,b[i]) -goa; } for(int i=1;i<=n;i++) { node x=ask(b[i]-1); fa[p[i].id][0]=minn[p[i].id][0]=x.id; for(int j=1;j<=20;j++){ fa[p[i].id][j]=fa[fa[p[i].id][j-1]][j-1]; minn[p[i].id][j]=min(minn[fa[p[i].id][j-1]][j-1],minn[p[i].id][j-1]); } node y=node{x.dis+1,p[i].id}; add(b[i],y); } int ss=ask(n).id; while(ss){ sta[++tp]=ss; ss=fa[ss][0]; } sort(sta+1,sta+tp+1); for(int i=1;i<=tp;i++){ printf("%lld ",sta[i]); } return ; } signed main() { // freopen("driver4.in","r",stdin); n=read();k=read(); for(int i=1;i<=n;i++) { p[i].x=read(); p[i].a=read(); p[i].id=i; } l=0;r=86400; sort(p+1,p+1+n,cmp); flag=1; while(l<=r) { mid=(l+r)>>1; if(check(mid)) { l=mid+1; ans=mid; } else { r=mid-1; } } printf("%lld ",ans); if(flag) puts("-1"); else slove(ans); return 0; }