The 20th Zhejiang Provincial Collegiate Programming Contest Sponsored by TuSimple
題解：
https://files.cnblogs.com/files/clrs97/2023_ZJCPC_Tutorial.pdf
Code：
A. Look and Say
#include<bits/stdc++.h>
using namespace std;
int main()
{
ios_base::sync_with_stdio(false);
int n;
cin>>n;
string s;
cin>>s;
char pre=' ';
int cnt=0;
for(auto ch:s)
{
if(ch==pre)cnt++;
else
{
if(cnt)cout<<cnt<<pre;
pre=ch;cnt=1;
}
}
cout<<cnt<<pre;
return 0;
}
B. Master of Polygon
#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=200005,M=200005,K=17,inf=~0U>>1;
int n,m,cq,i,xl,xr;
bool ans[M];
int idseg[K][N],idque[K][M];
struct P{
int x,y;
P(){}
P(int _x,int _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);}
ll operator*(const P&b)const{return 1LL*x*b.x+1LL*y*b.y;}
bool operator==(const P&b)const{return x==b.x&&y==b.y;}
void read(){scanf("%d%d",&x,&y);}
}a[N];
struct Line{
P a,b;
int xl,xr;
int sx,sy,dx,dy;
ll base;
void fix(){
if(a.x>b.x)swap(a,b);
xl=a.x,xr=b.x;
sx=a.x,sy=a.y,dx=b.x-a.x,dy=b.y-a.y;
base=1LL*sy*dx-1LL*sx*dy;
}
}seg[N],que[M];
struct Frac{
ll u,d;
Frac(){}
Frac(ll _u,ll _d){
u=_u,d=_d;
if(d<0)u*=-1,d*=-1;
}
bool operator<(const Frac&b)const{return u*b.d<b.u*d;}
bool operator>(const Frac&b)const{return u*b.d>b.u*d;}
bool operator<=(const Frac&b)const{return u*b.d<=b.u*d;}
bool operator>=(const Frac&b)const{return u*b.d>=b.u*d;}
}slo[M];
inline int sgn(ll x){
if(x>0)return 1;
return x?-1:0;
}
inline ll cross(const P&a,const P&b){return 1LL*a.x*b.y-1LL*a.y*b.x;}
inline void umin(int&a,int b){a>b?(a=b):0;}
inline void umax(int&a,int b){a<b?(a=b):0;}
inline Frac gety(const Line&a,int x){
if(a.dx==0)return Frac(a.sy,1);
return Frac(a.base+1LL*x*a.dy,a.dx);
}
inline bool point_on_segment(const P&p,const P&a,const P&b){
return cross(b-a,p-a)==0&&(p-a)*(p-b)<=0;
}
inline bool has_intersection(const Line&A,const Line&B){
if(!A.dx&&!A.dy)return point_on_segment(A.a,B.a,B.b);
const P&a=A.a;
const P&b=A.b;
const P&p=B.a;
const P&q=B.b;
int d1=sgn(cross(b-a,p-a)),d2=sgn(cross(b-a,q-a));
int d3=sgn(cross(q-p,a-p)),d4=sgn(cross(q-p,b-p));
if(d1*d2<0&&d3*d4<0)return 1;
if((d1==0&&point_on_segment(p,a,b))||
(d2==0&&point_on_segment(q,a,b))||
(d3==0&&point_on_segment(a,p,q))||
(d4==0&&point_on_segment(b,p,q)))return 1;
return 0;
}
namespace CaseWholeSeg{
int cnt,q[N];
inline void init(){cnt=0;}
inline void add(int x){q[++cnt]=x;}
inline bool cmpseg(int A,int B){
const Line&p=seg[A];
const Line&q=seg[B];
int x=p.a==q.a?min(p.xr,q.xr):max(p.xl,q.xl);
return gety(p,x)<gety(q,x);
}
inline void work(){sort(q+1,q+cnt+1,cmpseg);}
inline bool ask(const Line&p){
int l=1,r=cnt,mid;
while(l<=r){
mid=(l+r)>>1;
const Line&o=seg[q[mid]];
if(has_intersection(p,o))return 1;
int x=max(p.xl,o.xl);
if(gety(p,x)<gety(o,x))r=mid-1;else l=mid+1;
}
return 0;
}
}
namespace CaseWholeQue{
int xl,xr;
int cs,idseg[N];
int cq,idque[M];
Frac yl[M],yr[M];
int cnt,cp,cl,cr,idl[N],idr[N];
P pool[N*2];
int ccur,chull;
struct Component{
int st,en;
bool isl,isr;
Frac lmi,lma,rmi,rma;
void upl(const Frac&b){
if(!isl){
isl=1;
lmi=lma=b;
return;
}
if(lmi>b)lmi=b;
if(lma<b)lma=b;
}
void upr(const Frac&b){
if(!isr){
isr=1;
rmi=rma=b;
return;
}
if(rmi>b)rmi=b;
if(rma<b)rma=b;
}
}com[N];
struct Point{
int x;Frac y;
Point(){}
Point(const P&b){x=b.x,y=Frac(b.y,1);}
Point(int _x,const Frac&_y){x=_x,y=_y;}
}cur[N*2],hull[N*2];
inline bool cmpx(const P&a,const P&b){return a.x<b.x;}
inline void init(int _xl,int _xr){xl=_xl,xr=_xr;cs=cq=0;}
inline void addseg(int x){idseg[++cs]=x;}
inline void addque(int x){
idque[++cq]=x;
yl[x]=gety(que[x],xl);
yr[x]=gety(que[x],xr);
}
inline Frac slope(const Point&a,const Point&b){//a.x<b.x
return Frac(b.y.u*a.y.d-a.y.u*b.y.d,(b.x-a.x)*a.y.d*b.y.d);
}
namespace CaseLeft{
inline bool cmpyl(int x,int y){return yl[x]<yl[y];}
inline bool cmplma(int x,int y){return com[x].lma<com[y].lma;}
inline bool cmplmi(int x,int y){return com[x].lmi>com[y].lmi;}
inline void ext_down(int&n,Point*q,const Point&p){
if(n&&q[n].x==p.x){
if(q[n].y>=p.y)return;
n--;
}
while(n>1&&slope(p,q[n])<=slope(q[n],q[n-1]))n--;
q[++n]=p;
}
inline bool notin_down(const Point&p){
if(chull<=1)return 1;
if(p.x>hull[1].x)return 1;
int l=2,r=chull-1,t=1;
while(l<=r){
int mid=(l+r)>>1;
if(p.x==hull[mid].x)return p.y>=hull[mid].y;
if(p.x>hull[mid].x)r=mid-1;else l=(t=mid)+1;
}
return slope(hull[t+1],p)>=slope(p,hull[t]);
}
inline void ext_up(int&n,Point*q,const Point&p){
if(n&&q[n].x==p.x){
if(q[n].y<=p.y)return;
n--;
}
while(n>1&&slope(p,q[n])>=slope(q[n],q[n-1]))n--;
q[++n]=p;
}
inline bool notin_up(const Point&p){
if(chull<=1)return 1;
if(p.x>hull[1].x)return 1;
int l=2,r=chull-1,t=1;
while(l<=r){
int mid=(l+r)>>1;
if(p.x==hull[mid].x)return p.y<=hull[mid].y;
if(p.x>hull[mid].x)r=mid-1;else l=(t=mid)+1;
}
return slope(hull[t+1],p)<=slope(p,hull[t]);
}
inline void solve(){
if(!cl)return;
int i,j,k,A,B;
sort(idque+1,idque+cq+1,cmpyl);
sort(idl+1,idl+cl+1,cmplma);
//left
Frac minl;
for(i=cq,j=cl;i;i--){
A=idque[i];
if(ans[A])continue;
while(j){
B=idl[j];
if(com[B].lma<yl[A])break;
if(j==cl)minl=com[B].lmi;
else if(minl>com[B].lmi)minl=com[B].lmi;
j--;
}
if(j<cl&&minl<=yl[A])ans[A]=1;
}
//down
chull=0;
for(i=j=1;i<=cq;i++){
A=idque[i];
if(ans[A])continue;
while(j<=cl){
B=idl[j];
if(com[B].lma>=yl[A])break;
ccur=0;
if(com[B].isr)ext_down(ccur,cur,Point(xr,com[B].rma));
for(k=com[B].en;k>=com[B].st;k--)ext_down(ccur,cur,pool[k]);
ext_down(ccur,cur,Point(xl,com[B].lma));
if(com[B].isr){
chull=ccur;
for(k=1;k<=ccur;k++)hull[k]=cur[k];
}else{
k=ccur;
while(k>1&¬in_down(cur[k-1]))k--;
while(chull&&hull[chull].x<=cur[k].x)chull--;
for(;k<=ccur;k++)ext_down(chull,hull,cur[k]);
}
j++;
}
if(chull<=1)continue;
int l=1,r=chull-1;
if(hull[1].x==xr){
if(hull[1].y>=yr[A]){
ans[A]=1;
continue;
}
if(chull==2)continue;
l++;
}
int t=r--;
const Frac&v=slo[A];
//min slope(hull[t+1],hull[t]) >= v
while(l<=r){
int mid=(l+r)>>1;
if(slope(hull[mid+1],hull[mid])>=v)r=(t=mid)-1;else l=mid+1;
}
if(slope(que[A].a,hull[t])>=slope(hull[t],que[A].b))ans[A]=1;
}
//up
sort(idl+1,idl+cl+1,cmplmi);
chull=0;
for(i=cq,j=1;i;i--){
A=idque[i];
if(ans[A])continue;
while(j<=cl){
B=idl[j];
if(com[B].lmi<=yl[A])break;
ccur=0;
if(com[B].isr)ext_up(ccur,cur,Point(xr,com[B].rmi));
for(k=com[B].en;k>=com[B].st;k--)ext_up(ccur,cur,pool[k]);
ext_up(ccur,cur,Point(xl,com[B].lmi));
if(com[B].isr){
chull=ccur;
for(k=1;k<=ccur;k++)hull[k]=cur[k];
}else{
k=ccur;
while(k>1&¬in_up(cur[k-1]))k--;
while(chull&&hull[chull].x<=cur[k].x)chull--;
for(;k<=ccur;k++)ext_up(chull,hull,cur[k]);
}
j++;
}
if(chull<=1)continue;
int l=1,r=chull-1;
if(hull[1].x==xr){
if(hull[1].y<=yr[A]){
ans[A]=1;
continue;
}
if(chull==2)continue;
l++;
}
int t=r--;
const Frac&v=slo[A];
while(l<=r){
int mid=(l+r)>>1;
if(slope(hull[mid+1],hull[mid])<=v)r=(t=mid)-1;else l=mid+1;
}
if(slope(que[A].a,hull[t])<=slope(hull[t],que[A].b))ans[A]=1;
}
}
}
namespace CaseRight{
inline bool cmpyr(int x,int y){return yr[x]<yr[y];}
inline bool cmprma(int x,int y){return com[x].rma<com[y].rma;}
inline bool cmprmi(int x,int y){return com[x].rmi>com[y].rmi;}
inline void ext_down(int&n,Point*q,const Point&p){
if(n&&q[n].x==p.x){
if(q[n].y>=p.y)return;
n--;
}
while(n>1&&slope(q[n],p)>=slope(q[n-1],q[n]))n--;
q[++n]=p;
}
inline bool notin_down(const Point&p){
if(chull<=1)return 1;
if(p.x<hull[1].x)return 1;
int l=2,r=chull-1,t=1;
while(l<=r){
int mid=(l+r)>>1;
if(p.x==hull[mid].x)return p.y>=hull[mid].y;
if(p.x<hull[mid].x)r=mid-1;else l=(t=mid)+1;
}
return slope(hull[t],p)>=slope(p,hull[t+1]);
}
inline void ext_up(int&n,Point*q,const Point&p){
if(n&&q[n].x==p.x){
if(q[n].y<=p.y)return;
n--;
}
while(n>1&&slope(q[n],p)<=slope(q[n-1],q[n]))n--;
q[++n]=p;
}
inline bool notin_up(const Point&p){
if(chull<=1)return 1;
if(p.x<hull[1].x)return 1;
int l=2,r=chull-1,t=1;
while(l<=r){
int mid=(l+r)>>1;
if(p.x==hull[mid].x)return p.y<=hull[mid].y;
if(p.x<hull[mid].x)r=mid-1;else l=(t=mid)+1;
}
return slope(hull[t],p)<=slope(p,hull[t+1]);
}
inline void solve(){
if(!cr)return;
int i,j,k,A,B;
sort(idque+1,idque+cq+1,cmpyr);
sort(idr+1,idr+cr+1,cmprma);
//right
Frac minl;
for(i=cq,j=cr;i;i--){
A=idque[i];
if(ans[A])continue;
while(j){
B=idr[j];
if(com[B].rma<yr[A])break;
if(j==cr)minl=com[B].rmi;
else if(minl>com[B].rmi)minl=com[B].rmi;
j--;
}
if(j<cr&&minl<=yr[A])ans[A]=1;
}
//down
chull=0;
for(i=j=1;i<=cq;i++){
A=idque[i];
if(ans[A])continue;
while(j<=cr){
B=idr[j];
if(com[B].rma>=yr[A])break;
ccur=0;
if(com[B].isl)ext_down(ccur,cur,Point(xl,com[B].lma));
for(k=com[B].st;k<=com[B].en;k++)ext_down(ccur,cur,pool[k]);
ext_down(ccur,cur,Point(xr,com[B].rma));
if(com[B].isl){
chull=ccur;
for(k=1;k<=ccur;k++)hull[k]=cur[k];
}else{
k=ccur;
while(k>1&¬in_down(cur[k-1]))k--;
while(chull&&hull[chull].x>=cur[k].x)chull--;
for(;k<=ccur;k++)ext_down(chull,hull,cur[k]);
}
j++;
}
if(chull<=1)continue;
int l=1,r=chull-1;
if(hull[1].x==xl){
if(hull[1].y>=yl[A]){
ans[A]=1;
continue;
}
if(chull==2)continue;
l++;
}
int t=r--;
const Frac&v=slo[A];
//min slope(hull[t],hull[t+1]) <= v
while(l<=r){
int mid=(l+r)>>1;
if(slope(hull[mid],hull[mid+1])<=v)r=(t=mid)-1;else l=mid+1;
}
if(slope(que[A].a,hull[t])>=slope(hull[t],que[A].b))ans[A]=1;
}
//up
sort(idr+1,idr+cr+1,cmprmi);
chull=0;
for(i=cq,j=1;i;i--){
A=idque[i];
if(ans[A])continue;
while(j<=cr){
B=idr[j];
if(com[B].rmi<=yr[A])break;
ccur=0;
if(com[B].isl)ext_up(ccur,cur,Point(xl,com[B].lmi));
for(k=com[B].st;k<=com[B].en;k++)ext_up(ccur,cur,pool[k]);
ext_up(ccur,cur,Point(xr,com[B].rmi));
if(com[B].isl){
chull=ccur;
for(k=1;k<=ccur;k++)hull[k]=cur[k];
}else{
k=ccur;
while(k>1&¬in_up(cur[k-1]))k--;
while(chull&&hull[chull].x>=cur[k].x)chull--;
for(;k<=ccur;k++)ext_up(chull,hull,cur[k]);
}
j++;
}
if(chull<=1)continue;
int l=1,r=chull-1;
if(hull[1].x==xl){
if(hull[1].y<=yl[A]){
ans[A]=1;
continue;
}
if(chull==2)continue;
l++;
}
int t=r--;
const Frac&v=slo[A];
//min slope(hull[t],hull[t+1]) >= v
while(l<=r){
int mid=(l+r)>>1;
if(slope(hull[mid],hull[mid+1])>=v)r=(t=mid)-1;else l=mid+1;
}
if(slope(que[A].a,hull[t])<=slope(hull[t],que[A].b))ans[A]=1;
}
}
}
inline void work(){
if(!cs||!cq)return;
int i,j,k,x;
static int q[N];
static bool vis[N],is[N];
for(i=1;i<=cs;i++){
x=idseg[i];
is[x]=1;
vis[x]=0;
}
cnt=cp=cl=cr=0;
for(i=1;i<=cs;i++){
x=idseg[i];
if(vis[x])continue;
cnt++;
com[cnt].st=cp+1;
com[cnt].isl=com[cnt].isr=0;
vis[x]=1;
int head=1,tail=1;
q[1]=x;
while(head<=tail){
x=q[head++];
const Line&p=seg[x];
if(p.xl>xl&&p.xr<xr){
pool[++cp]=p.a;
pool[++cp]=p.b;
}else if(p.xr<xr){
if(p.xl==p.xr){
com[cnt].upl(Frac(p.a.y,1));
com[cnt].upl(Frac(p.b.y,1));
}else{
pool[++cp]=p.b;
com[cnt].upl(gety(p,xl));
}
}else{
if(p.xl==p.xr){
com[cnt].upr(Frac(p.a.y,1));
com[cnt].upr(Frac(p.b.y,1));
}else{
pool[++cp]=p.a;
com[cnt].upr(gety(p,xr));
}
}
for(j=x-1;j<=x+1;j+=2){
k=j;
if(k<0)k+=n;
if(k>=n)k-=n;
if(!is[k]||vis[k])continue;
const P&v=j<x?a[x]:a[x+1];
if(v.x<xl||v.x>xr)continue;
vis[k]=1;
q[++tail]=k;
}
}
com[cnt].en=cp;
if(com[cnt].isl)idl[++cl]=cnt;
if(com[cnt].isr)idr[++cr]=cnt;
sort(pool+com[cnt].st,pool+cp+1,cmpx);
}
for(i=1;i<=cs;i++)is[idseg[i]]=0;
CaseLeft::solve();
CaseRight::solve();
}
}
void solve(int o,int l,int r,int cs,int cq){
if(l>=r||!cs||!cq)return;
//Case 1: whole seg
CaseWholeSeg::init();
CaseWholeQue::init(l,r);
for(int i=0;i<cs;i++){
int id=idseg[o][i];
int a=seg[id].xl,b=seg[id].xr;
if(a<=l&&b>=r)CaseWholeSeg::add(id);
else CaseWholeQue::addseg(id);
}
CaseWholeSeg::work();
for(int i=0;i<cq;i++){
int id=idque[o][i];
int a=que[id].xl,b=que[id].xr;
if(CaseWholeSeg::ask(que[id]))ans[id]=1;
else if(a<=l&&b>=r)CaseWholeQue::addque(id);
}
//Case 2: whole query, partial seg
CaseWholeQue::work();
if(l+1==r)return;
int mid=(l+r)>>1;
for(int _=0;_<2;_++){
int _l,_r,_cs=0,_cq=0;
if(_==0)_l=l,_r=mid;else _l=mid,_r=r;
for(int i=0;i<cs;i++){
int id=idseg[o][i];
int a=seg[id].xl,b=seg[id].xr;
if(a<=l&&b>=r)continue;
if(a>_r||b<_l)continue;
idseg[o+1][_cs++]=id;
}
for(int i=0;i<cq;i++){
int id=idque[o][i];
if(ans[id])continue;
int a=que[id].xl,b=que[id].xr;
if(a<=l&&b>=r)continue;
if(a>_r||b<_l)continue;
idque[o+1][_cq++]=id;
}
solve(o+1,_l,_r,_cs,_cq);
}
}
namespace CaseBothSameX{
int i,l,r,x,ce;
struct E{
int x,y,v,p;
E(){}
E(int _x,int _y,int _v,int _p){x=_x,y=_y,v=_v,p=_p;}
}e[N+M];
inline bool cmpe(const E&a,const E&b){
if(a.x!=b.x)return a.x<b.x;
if(a.y!=b.y)return a.y<b.y;
return a.p<b.p;
}
void solve(){
for(i=0;i<cq;i++){
x=idque[0][i];
if(ans[x])continue;
if(que[x].xl!=que[x].xr)continue;
l=que[x].a.y,r=que[x].b.y;
if(l>r)swap(l,r);
e[ce++]=E(que[x].xl,r,l,x);
}
for(i=0;i<n;i++)if(a[i].x==a[i+1].x){
l=a[i].y,r=a[i+1].y;
if(l>r)swap(l,r);
e[ce++]=E(a[i].x,l,r,-1);
}
sort(e,e+ce,cmpe);
for(i=0;i<ce;i++){
if(i==0||e[i].x!=e[i-1].x)r=-inf;
if(e[i].p<0)umax(r,e[i].v);
else if(r>=e[i].v)ans[e[i].p]=1;
}
}
}
int main(){
scanf("%d%d",&n,&m);
xl=inf,xr=-inf;
for(i=0;i<n;i++){
a[i].read();
umin(xl,a[i].x);
umax(xr,a[i].x);
}
a[n]=a[0];
for(i=0;i<n;i++){
seg[i].a=a[i];
seg[i].b=a[i+1];
seg[i].fix();
idseg[0][i]=i;
}
for(i=0;i<m;i++){
que[i].a.read();
que[i].b.read();
que[i].fix();
umax(que[i].xl,xl);
umin(que[i].xr,xr);
if(que[i].xl>que[i].xr)continue;
if(que[i].xl==que[i].xr&&que[i].a.x!=que[i].b.x){
if(que[i].xl==xl)que[i].a=que[i].b;
else que[i].b=que[i].a;
que[i].fix();
}
idque[0][cq++]=i;
if(que[i].xl<que[i].xr)slo[i]=Frac(que[i].b.y-que[i].a.y,que[i].b.x-que[i].a.x);
}
solve(0,xl,xr,n,cq);
CaseBothSameX::solve();
for(i=0;i<m;i++)puts(ans[i]?"YES":"NO");
}
C. Shuttle Tour
#include<cstdio>
typedef long long ll;
const int N=200005,K=55;
char on[N];
int n,m,i,op,x,y,z,g[N],v[N<<1],w[N<<1],nxt[N<<1],ed,seg[N];
int at[N],pool[N],pos[N],cp;
int cnt,pre[K],len[K],cross[K],start[K];
ll sum[N];
inline void umin(int&a,int b){a>b?(a=b):0;}
inline void umax(int&a,int b){a<b?(a=b):0;}
struct E{
int l[K],r[K];bool have;
void clr(){
for(int i=1;i<=cnt;i++){
l[i]=N;
r[i]=0;
}
have=0;
}
void init(int x,int o){
clr();
if(o){
l[at[x]]=r[at[x]]=pos[x];
have=1;
}
}
void operator+=(const E&o){
for(int i=1;i<=cnt;i++){
umin(l[i],o.l[i]);
umax(r[i],o.r[i]);
}
have|=o.have;
}
ll cal(){
if(!have)return -1;
static int sub[K];
int i,j,k;
ll ret=0;
for(i=1;i<=cnt;i++){
sub[i]=l[i]<=r[i];
}
for(i=cnt;i;i--)sub[pre[i]]+=sub[i];
for(i=cnt;i;i--){
j=pre[i],k=cross[i];
if(sub[i]&&sub[i]<sub[1]){
umin(l[j],k);
umax(r[j],k);
ret+=len[i];
umin(l[i],start[i]);
umax(r[i],start[i]);
}
if(l[i]<r[i])ret+=sum[pool[r[i]]]-sum[pool[l[i]]];
}
return ret*2;
}
}val[524305],ans;
inline void add(int x,int y,int z){v[++ed]=y;w[ed]=z;nxt[ed]=g[x];g[x]=ed;}
void dfs(int x,int y,int z){
pool[++cp]=x;
pos[x]=cp;
at[x]=z;
bool first=1;
for(int i=g[x];i;i=nxt[i]){
int u=v[i];
if(u==y)continue;
sum[u]=sum[x]+w[i];
if(first){
dfs(u,x,z);
first=0;
}else{
cnt++;
pre[cnt]=z;
len[cnt]=w[i];
cross[cnt]=pos[x];
start[cnt]=cp+1;
dfs(u,x,cnt);
}
}
}
inline void up(int x){
val[x]=val[x<<1];
val[x]+=val[x<<1|1];
}
void build(int x,int a,int b){
if(a==b){
seg[a]=x;
val[x].init(a,on[a]);
return;
}
int mid=(a+b)>>1;
build(x<<1,a,mid);
build(x<<1|1,mid+1,b);
up(x);
}
inline void change(int x){
int y=seg[x];
val[y].init(x,on[x]);
for(y>>=1;y;y>>=1)up(y);
}
void ask(int x,int a,int b,int c,int d){
if(c<=a&&b<=d){
ans+=val[x];
return;
}
int mid=(a+b)>>1;
if(c<=mid)ask(x<<1,a,mid,c,d);
if(d>mid)ask(x<<1|1,mid+1,b,c,d);
}
int main(){
scanf("%d%d%s",&n,&m,on+1);
for(i=1;i<=n;i++)on[i]-='0';
for(i=1;i<n;i++)scanf("%d%d%d",&x,&y,&z),add(x,y,z),add(y,x,z);
cnt=1;
dfs(1,0,1);
build(1,1,n);
while(m--){
scanf("%d%d",&op,&x);
if(op==1){
on[x]^=1;
change(x);
}else{
scanf("%d",&y);
ans.clr();
ask(1,1,n,x,y);
printf("%lld\n",ans.cal());
}
}
}
D. Master of Both III
#include<bits/stdc++.h>
using namespace std;
const int N=22,P=998244353;
int n,w[N];
long long f[1<<N];
void cmin(long long &a,long long b)
{
a=a<b?a:b;
}
int main()
{
scanf("%d",&n);
for(int i=0;i<n;i++)
scanf("%d",&w[i]);
reverse(w+1,w+n);
for(int S=0;S<(1<<n);S++)
f[S]=1e18;
f[0]=f[1]=0;
int A=(1<<n)-1;
for(long long S=1;S<(1<<n);S++)
for(int i=1;i<n;i++)
cmin(f[S|((S<<i)&A)|((S<<i)>>n)],f[S]+w[i]);
for(int S=A;S>=0;S--)
for(int i=0;i<n;i++)
if(!(S>>i&1))
cmin(f[S],f[S^(1<<i)]);
long long ans=0;
for(int S=0;S<(1<<n);S++)
{
ans+=f[S]*S;
ans%=P;
}
printf("%lld\n",ans);
}
E. Interval Sum
#include<bits/stdc++.h>
using namespace std;
int main()
{
ios_base::sync_with_stdio(false);
int n;
cin>>n;
if(n%2==0)
{
cout<<n/2<<' ';
}
cout<<n<<' ';
for(int i=1;i<=(n-1)/2;i++)
cout<<i<<' '<<n-i<<' ';
cout<<endl;
return 0;
}
F. Turn on the Light
#include<bits/stdc++.h>
using namespace std;
const int N=33;
int n;
void solve(int l,int r,int cl,int cr)
{
if(l==r)
{
printf("! %d\n",l);
fflush(stdout);
// exit(0);
return;
}
if(r==l+1)
{
printf("? %d\n",l);
fflush(stdout);
int x;
scanf("%d",&x);
if(x==abs(cl-cr))
solve(l,l,cl,cr);
else
solve(r,r,cl+1,cr);
return;
}
if(cl==cr)
{
printf("? %d\n",r);
fflush(stdout);
int x;
scanf("%d",&x);
if(x==abs(cl-cr))
solve(r,r,cl,cr);
else
solve(l,r-1,cl,cr+1);
}
else
{
int mid=(l+r)>>1;
printf("? %d\n",mid);
fflush(stdout);
int x;
scanf("%d",&x);
if(x==abs(cl-cr))
solve(mid,mid,cl,cr);
else if(x==abs(cl-(cr+1)))
solve(l,mid-1,cl,cr+1);
else
solve(mid+1,r,cl+1,cr);
}
}
int main()
{
scanf("%d",&n);
solve(1,n,0,0
);
}
G. Puzzle: Kusabi
#include<bits/stdc++.h>
using namespace std;
int main()
{
ios_base::sync_with_stdio(false);
int n;
cin>>n;
vector<int> pa(n+5),dep(n+5);
vector<int> ty(n+5);
dep[1]=1;
for(int i=2;i<=n;i++)
{
int u,v;
string s;
cin>>u>>v>>s;
if(s=="Chang")ty[i]=3;
else if(s=="Tong")ty[i]=2;
else if(s=="Duan")ty[i]=1;
pa[i]=v;
dep[i]=dep[v]+1;
}
vector<pair<int,int>> ans;
vector<vector<tuple<int,int,int>>> rem(n+5);
for(int u=n;u>=1;u--)
{
if(ty[u])rem[u].emplace_back(u,ty[u],dep[u]);
vector<pair<int,int>> spl[5];
// cerr<<"merge "<<u<<endl;
for(auto [id,t,d]:rem[u])
{
// cerr<<id<<' '<<t<<' '<<d<<endl;
spl[t].emplace_back(d,id);
}
for(int i=1;i<=3;i++)sort(spl[i].begin(),spl[i].end());
int fl=0;
while(not spl[2].empty())
{
auto [d1,x]=spl[2].back();spl[2].pop_back();
if(spl[2].empty())
{
if(fl)return cout<<"NO"<<endl,0;
rem[pa[u]].emplace_back(x,2,d1);
fl=1;
break;
}
auto [d2,y]=spl[2].back();spl[2].pop_back();
if(d1!=d2)
{
if(fl or spl[2].empty())return cout<<"NO"<<endl,0;
rem[pa[u]].emplace_back(x,2,d1);
fl=1;
tie(d1,x)=spl[2].back();spl[2].pop_back();
}
if(d1!=d2)return cout<<"NO"<<endl,0;
ans.emplace_back(x,y);
}
if(spl[1].size()!=spl[3].size() and fl)return cout<<"NO"<<endl,0;
if(spl[1].size()==spl[3].size())
{
for(int i=0;i<(int)spl[1].size();i++)
{
if(spl[1][i].first<spl[3][i].first)ans.emplace_back(spl[1][i].second,spl[3][i].second);
else return cout<<"NO"<<endl,0;
}
}
else if(spl[1].size()>spl[3].size())//keep shortest in 1
{
if((int)spl[1].size()>(int)spl[3].size()+1)return cout<<"NO"<<endl,0;
for(int i=spl[3].size()-1,j=spl[1].size()-1;i>=0;i--,j--)
{
if(spl[1][j].first<spl[3][i].first)ans.emplace_back(spl[1][j].second,spl[3][i].second);
else
{
if(fl)return cout<<"NO"<<endl,0;
else rem[pa[u]].emplace_back(spl[1][j].second,1,spl[1][j].first),fl=1,i++;
}
}
if(not fl)rem[pa[u]].emplace_back(spl[1][0].second,1,spl[1][0].first);
}
else //keep longest in 3
{
if((int)spl[3].size()>(int)spl[1].size()+1)return cout<<"NO"<<endl,0;
for(int i=0,j=0;i<(int)spl[1].size();i++,j++)
{
if(spl[1][i].first<spl[3][j].first)ans.emplace_back(spl[1][i].second,spl[3][j].second);
else
{
if(fl)return cout<<"NO"<<endl,0;
else rem[pa[u]].emplace_back(spl[3][j].second,3,spl[3][j].first),fl=1,i--;
}
}
if(not fl)rem[pa[u]].emplace_back(spl[3][spl[3].size()-1].second,3,spl[3][spl[3].size()-1].first);
}
}
if(not rem[0].empty())return cout<<"NO"<<endl,0;
cout<<"YES"<<endl;
for(auto [x,y]:ans)cout<<x<<' '<<y<<endl;
return 0;
}
H. Puzzle: Tapa
#include<bits/stdc++.h>
using namespace std;
int main()
{
ios_base::sync_with_stdio(false);
int n,m;
cin>>n>>m;
vector<string> S(2*n+5);
for(int i=1;i<=2*n-1;i++)
{
string s;
cin>>s;
S[i]=' '+s;
for(int j=1;j<=2*m-1;j++)
if(S[i][j]=='.')
S[i][j]='#';
}
vector<vector<int>> G(n*m+5);
auto getty=[&](int x,int y){return (x==1 or x==n) or (y==1 or y==m);};
auto geths=[&](int x,int y){return (x-1)*m+y;};
auto addedge=[&](int u,int v){G[u].push_back(v);G[v].push_back(u);};
for(int i=1;i<=n;i++)
for(int j=1;j<=m;j++)
{
if(S[2*i-1][2*j-1]=='2' or S[2*i-1][2*j-1]=='4' or S[2*i-1][2*j-1]=='7')
{
if(j<m)
{
if(m==2 and i!=1 and i!=n){}
else if(S[2*i-1][2*j+1]=='2' or S[2*i-1][2*j+1]=='4' or S[2*i-1][2*j+1]=='7')
if(getty(i,j)==getty(i,j+1))
addedge(geths(i,j),geths(i,j+1));
}
if(i<n)
{
if(n==2 and j!=1 and j!=m){}
else if(S[2*i+1][2*j-1]=='2' or S[2*i+1][2*j-1]=='4' or S[2*i+1][2*j-1]=='7')
if(getty(i,j)==getty(i+1,j))
addedge(geths(i,j),geths(i+1,j));
}
}
}
vector<int> ma(n*m+5);
for(int i=1;i<=n;i++)
for(int j=1;j<=m;j++)
{
if((i+j)%2==0 and (S[2*i-1][2*j-1]=='2' or S[2*i-1][2*j-1]=='4' or S[2*i-1][2*j-1]=='7'))
{
int u=geths(i,j);
for(auto v:G[u])
{
if(!ma[v])
{
// cerr<<"match "<<u<<' '<<v<<endl;
ma[u]=v,ma[v]=u;
break;
}
}
}
}
for(int i=1;i<=n;i++)
for(int j=1;j<=m;j++)
{
if((i+j)%2==0 and (S[2*i-1][2*j-1]=='2' or S[2*i-1][2*j-1]=='4' or S[2*i-1][2*j-1]=='7'))
{
int u=geths(i,j);
if(!ma[u])
{
vector<int> vis(n*m+5);
function<bool(int)> dfs=[&](int u)
{
// cerr<<"dfs "<<u<<endl;
for(auto v:G[u])
{
if(not vis[v])
{
vis[v]=1;
if(!ma[v] or dfs(ma[v]))
{
// cerr<<"match "<<u<<' '<<v<<endl;
ma[u]=v,ma[v]=u;
return true;
}
}
}
return false;
};
if(not dfs(u))
{
cout<<"NO"<<endl;
return 0;
}
}
}
}
for(int i=1;i<=n;i++)
for(int j=1;j<=m;j++)
{
if((S[2*i-1][2*j-1]=='2' or S[2*i-1][2*j-1]=='4' or S[2*i-1][2*j-1]=='7') and not ma[geths(i,j)])
{
cout<<"NO"<<endl;
return 0;
}
if(ma[geths(i,j)])
{
int v=ma[geths(i,j)];
int x=(v-1)/m+1,y=(v-1)%m+1;
if(x>i)S[2*i-1+1][2*j-1]='.';
else if(y>j)S[2*i-1][2*j-1+1]='.';
}
}
cout<<"YES"<<endl;
for(int i=1;i<=2*n-1;i++)
{
for(int j=1;j<=2*m-1;j++)
cout<<S[i][j];
cout<<endl;
}
return 0;
}
I. Equation Discovering
#include <bits/stdc++.h>
using namespace std;
inline void TestComplexity() {
int n = 11;
int unary = 2;
int binary = 4;
int ter = 1;
int f[20][20];
memset(f, 0, sizeof f);
f[0][0] = 1;
for (int i = 0; i < n; ++i)
for (int j = 0; j <= i; ++j) {
f[i + 1][j + 1] += f[i][j] * ter;
if (j >= 1) f[i + 1][j] += f[i][j] * unary;
if (j >= 2) f[i + 1][j - 1] += f[i][j] * binary;
}
printf("%d\n", f[n][1]);
// 2240512
// time complexity = 2240512 * 20 = 4e7
}
const int N = 20;
int n;
double dx[N], dy[N];
struct StackItem {
int size;
double a[N];
};
StackItem operator+(const StackItem &u, const StackItem &v) {
StackItem ans;
ans.size = u.size + v.size;
for (int i = 0; i < n; ++i) ans.a[i] = u.a[i] + v.a[i];
return ans;
}
StackItem operator-(const StackItem &u, const StackItem &v) {
StackItem ans;
ans.size = u.size + v.size;
for (int i = 0; i < n; ++i) ans.a[i] = u.a[i] - v.a[i];
return ans;
}
StackItem operator*(const StackItem &u, const StackItem &v) {
StackItem ans;
ans.size = u.size + v.size;
for (int i = 0; i < n; ++i) ans.a[i] = u.a[i] * v.a[i];
return ans;
}
StackItem operator/(const StackItem &u, const StackItem &v) {
StackItem ans;
ans.size = u.size + v.size;
for (int i = 0; i < n; ++i) ans.a[i] = u.a[i] / v.a[i];
return ans;
}
StackItem Sin(StackItem u) {
for (int i = 0; i < n; ++i) u.a[i] = sin(u.a[i]);
return u;
}
StackItem Cos(StackItem u) {
for (int i = 0; i < n; ++i) u.a[i] = cos(u.a[i]);
return u;
}
StackItem MakeX() {
StackItem ans;
ans.size = 1;
for (int i = 0; i < n; ++i) ans.a[i] = dx[i];
return ans;
}
bool Test(const StackItem &u) {
for (int i = 0; i < n; ++i) if (abs(u.a[i] - dy[i]) / max(1.0, abs(dy[i])) > 1e-3) return 0;
return 1;
}
bool TestDiv(const StackItem &u) {
for (int i = 0; i < n; ++i) if (abs(u.a[i]) < 0.02) return 0;
return 1;
}
StackItem sta[N], backup[N][2];
char sol[N];
namespace PrintOut {
int c[N][2], sta[N];
void Print(char *sol, int x) {
if (sol[x] == 'x') {
printf("x");
} else if (sol[x] == 'c') {
printf("cos(");
Print(sol, c[x][0]);
printf(")");
} else if (sol[x] == 's') {
printf("sin(");
Print(sol, c[x][0]);
printf(")");
} else if (sol[x] == '+' || sol[x] == '-' || sol[x] == '*' || sol[x] == '/') {
printf("(");
Print(sol, c[x][0]);
printf("%c", sol[x]);
Print(sol, c[x][1]);
printf(")");
}
}
void Solve(char *sol) {
int top = 0;
for (int i = 0; sol[i]; ++i) {
if (sol[i] == '+' || sol[i] == '-' || sol[i] == '*' || sol[i] == '/') {
c[i][0] = sta[top - 2];
c[i][1] = sta[top - 1];
top -= 2;
} else if (sol[i] == 'c' || sol[i] == 's') {
c[i][0] = sta[top - 1];
top -= 1;
}
sta[top++] = i;
}
Print(sol, sta[top - 1]);
puts("");
}
}
inline void Dfs(int ps, int top) {
if (top == 1 && Test(sta[top - 1])) {
sol[ps] = 0;
PrintOut::Solve(sol);
exit(0);
}
if (ps == 10) return;
if (top + 1 - (10 - ps - 1) <= 1) {
sol[ps] = 'x';
sta[top] = MakeX();
Dfs(ps + 1, top + 1);
}
if (top - (10 - ps - 1) <= 1 && top) {
backup[ps][0] = sta[top - 1];
sol[ps] = 'c'; sta[top - 1] = Cos(backup[ps][0]); Dfs(ps + 1, top);
sol[ps] = 's'; sta[top - 1] = Sin(backup[ps][0]); Dfs(ps + 1, top);
sta[top - 1] = backup[ps][0];
}
if (top >= 2) {
backup[ps][0] = sta[top - 2]; backup[ps][1] = sta[top - 1];
if (backup[ps][0].size <= backup[ps][1].size) {
sol[ps] = '+'; sta[top - 2] = backup[ps][0] + backup[ps][1]; Dfs(ps + 1, top - 1);
sol[ps] = '*'; sta[top - 2] = backup[ps][0] * backup[ps][1]; Dfs(ps + 1, top - 1);
}
sol[ps] = '-'; sta[top - 2] = backup[ps][0] - backup[ps][1]; Dfs(ps + 1, top - 1);
if (TestDiv(backup[ps][1])) {
sol[ps] = '/'; sta[top - 2] = backup[ps][0] / backup[ps][1]; Dfs(ps + 1, top - 1);
}
sta[top - 2] = backup[ps][0]; sta[top - 1] = backup[ps][1];
}
}
int main() {
scanf("%d", &n);
for (int i = 0; i < n; ++i) {
scanf("%lf%lf", dx + i, dy + i);
}
Dfs(0, 0);
return 0;
}
J. Stage Clear
#include<cstdio>
#include<algorithm>
#include<queue>
using namespace std;
typedef long long ll;
const int N=47,LIM=26;
const ll inf=1LL<<60;
int n,m,i,x,y,deg[N],pre[N][N];ll ans=inf;
struct P{
ll a,b;
P(){}
P(ll _a,ll _b){a=_a,b=_b;}
bool operator<(const P&o)const{
int sgn1=a<b,sgn2=o.a<o.b;
if(sgn1!=sgn2)return sgn1<sgn2;
if(a<b)return a>o.a;
return b<o.b;
}
void operator+=(const P&o){
ll na=max(a,a-b+o.a),nb=b+o.b-a-o.a+na;
a=na,b=nb;
}
}a[N],init[N];
inline void up(ll&a,ll b){a>b?(a=b):0;}
namespace SMALL{
int m,S,i,j,k,mask[N];ll va[N],vb[N],f[(1<<(LIM-1))+1];
void solve(){
for(i=2;i<=n;i++){
S=0;
for(j=0;j<deg[i];j++){
k=pre[i][j];
if(k>1)S|=1<<(k-2);else S|=1<<n;
}
mask[i-2]=S;
va[i-2]=a[i].a;
vb[i-2]=a[i].b;
}
n--;
m=1<<n;
for(S=1;S<m;S++)f[S]=inf;
for(S=0;S<m;S++){
ll tmp=f[S];
if(tmp>=inf)continue;
for(i=0;i<n;i++)if(!(S>>i&1)){
if((mask[i]&S)==mask[i])continue;
ll now=tmp;
now-=vb[i];
if(now<0)now=0;
now+=va[i];
up(f[S^(1<<i)],now);
}
}
ans=f[m-1];
}
}
namespace BIG{
int fa[N],f[N],vis[N],del[N],pos;
typedef pair<int,int>PI;
typedef pair<P,PI>PII;
priority_queue<PII>q;
int F(int x){return del[f[x]]?f[x]=F(f[x]):f[x];}
inline void solve_tree(){
int i,x,y;
for(pos=i=0;i<=n;i++)vis[i]=del[i]=0;
a[1]=P(0,0);
for(i=2;i<=n;i++)a[i]=init[i],f[i]=fa[i];
for(i=2;i<=n;i++)q.push(PII(a[i],PI(0,i)));
while(!q.empty()){
PII t=q.top();
q.pop();
x=t.second.second;
if(del[x])continue;
if(t.second.first!=vis[x])continue;
del[x]=1;
y=F(x);
a[y]+=a[x];
if(y>1)q.push(PII(a[y],PI(vis[y]=++pos,y)));
}
up(ans,a[1].a);
}
void dfs(int x){
if(x>n){
solve_tree();
return;
}
for(int i=0;i<deg[x];i++){
fa[x]=pre[x][i];
dfs(x+1);
}
}
void solve(){
for(i=1;i<=n;i++)init[i]=a[i];
dfs(2);
}
}
int main(){
scanf("%d%d",&n,&m);
for(i=2;i<=n;i++)scanf("%lld%lld",&a[i].a,&a[i].b);
while(m--){
scanf("%d%d",&x,&y);
pre[y][deg[y]++]=x;
}
if(n<=LIM)SMALL::solve();else BIG::solve();
printf("%lld",ans);
}
K. Lazy but Diligent
#include<bits/stdc++.h>
using namespace std;
#define N 420
struct course{
int s,t,p;
bool operator < (const course &c) const{
return s<c.s;
}
}a[N];
int n,m,q,s,t,f[N][N],dp[N][N];
void cmin(int &x,int y){x=min(x,y);}
void cmax(int &x,int y){x=max(x,y);}
int main(){
ios::sync_with_stdio(0); cin.tie(0);
cin>>n>>m>>q>>t>>s;
memset(f,0x3f,sizeof f);
for (int i=1;i<=n;++i) f[i][i]=0;
for (int i=1;i<=m;++i){
int x,y,z; cin>>x>>y>>z;
cmin(f[x][y],z); cmin(f[y][x],z);
}
for (int k=1;k<=n;++k){
for (int i=1;i<=n;++i){
for (int j=1;j<=n;++j){
cmin(f[i][j],f[i][k]+f[k][j]);
}
}
}
for (int i=1;i<=q;++i){
cin>>a[i].s>>a[i].t>>a[i].p;
}
a[0].s=a[0].t=0; a[0].p=1;
++q; a[q].s=a[q].t=t; a[q].p=1;
sort(a,a+q+1);
memset(dp,0xcf,sizeof dp);
dp[0][0]=0;
for (int i=1;i<=q;++i){
for (int j=1;j<=i;++j){
for (int k=0;k<i;++k){
int ti=a[i].s-a[k].t;
int x=a[i].p,y=a[k].p;
if (f[x][y]<=ti) cmax(dp[i][j],dp[k][j-1]);
if (int dlt=ti-f[1][x]-f[1][y];dlt>=0) cmax(dp[i][j],dp[k][j-1]+dlt);
}
}
}
int ans=0;
for (int i=1;i<=q;++i) if (dp[q][i]>=s) ans=i;
cout<<ans-1<<'\n';
}
L. Barkley
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
using pii=pair<ll,int>;
#define fs first
#define sd second
#define mp make_pair
const int N=1e5+1e3+7;
int n,q;
ll a[N];
vector<pii>g[N];
ll ans;
void dfs(int x,ll G,int t,int k)
{
if(x<t)
{
ans=max(ans,G);
return;
}
if(!k)
{
for(auto [w,p]:g[x])
if(p<=t)
{
ans=max(ans,__gcd(G,w));
break;
}
return;
}
dfs(x-1,G,t,k-1);
for(auto [w,p]:g[x])
dfs(p-2,__gcd(G,w),t,k-1);
}
int main()
{
scanf("%d%d",&n,&q);
for(int i=1;i<=n;i++)
scanf("%lld",&a[i]);
for(int i=1;i<=n;i++)
{
vector<pii>ng=g[i-1];
for(auto &[x,y]:ng)
x=__gcd(x,a[i]);
ng.push_back({a[i],i});
for(auto [x,y]:ng)
if(!g[i].size()||x!=g[i].back().fs)
g[i].push_back({x,y});
}
for(int i=1;i<=n;i++)
reverse(g[i].begin(),g[i].end());
while(q--)
{
int l,r,k;
scanf("%d%d%d",&l,&r,&k);
ans=0;
dfs(r,0,l,k);
printf("%lld\n",ans);
}
}
M. A Wine and Four Dishes
#include<bits/stdc++.h>
using namespace std;
const int N=33;
int n,x,y;
int a[N],b[N];
int main()
{
scanf("%d%d%d",&n,&x,&y);
for(int i=1;i<=n;i++)
scanf("%d%d",&a[i],&b[i]);
if(!x&&!y)
{
puts("0");
return 0;
}
int ans=0;
if(x)
{
int mx=-1;
for(int i=1;i<=n;i++)
if(a[i]==1)
mx=max(mx,b[i]);
if(mx==-1)
{
puts("IMPOSSIBLE");
return 0;
}
for(int i=1;i<=n;i++)
if(a[i]==1&&b[i]==mx)
{
y-=b[i];
b[i]=0;
break;
}
ans++;
}
sort(b+1,b+n+1);
for(int i=n;i>=1;i--)
{
if(y<=0)
break;
ans++;
y-=b[i];
}
if(y>0)
puts("IMPOSSIBLE");
else
printf("%d\n",ans);
}
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