The 2019 China Collegiate Programming Contest Harbin Site
题解:
https://files.cnblogs.com/files/clrs97/HarbinEditorialV2.zip
Code:
A. Artful Paintings
/* let x=f[n] f[i-1]-f[i]<=0 i -> i-1 0 f[i]-f[i-1]<=1 i-1 -> i 1 f[l-1]-f[r]<=-k r -> l-1 -k f[r]-f[l-1]<=-k+x l-1 -> r -k+x f[n]-f[0]<=x 0 -> n x f[0]-f[n]<=-x n -> 0 -x for each cycle whose cost is A+Bx, we have A+Bx>=0 -> x>=(-A/B) so find a cycle with minimum average cost */ #include<cstdio> #include<vector> #include<algorithm> using namespace std; typedef pair<int,int>P; const int N=3010,M=3010,inf=1000000000; int Case,n,m1,m2,i,j,k,x,y,z,f[N][N],h[N],ans,nu,nd,tu,td,cnt[N<<1]; vector<P>g[N]; struct E{int u,v,w;}e[M]; inline void up(int&a,int b){a>b?(a=b):0;} inline void cal(int u,int d){ if(u>=0)return; u=-u; u=u/d+((u%d)>0); if(u>ans)ans=u; } inline void solve(){ int i,j,x,y,base; for(i=n;i>1;i--)up(h[i-1],h[i]); for(i=1;i<n;i++)up(h[i+1],h[i]+1); base=h[n]; //h[n] is stable now //h[i]=h[i+1] or h[i+1]-1 //h[n]-h[i] in [0..n] //h[n]-h[i]+i in [0..2n] for(i=1;i<=n;i++)cnt[base-h[i]+i]++; for(i=n;i;i--){ cnt[base-h[i]+i]--; if(i<n){ up(h[i],h[i+1]); if(cnt[base-h[i+1]+i+1])h[i]=h[i+1]-1; } for(j=0;j<g[i].size();j++){ x=g[i][j].first; y=h[i]+g[i][j].second; if(h[x]>y){ cnt[base-h[x]+x]--; h[x]=y; cnt[base-h[x]+x]++; } } } } int main(){ scanf("%d",&Case); while(Case--){ scanf("%d%d%d",&n,&m1,&m2);n++; for(i=1;i<=n;i++)g[i].clear(); while(m1--)scanf("%d%d%d",&x,&y,&z),g[y+1].push_back(P(x,-z)); for(i=1;i<=m2;i++){ scanf("%d%d%d",&x,&y,&z); e[i].u=x; e[i].v=y+1; e[i].w=-z; } e[++m2].u=1; e[m2].v=n; e[m2].w=0; ans=0; //case 1: not passed the edge n -> 0 -x for(i=0;i<=n;i++)for(j=1;j<=n;j++)f[i][j]=inf; f[0][1]=0; for(i=0;i<=n;i++){ for(j=1;j<=n;j++)h[j]=f[i][j]; solve(); for(j=1;j<=n;j++)f[i][j]=h[j]; if(i<n)for(j=1;j<=m2;j++)up(f[i+1][e[j].v],f[i][e[j].u]+e[j].w); } for(i=1;i<=n;i++){ nu=-inf,nd=1; for(j=0;j<n;j++){ tu=f[n][i]-f[j][i],td=n-j; if(1LL*nu*td<1LL*tu*nd)nu=tu,nd=td; } cal(nu,nd); } //case 2: passed the edge n -> 0 -x for(i=2;i<=n;i++)cal(f[i][n],i-1); printf("%d\n",ans); } }
B. Binary Numbers
/* lcp(a[i],l[i])>=lcp(a[i-1],l[i]) lcp(a[i],r[i])>=lcp(a[i+1],r[i]) f[i][lcp(a[i],l[i+1])][lcp(a[i],r[i])] */ #include<cstdio> const int N=131100,K=20,P=100000007; int Case,m,n,i,j,k,l[N],r[N],A,B,C,D,f[K][K],g[K][K]; inline int cal(int a,int b){ int ret=0; for(int i=m-1;~i;i--)if((a>>i&1)==(b>>i&1))ret++;else break; return ret; } inline void up(int&a,int b){a=a+b<P?a+b:a+b-P;} inline void clr(){for(j=0;j<=m;j++)for(k=0;k<=m;k++)g[j][k]=0;} inline void nxt(){ for(j=0;j<=m;j++)for(k=0;k<=m;k++){ f[j][k]=g[j][k]; if(j)up(f[j][k],f[j-1][k]); } for(j=0;j<=m;j++)for(k=m-1;~k;k--)up(f[j][k],f[j][k+1]); } int main(){ scanf("%d",&Case); while(Case--){ scanf("%d%d",&m,&n); for(i=1;i<=n;i++)scanf("%d%d",&l[i],&r[i]); clr(); g[0][m]=1; nxt(); for(i=1;i<=n;i++){ clr(); for(j=l[i];j<=r[i];j++){ A=cal(j,l[i]); B=cal(j,r[i]); C=i<n?cal(j,l[i+1]):0; D=i>1?cal(j,r[i-1]):0; g[C][B]=(1LL*f[A][D]*j+g[C][B])%P; } nxt(); } printf("%d\n",f[m][0]); } }
C. Competition in Swiss-system
#include<cstdio> typedef long long ll; const int N=10010,M=20; int Case,n,m,i,j,a[N],g[N][M],cg[N];bool v[N]; ll gcd(ll a,ll b){return b?gcd(b,a%b):a;} struct P{ ll u,d; P(){} P(ll _u,ll _d){u=_u,d=_d;} void operator+=(const P&b){ ll x=gcd(d,b.d); u=u*(b.d/x)+(d/x)*b.u; d=d/x*b.d; } P fix()const{ if(u*3<d)return P(1,3); return P(u,d); } void write(){ if(!u)printf("0/1"); else{ ll x=gcd(u,d); u/=x,d/=x; printf("%lld/%lld",u,d); } } }mw[N],gw[N]; inline void calomw(int x){ if(!cg[x]){ printf("1/3"); return; } P now(0,1); for(int i=0;i<cg[x];i++)now+=mw[g[x][i]].fix(); now.d*=cg[x]; now.write(); } inline void calogw(int x){ if(!cg[x]){ printf("1/3"); return; } P now(0,1); for(int i=0;i<cg[x];i++)now+=gw[g[x][i]].fix(); now.d*=cg[x]; now.write(); } int main(){ scanf("%d",&Case); while(Case--){ scanf("%d%d",&n,&m); for(i=1;i<=m;i++)scanf("%d",&a[i]); for(i=1;i<=n;i++){ mw[i]=P(0,0); gw[i]=P(0,0); } for(i=1;i<=n;i++)cg[i]=0; for(i=1;i<=m;i++){ printf("Round %d\n",i); for(j=1;j<=n;j++)v[j]=0; for(j=1;j<=a[i];j++){ int p1,p2,w1,w2,d; scanf("%d%d%d%d%d",&p1,&p2,&w1,&w2,&d); if(w1>w2)mw[p1].u+=3; else if(w1<w2)mw[p2].u+=3; else{ mw[p1].u++; mw[p2].u++; } mw[p1].d+=3; mw[p2].d+=3; gw[p1].u+=3*w1+d; gw[p2].u+=3*w2+d; gw[p1].d+=3*(w1+w2+d); gw[p2].d+=3*(w1+w2+d); g[p1][cg[p1]++]=p2; g[p2][cg[p2]++]=p1; v[p1]=v[p2]=1; } for(j=1;j<=n;j++)if(!v[j]){ mw[j].u+=3; mw[j].d+=3; gw[j].u+=6; gw[j].d+=6; } for(j=1;j<=n;j++){ printf("%lld ",mw[j].u); calomw(j); putchar(' '); gw[j].fix().write(); putchar(' '); calogw(j); puts(""); } } } }
D. Driverless Car
#include<cstdio> #include<algorithm> #include<cmath> using namespace std; typedef long double ld; const ld eps=1e-9; const int N=10000; inline int sgn(ld x){ if(x>eps)return 1; if(x<-eps)return -1; return 0; } struct P{ ld x,y; P(){x=y=0;} P(ld _x,ld _y){x=_x,y=_y;} P operator+(const P&b)const{return P(x+b.x,y+b.y);} P operator-(const P&b)const{return P(x-b.x,y-b.y);} void operator-=(const P&b){*this=*this-b;} P operator*(const ld&b)const{return P(x*b,y*b);} ld len()const{return hypot(x,y);} P rotate(ld c)const{return P(x*cos(c)-y*sin(c),x*sin(c)+y*cos(c));} P rot90()const{return P(-y,x);} P rot270()const{return P(y,-x);} void flip(){x=-x,y=-y;} void read(){ double _x,_y; scanf("%lf%lf",&_x,&_y); x=_x,y=_y; } }a[4],A,B,C,D,f[2][2]; ld ans; struct E{ P A,B;//A->B left hand E(){} E(const P&_A,const P&_B){A=_A,B=_B;} }e[N]; int cnt,tp[2];ld pool[N],v[N]; inline ld cross(const P&a,const P&b){return a.x*b.y-a.y*b.x;} inline int line_intersection(const P&a,const P&b,const P&p,const P&q,P&o,ld&t){ ld U=cross(p-a,q-p),D=cross(b-a,q-p); if(sgn(D)==0)return sgn(U)==0?2:0; o=a+(b-a)*(U/D); t=U/D; return 1; } inline void work(const P&A,const P&B,int S,int o){ if(S==0){ //closer to A e[++cnt]=E(A,A+((B-A).rot90())); f[o][0]=A; tp[o]=0; } if(S==1){ //closer to B e[++cnt]=E(B,B+((A-B).rot90())); f[o][0]=B; tp[o]=0; } if(S==2){ //the line e[++cnt]=E(A,A+((B-A).rot270())); e[++cnt]=E(B,B+((A-B).rot270())); f[o][0]=A; f[o][1]=B; tp[o]=1; } } inline bool check(const P&X){ for(int i=1;i<=cnt;i++)if(sgn(cross(X-e[i].A,e[i].B-e[i].A))>0)return 0; return 1; } inline void calline(const P&A,const P&B){ int i,m=0; for(i=1;i<=cnt;i++){ P o;ld t; int tmp=line_intersection(A,B,e[i].A,e[i].B,o,t); if(tmp==2)return; if(tmp==1)pool[++m]=t; } sort(pool+1,pool+m+1); ld ret=0; for(i=2;i<=m;i++)if(check(A+(B-A)*(pool[i]+pool[i-1])*0.5))ret+=pool[i]-pool[i-1]; ans+=ret*((B-A).len()); } inline ld mysqrt(ld x){ if(sgn(x)<=0)return 0; return sqrt(x); } inline bool getroot(ld A,ld B,ld C,ld&x,ld&y){ ld D=B*B-4*A*C; if(sgn(D)<0)return 0; D=mysqrt(D); x=(-B-D)/(A*2); y=(-B+D)/(A*2); return 1; } inline ld integrate(ld A,ld x){ return (mysqrt(A*x*x+1)*x+log(fabs(2*A*x+2*mysqrt(A*(A*x*x+1))))/mysqrt(A))/2; } inline void solve(){ if(tp[0]>tp[1]){ swap(tp[0],tp[1]); swap(f[0][0],f[1][0]); swap(f[0][1],f[1][1]); } P A=f[0][0],B=f[0][1],C=f[1][0],D=f[1][1]; if(tp[0]==0&&tp[1]==0){ //point A and point C P E=(A+C)*0.5; calline(((A-E).rot90())+E,E); }else if(tp[0]==1&&tp[1]==1){ //line AB and line CD P o; ld t; int res=line_intersection(A,B,C,D,o,t); if(res==0){ o=(A+C)*0.5; calline(o,o+D-C); }else{ if((A-o).len()<(B-o).len())swap(A,B); if((C-o).len()<(D-o).len())swap(C,D); ld w=(atan2(A.y-o.y,A.x-o.x)+atan2(C.y-o.y,C.x-o.x))*0.5; P E(cos(w),sin(w)); calline(o,o+E); calline(o,o+(E.rot90())); } }else{ //point A and line CD //x^2=py D=D-C; A=A-C; int i; for(i=1;i<=cnt;i++)e[i].A-=C,e[i].B-=C; ld w=atan2(D.y,D.x); A=A.rotate(-w); for(i=1;i<=cnt;i++)e[i].A=e[i].A.rotate(-w),e[i].B=e[i].B.rotate(-w); if(A.y<0){ A.flip(); for(i=1;i<=cnt;i++)e[i].A.flip(),e[i].B.flip(); } C=P(A.x,A.y*0.5); ld p=A.y*2; if(!sgn(p))return; int m=0; for(i=1;i<=cnt;i++){ e[i].A-=C,e[i].B-=C; ld dx=e[i].A.x-e[i].B.x; if(!sgn(dx)){ pool[++m]=e[i].A.x; continue; } //y=kx+b ld k=(e[i].A.y-e[i].B.y)/dx,b=e[i].A.y-k*e[i].A.x; //x^2-pkx-pb=0 ld x,y; if(getroot(1,-p*k,-p*b,x,y)){ pool[++m]=x; pool[++m]=y; } } sort(pool+1,pool+m+1); for(i=1;i<=m;i++){ v[i]=integrate(4/p/p,pool[i]); if(i>1){ ld x=(pool[i-1]+pool[i])*0.5; if(check(P(x,x*x/p)))ans+=v[i]-v[i-1]; } } } } int main(){ int Case,i,j,k; scanf("%d",&Case); while(Case--){ int xl,yl,xr,yr; scanf("%d%d%d%d",&xl,&yl,&xr,&yr); a[0]=P(xl,yl); a[1]=P(xr,yl); a[2]=P(xr,yr); a[3]=P(xl,yr); A.read(); B.read(); C.read(); D.read(); ans=0; for(i=0;i<3;i++)for(j=0;j<3;j++){ cnt=0; for(k=0;k<4;k++)e[++cnt]=E(a[k],a[(k+1)%4]); work(A,B,i,0); work(C,D,j,1); solve(); } printf("%.15f\n",(double)ans); } }
E. Exchanging Gifts
#include<cstdio> typedef long long ll; const int N=1000010; int Case,n,i,j,x,y,z,ans,type[N],a[N],b[N],st[N],en[N],pool[N],cnt;ll g[N],len[N]; struct Info{ int x;ll v; Info(){} Info(int _x,ll _v){x=_x,v=_v;} Info operator+(const Info&b)const{ if(x==b.x)return Info(x,v+b.v); if(v>b.v)return Info(x,v-b.v); return Info(b.x,b.v-v); } }f[N]; int main(){ scanf("%d",&Case); while(Case--){ scanf("%d",&n); cnt=0; for(i=1;i<=n;i++){ scanf("%d",&type[i]); if(type[i]==2)scanf("%d%d",&a[i],&b[i]); else{ scanf("%d",&x); st[i]=cnt+1; while(x--){ scanf("%d",&y); pool[++cnt]=y; } en[i]=cnt; } } for(i=1;i<=n;i++)if(type[i]==2){ f[i]=f[a[i]]+f[b[i]]; len[i]=len[a[i]]+len[b[i]]; }else{ x=y=0; len[i]=en[i]-st[i]+1; for(j=st[i];j<=en[i];j++){ z=pool[j]; if(!y)x=z,y++; else if(x==z)y++; else y--; } f[i]=Info(x,y); } ans=f[n].x; for(i=1;i<=n;i++)if(type[i]==2)g[i]=g[a[i]]+g[b[i]]; else{ x=0; for(j=st[i];j<=en[i];j++)if(pool[j]==ans)x++; g[i]=x; } ll t=g[n]*2-len[n]; if(t<0)t=0; t=len[n]-t; printf("%lld\n",t); } }
F. Fixing Banners
#include<cstdio> #include<cstring> #include<string> const int N=6; int Case,i,j,k,len,S,f[1<<N],g[1<<N];char b[2000010];std::string a="harbin"; int main(){ scanf("%d",&Case); while(Case--){ for(i=0;i<1<<N;i++)f[i]=0; f[0]=1; for(i=0;i<N;i++){ scanf("%s",b); len=strlen(b); S=0; for(j=0;j<len;j++)for(k=0;k<N;k++)if(b[j]==a[k])S|=1<<k; for(j=0;j<1<<N;j++)g[j]=0; for(j=0;j<1<<N;j++)for(k=0;k<N;k++)if(S>>k&1)g[j|(1<<k)]|=f[j]; for(j=0;j<1<<N;j++)f[j]=g[j]; } puts(f[(1<<N)-1]?"Yes":"No"); } }
G. Game Store
#include<cstdio> typedef long long ll; typedef unsigned long long ull; const int K=60; int n;ll x,y,ans,w[K];ull a[K][2];bool v[K]; inline void ins(ull x,ull y,ll z){ for(int i=0;i<K;i++)if((x>>i&1)||(y>>i&1)){ if(!v[i]){ v[i]=1; a[i][0]=x; a[i][1]=y; w[i]=z; ans+=z; return; } if(w[i]<z){ ull A=a[i][0],B=a[i][1];ll C=w[i]; a[i][0]=x; a[i][1]=y; w[i]=z; ans+=z-C; x=A; y=B; z=C; } ull C=a[i][0],D=a[i][1]; while((x>>i&1)||(y>>i&1)){ ull t=((x|y)&(C|D))^(y&D); x^=C^(y&D)^((y^D)&t); y^=D^t; } } } int main(){ scanf("%d",&n); while(n--){ ll x,y; scanf("%lld%lld",&x,&y);//1<=x<=1e18 1<=y<=1e9 x^=ans,y^=ans; ins(0,x,y); printf("%lld\n",ans); } }
H. Highway Buses
#include<cstdio> #include<algorithm> #include<queue> #include<vector> using namespace std; typedef long long ll; typedef pair<ll,int>P; const int N=200010,M=N*20,K=55; const ll inf=1LL<<60; int n,m,day,i,x,y,a[N],b[N],lim[N],cost[N],g[N],v[N<<1],nxt[N<<1],ok[N<<1],ed; int f[N],son[N],all,now; int _st[N],st[N],en[N],cur,q[M][2],vis[N]; int G[N],V[M],W[M],NXT[M],ED; priority_queue<P,vector<P>,greater<P> >Q; ll dis[N],fin[N]; int dsu[N]; inline void add(int x,int y){v[++ed]=y;nxt[ed]=g[x];g[x]=ed;ok[ed]=1;} inline void ADD(int x,int y,int z){V[++ED]=y;W[ED]=z;NXT[ED]=G[x];G[x]=ED;} void findroot(int x,int y){ son[x]=1;f[x]=0; for(int i=g[x];i;i=nxt[i])if(ok[i]&&v[i]!=y){ findroot(v[i],x); son[x]+=son[v[i]]; if(son[v[i]]>f[x])f[x]=son[v[i]]; } if(all-son[x]>f[x])f[x]=all-son[x]; if(f[x]<f[now])now=x; } inline void bfs(int S){ vis[S]=S; q[++cur][0]=S; q[cur][1]=0; int h=cur; while(h<=cur){ int x=q[h][0],y=q[h++][1]+1; for(int i=g[x];i;i=nxt[i])if(ok[i]&&vis[v[i]]!=S){ vis[v[i]]=S; q[++cur][0]=v[i]; q[cur][1]=y; } } } void solve(int x){ st[x]=cur+1; bfs(x); en[x]=cur; for(int i=st[x];i<=cur;i++)ADD(q[i][0],x,q[i][1]); for(int i=g[x];i;i=nxt[i])if(ok[i]){ ok[i^1]=0; f[0]=all=son[v[i]]; findroot(v[i],now=0); solve(now); } } inline void extend(int x,ll y){ if(vis[x])return; vis[x]=1; dis[x]=y; Q.push(P(y+cost[x],x)); } inline void go(int x,int lim,ll y){ int&h=st[x],t=en[x]; while(h<=t){ if(q[h][1]>lim)break; extend(q[h++][0],y); } } int DSU(int x){return dsu[x]==x?x:dsu[x]=DSU(dsu[x]);} namespace VIP{ bool is[N],vis[N]; int pool[K],cp,q[K][N],d[K][N],st[K]; int i,j,k,h,t,x,y,g[N],v[(N+K)<<1],nxt[(N+K)<<1],ed; inline void add(int x,int y){v[++ed]=y;nxt[ed]=g[x];g[x]=ed;} inline void set(int x){ if(is[x])return; is[x]=1; pool[cp++]=x; } inline void ext(int x){ if(vis[x])return; vis[x]=1; q[i][++t]=x; d[i][x]=y; } inline void init(){ for(i=0;i<cp;i++){ for(j=1;j<=n;j++)vis[j]=0; y=0; h=1,t=0; ext(pool[i]); while(h<=t){ x=q[i][h++]; y=d[i][x]+1; for(k=g[x];k;k=nxt[k])ext(v[k]); } } } inline void go(int x,ll y,int lim){ int&h=st[x]; while(h<=n){ if(d[x][q[x][h]]>lim)break; extend(q[x][h++],y); } } } inline void work(int day){ for(i=1;i<=n;i++){ vis[i]=0; st[i]=_st[i]; cost[i]=a[i]+1LL*b[i]*(day-1); } for(i=0;i<VIP::cp;i++)VIP::st[i]=1; extend(1,0); while(!Q.empty()){ P t=Q.top();Q.pop(); for(i=G[t.second];i;i=NXT[i])go(V[i],lim[t.second]-W[i],t.first); for(i=0;i<VIP::cp;i++)VIP::go(i,t.first,lim[t.second]-VIP::d[i][t.second]); } for(i=1;i<=n;i++)fin[i]=min(fin[i],dis[i]); } int main(){ scanf("%d%d%d",&n,&m,&day); for(i=1;i<=n;i++)scanf("%d%d%d",&lim[i],&a[i],&b[i]); for(i=1;i<=n;i++)dsu[i]=i; ed=1; while(m--){ scanf("%d%d",&x,&y); VIP::add(x,y); VIP::add(y,x); if(DSU(x)==DSU(y)){ VIP::set(x); }else{ dsu[dsu[x]]=dsu[y]; add(x,y); add(y,x); } } f[0]=all=n;findroot(1,now=0);solve(now); VIP::init(); for(i=1;i<=n;i++)fin[i]=inf,_st[i]=st[i]; work(1); work(day); for(i=1;i<=n;i++)printf("%lld\n",fin[i]); }
I. Interesting Permutation
#include<cstdio> const int P=1000000007; int Case,n,i,a[100010]; inline int solve(){ scanf("%d",&n); for(i=1;i<=n;i++)scanf("%d",&a[i]); if(a[1])return 0; int gap=a[1],slot=0,ans=1; for(i=2;i<=n;i++){ if(a[i]<gap)return 0; if(a[i]>=n)return 0; if(a[i]==gap){ if(!slot)return 0; ans=1LL*ans*slot%P; slot--; }else{ ans=2LL*ans%P; slot+=a[i]-gap-1; gap=a[i]; } } return ans; } int main(){ scanf("%d",&Case); while(Case--)printf("%d\n",solve()); }
J. Justifying the Conjecture
#include<cstdio> int Case,n; int main(){ scanf("%d",&Case); while(Case--){ scanf("%d",&n); if(n<=5){ puts("-1"); continue; } if(n&1)printf("3 %d\n",n-3); else printf("2 %d\n",n-2); } }
K. Keeping Rabbits
#include<cstdio> #include<cstdlib> using namespace std; int Case,n,k,i;double a[100010],s; int main(){ scanf("%d",&Case); while(Case--){ scanf("%d%d",&n,&k); s=0; for(i=1;i<=n;i++)scanf("%lf",&a[i]),s+=a[i]; for(i=1;i<=n;i++)printf("%.15f%c",a[i]+a[i]*k/s,i<n?' ':'\n'); } }
L. LRU Algorithm
#include<cstdio> typedef unsigned long long ull; const int N=5010,M=200010; int Case,n,q,m,i,j,a[N],b[N],len[M],ans[M];ull goal[M],f[N]; inline void cal(int n){for(int i=1;i<=n;i++)f[i]=f[i-1]*13331+b[i]+19260817;} inline void ext(int x){ int i; for(i=1;i<=n;i++)if(b[i]==x)break; for(;i<n;i++)b[i]=b[i+1]; for(i=n;i>1;i--)b[i]=b[i-1]; b[1]=x; } int main(){ scanf("%d",&Case); while(Case--){ scanf("%d%d",&n,&q); for(i=1;i<=n;i++)scanf("%d",&a[i]); for(i=1;i<=q;i++){ scanf("%d",&m); len[i]=m; for(j=1;j<=m;j++)scanf("%d",&b[j]); cal(m); goal[i]=f[m]; ans[i]=0; } for(i=1;i<=n;i++)b[i]=0; for(i=0;i<=n;i++){ if(i)ext(a[i]); cal(n); for(j=1;j<=q;j++)if(f[len[j]]==goal[j])ans[j]=1; } for(i=1;i<=q;i++)puts(ans[i]?"Yes":"No"); } }