The 2023 ICPC Asia Hong Kong Regional Programming Contest (The 1st Universal Cup, Stage 2: Hong Kong)
題解：
https://files.cnblogs.com/files/clrs97/2022Hong_Kong_Tutorial.pdf
Code：
A. TreeScript
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int t;
for (cin >> t; t; t -= 1) {
int n;
cin >> n;
vector<int> p(n + 1);
vector<vector<int>> g(n + 1);
vector<int> dp(n + 1);
for (int i = 1; i <= n; i += 1)
cin >> p[i];
for (int i = n; i >= 1; i -= 1) {
if (g[i].empty()) dp[i] = 1;
else if (g[i].size() == 1) dp[i] = g[i][0];
else {
sort(g[i].begin(), g[i].end(), greater<int>());
dp[i] = max(g[i][0], g[i][1] + 1);
}
g[p[i]].push_back(dp[i]);
}
cout << dp[1] << "\n";
}
return 0;
}
B. Big Picture
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const LL mod=998244353;
const LL N=1200;
LL a[N][N],b[N][N],n,m,e1[N][N];
void upd(LL &x,LL y){x=(x+y)%mod;}
int main(){
ios::sync_with_stdio(0); cin.tie(0);
cin>>n>>m;
for (LL i=1;i<=n;++i){
for (LL j=1;j<=m;++j){
cin>>a[i][j];
upd(a[i][j],a[i][j-1]);
}
}
for (LL i=1;i<=n;++i){
for (LL j=1;j<=m;++j){
cin>>b[i][j];
upd(b[i][j],b[i-1][j]);
}
}
LL E=0,V=0,S=0;
// E: [out edge]
// V: [node]
// S: [inside edge] - [fake face]
auto pr=[&](LL i,LL j)->LL
{
if (i==0||j==0) return 1;
return 1-a[i][j-1]*b[i-1][j]%mod;
};
for (LL i=1;i<=n;++i){
for (LL j=1;j<=m;++j){
upd(V,pr(i,j));
// cerr<<i<<' '<<j<<' '<<pr(i,j)<<'\n';
}
}
for (LL i=1;i<=n;++i){
for (LL j=1;j<=m;++j){
if (j>1){// edge([i,j-1],[i,j])
LL p=0;
upd(p,1-pr(i,j-1));
upd(p,1-pr(i,j));
upd(p,-(a[i][j-2]*b[i-1][j-1]%mod*b[i-1][j]));
upd(E,1-p);
e1[i][j]=1-p;
}
if (i>1){// edge([i-1,j],[i,j])
LL p=0;
upd(p,1-pr(i-1,j));
upd(p,1-pr(i,j));
upd(p,-(b[i-2][j]*a[i-1][j-1]%mod*a[i][j-1]));
upd(E,1-p);
}
}
}
for (LL i=2;i<=n;++i){
for (LL j=2;j<=m;++j){
{//square
LL p1=(1-a[i][j-1])*e1[i-1][j]%mod;
LL p2=(a[i][j-1]-a[i][j-2])*(1-b[i-1][j])%mod*pr(i-1,j-1)%mod;
LL p3=a[i][j-2]*(1-b[i-1][j])%mod*(1-b[i-1][j-1])%mod;
upd(S,-(p1+p2+p3));
}
{//diag
LL p=a[i-1][j-2]*b[i-2][j-1]%mod*(a[i][j-1]-a[i][j-2])%mod*(b[i-1][j]-b[i-2][j])%mod;
upd(S,p);
}
}
}
// cerr<<E<<' '<<V<<' '<<S<<'\n';
LL ans=(1+1+1+E-V+S)%mod;
cout<<(ans+mod)%mod<<'\n';
}
C. Painting Grid
#include<bits/stdc++.h>
using namespace std;
int main()
{
ios_base::sync_with_stdio(false);
int T;
cin>>T;
while(T--)
{
int n,m;
cin>>n>>m;
int ok=1;
if(m<=10 and (1<<m)<n)ok=0;
if(n<=10 and (1<<n)<m)ok=0;
if(not ok or n*m%2==1)cout<<"NO\n";
else
{
cout<<"YES\n";
int sw=0;
if(m%2!=0)sw=1,swap(n,m);
vector<vector<int>> ans(n+5,vector<int>(m+5));
int mx;
for(int i=1;i<=m/2;i++)ans[1][i]=1,mx=1;
set<vector<int>> s;
vector<vector<int>> tmp;
{
auto rev=ans[1];
for(int i=1;i<=m;i++)rev[i]^=1;
tmp.push_back(rev);
s.insert(rev);s.insert(ans[1]);
}
for(int b=0;(1<<b)<m/2;b++)
{
// cerr<<"go "<<b<<endl;
for(int i=0;i<m/2;i++)
{
ans[b+2][i+1]=(i>>b)&1;
ans[b+2][i+m/2+1]=((i>>b)&1)^1;
}
auto rev=ans[b+2];
for(int i=1;i<=m;i++)rev[i]^=1;
tmp.push_back(rev);
s.insert(rev);s.insert(ans[b+2]);
mx=max(mx,b+2);
}
vector<int> now(m+5);
// auto chk=[&](){int ret=0;for(int i=1;i<=m;i++)ret+=now[i];return ret;};
auto nxt=[&](){for(int i=m;i>=1;i--)if(now[i]==1)now[i]=0;else {now[i]=1;return true;}return false;};
mx++;
while(mx+1<=n)
{
if(s.count(now))
{
if(nxt())
continue;
else
break;
}
auto rnow=now;
for(int i=1;i<=m;i++)rnow[i]^=1;
ans[mx]=now;
ans[mx+1]=rnow;
s.insert(now);
s.insert(rnow);
mx+=2;
nxt();
}
while(mx<=n)
{
ans[mx]=tmp.back();
tmp.pop_back();
mx++;
}
if(sw)
{
for(int i=1;i<=m;i++)
{
for(int j=1;j<=n;j++)
cout<<ans[j][i];
cout<<"\n";
}
}
else
{
for(int i=1;i<=n;i++)
{
for(int j=1;j<=m;j++)
cout<<ans[i][j];
cout<<"\n";
}
}
}
}
return 0;
}
D. Shortest Path Query
#include<cstdio>
#include<vector>
#include<algorithm>
using namespace std;
const int N=50005,Q=50005,MASK=1023,inf=~0U>>1;
int n,m,q,cnt,i,j,k,x,y,z,e[Q][2],ans[Q];
vector<int>g[N][2],h[N];
struct P{int x,y;P(){}P(int _x,int _y){x=_x,y=_y;}}hull[N*2];
vector<P>f[MASK+2],cur;
inline void up(int&a,int b){a>b?(a=b):0;}
inline void ext(const P&p,int dx,int dy){
if(cnt){
if(hull[cnt].y<=p.y+dy)return;
if(hull[cnt].x==p.x+dx)cnt--;
}
while(cnt>1&&1LL*(hull[cnt].y-hull[cnt-1].y)*(p.x+dx-hull[cnt].x)>=1LL*(p.y+dy-hull[cnt].y)*(hull[cnt].x-hull[cnt-1].x))cnt--;
hull[++cnt]=P(p.x+dx,p.y+dy);
}
inline void merge(const vector<P>&v,int dx,int dy){
cnt=0;
int i=0,j=0;
while(i<cur.size()&&j<v.size()){
if(cur[i].x<v[j].x+dx)ext(cur[i++],0,0);
else ext(v[j++],dx,dy);
}
while(i<cur.size())ext(cur[i++],0,0);
while(j<v.size())ext(v[j++],dx,dy);
cur.resize(cnt);
for(i=0;i<cnt;i++)cur[i]=hull[i+1];
}
int main(){
scanf("%d%d",&n,&m);
while(m--){
scanf("%d%d%d",&x,&y,&z);
g[y][z].push_back(x);
}
scanf("%d",&q);
for(i=1;i<=q;i++){
scanf("%d%d%d",&x,&y,&z);
e[i][0]=x;
e[i][1]=y;
h[z].push_back(i);
}
for(i=1;i<=n;i++){
cur.clear();
if(i==1)cur.push_back(P(0,0));
for(j=0;j<g[i][0].size();j++)merge(f[g[i][0][j]&MASK],1,0);
for(j=0;j<g[i][1].size();j++)merge(f[g[i][1][j]&MASK],0,1);
for(j=0;j<h[i].size();j++){
z=h[i][j];
x=e[z][0];
y=e[z][1];
int tmp=inf;
for(k=0;k<cur.size();k++)up(tmp,x*cur[k].x+y*cur[k].y);
ans[z]=tmp;
}
swap(cur,f[i&MASK]);
}
for(i=1;i<=q;i++)printf("%d\n",ans[i]);
}
E. Goose, Goose, DUCK?
#include<bits/stdc++.h>
using namespace std;
const int N=1e6+1e3+7,L=1e6;
int n,k,a[N];
vector<int>pos[N];
struct T{
int l,r,ls,rs;
int mx,cnt;
int tag;
}t[N*2+1];
int cnt;
void add(int x,int v)
{
t[x].tag+=v;
t[x].mx+=v;
}
void pushdown(int x)
{
if(t[x].tag)
{
add(t[x].ls,t[x].tag);
add(t[x].rs,t[x].tag);
t[x].tag=0;
}
}
void update(int x)
{
t[x].mx=max(t[t[x].ls].mx,t[t[x].rs].mx);
t[x].cnt=(t[x].mx==t[t[x].ls].mx)*t[t[x].ls].cnt+(t[x].mx==t[t[x].rs].mx)*t[t[x].rs].cnt;
}
int build(int l,int r)
{
int x=++cnt;
t[x].l=l,t[x].r=r;
if(l==r)
{
t[x].cnt=1;
return x;
}
int mid=(l+r)>>1;
t[x].ls=build(l,mid);
t[x].rs=build(mid+1,r);
update(x);
return x;
}
void change(int x,int l,int r,int v)
{
if(l<=t[x].l&&t[x].r<=r)
{
add(x,v);
return;
}
pushdown(x);
int mid=(t[x].l+t[x].r)>>1;
if(l<=mid)
change(t[x].ls,l,r,v);
if(r>mid)
change(t[x].rs,l,r,v);
update(x);
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cin>>n>>k;
for(int i=1;i<=n;i++)
cin>>a[i];
long long ans=0;
build(1,n);
for(int i=1;i<=n;i++)
{
change(1,i,i,L);
if(pos[a[i]].size()>=k)
{
int r=pos[a[i]][pos[a[i]].size()-k],l=pos[a[i]].size()==k?1:pos[a[i]][pos[a[i]].size()-k-1]+1;
change(1,l,r,1);
}
pos[a[i]].push_back(i);
if(pos[a[i]].size()>=k)
{
int r=pos[a[i]][pos[a[i]].size()-k],l=pos[a[i]].size()==k?1:pos[a[i]][pos[a[i]].size()-k-1]+1;
change(1,l,r,-1);
}
if(t[1].mx==L)
ans+=t[1].cnt;
}
cout<<ans<<"\n";
}
F. Sum of Numbers
#include <bits/stdc++.h>
using namespace std;
constexpr int base = 10;
struct Dec{
vector<int> d;
Dec(vector<int> d = {0}): d(d) {
assert(not d.empty());
}
bool is_zero() const {
return d.size() == 1 and d[0] == 0;
}
Dec& operator += (const Dec& dec) {
int carry = 0;
int msize = max(d.size(), dec.d.size());
d.resize(msize);
for (int i = 0; i < msize; i += 1) {
if (i < dec.d.size()) d[i] += dec.d[i];
d[i] += carry;
if (d[i] >= base) {
carry = 1;
d[i] -= base;
} else {
carry = 0;
}
}
if (carry) d.push_back(carry);
return *this;
}
bool operator < (const Dec& dec) const {
if (d.size() != dec.d.size())
return d.size() < dec.d.size();
for (int i = d.size() - 1; i >= 0; i -= 1)
if (d[i] != dec.d[i])
return d[i] < dec.d[i];
return false;
}
};
ostream& operator << (ostream& out, const Dec& dec) {
for (int i = dec.d.size() - 1; i >= 0; i -= 1)
out << dec.d[i];
return out;
};
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int t;
map<int, map<int, vector<vector<int>>>> mp;
for (cin >> t; t; t -= 1) {
int n, k;
string sr;
cin >> n >> k >> sr;
vector<int> p(n);
for (int i = 0; i < n; i += 1) {
p[i] = sr[n - i - 1] - '0';
}
auto f = [&](int L, int R) -> Dec {
return Dec(vector<int>(p.begin() + (n - 1 - R), p.begin() + (n - L)));
};
if (not mp.count(k)) {
vector<int> a(k);
function<void(int)> DFS = [&](int u) {
if (u == k) {
vector<int> s(k);
for (int i = 0; i < k; i += 1) {
if (i) s[i] = s[i - 1];
s[i] += a[i];
}
int ss = 0;
for (int si : s) ss += si;
mp[k][(ss % (k + 1) + k + 1) % (k + 1)].push_back(s);
return;
}
for (int i : {0, -1, 1}) {
a[u] = i;
DFS(u + 1);
}
};
DFS(0);
}
Dec ans;
for (auto s : mp[k][n % (k + 1)]) {
int ss = 0;
for (int si : s) ss += si;
int x = (n - ss) / (k + 1);
int ok = x > 0;
for (int si : s) ok &= x + si > 0;
if (not ok) continue;
Dec pans = f(0, x - 1);
int L = x;
for (int si : s) {
si += x;
if (not ans.is_zero() and si > ans.d.size()) {
ok = 0;
break;
}
pans += f(L, L + si - 1);
if (not ans.is_zero() and ans < pans) {
ok = 0;
break;
}
L += si;
}
if (not ok) continue;
if (ans.is_zero() or pans < ans)
ans = pans;
}
cout << ans << "\n";
}
return 0;
}
G. Paddle Star
#include<bits/stdc++.h>
using namespace std;
const double pi=acos(-1);
int T;
double l1,l2,alp,bet;
double trans(double deg)
{
return deg/180*pi;
}
double fix(double x)
{
return min(max(x,-1.0),1.0);
}
int main()
{
int Case=0;
scanf("%d",&T);
while(T--)
{
scanf("%lf%lf%lf%lf",&l1,&l2,&alp,&bet);
alp=trans(alp);
bet=trans(bet);
double ans=(l1+l2)*(l1+l2)*alp+l2*l2*bet;
if(bet<=pi/2)
{
printf("%.15lf\n",ans);
continue;
}
else
{
double rc=pi-bet;
double A=l1,B=l2;
double C=sqrt(max(A*A+B*B-2*A*B*cos(rc),0.0));
double rb=asin(fix(B*sin(rc)/C));
double ra=pi-rb-rc;
if(ra>=pi/2)
{
double t=min(rb,alp*2);
double S=0.5*A*B*sin(rc);
double rcc=pi-ra-(rb-t);
double AA=C/sin(rcc)*sin(ra);
S-=0.5*C*AA*sin(rb-t);
S-=C*C*t*0.5;
ans+=S*2;
}
else
{
double S=0.5*A*B*sin(rc);
double H=S*2/B;
double rL=acos(fix(H/C));
S-=0.5*C*H*sin(rL);
double rR=rb-rL;
double t=min(rR,alp*2);
S-=H*H*t*0.5;
S-=0.5*H*H*tan(rR-t);
ans+=S*2;
}
printf("%.15lf\n",ans);
}
}
}
H. Another Goose Goose Duck Problem
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define data dataa
#define rep(i,n) for(int i=1;i<=n;i++)
typedef long long LL;
int main()
{
int l,r,b,k;
scanf("%d%d%d%d",&l,&r,&b,&k);
printf("%lld\n",(LL)((l-1)/b+1)*b*k);
return 0;
}
I. Range Closest Pair of Points Query
#include<cstdio>
#include<vector>
using namespace std;
typedef unsigned int U;
typedef long long ll;
const int N=250005,Q=250005,BLK=9,M=(N>>BLK)+5,K=28,Base=(1<<21)-1;
const ll inf=1LL<<60;
int n,m,i,j,x,y,g[N],v[Q],nxt[Q];
int cb;ll val[N],mi[M],ans[Q];
struct P{int x,y;}a[N];
inline ll dis(const P&a,const P&b){return 1LL*(a.x-b.x)*(a.x-b.x)+1LL*(a.y-b.y)*(a.y-b.y);}
inline void up(ll&a,ll b){a>b?(a=b):0;}
inline void modify(int x,ll p){up(val[x],p);up(mi[x>>BLK],p);}
inline ll query(int x){
ll ret=inf;
int X=x>>BLK;
for(int i=x;(i>>BLK)==X&&i<=n;i++)up(ret,val[i]);
for(int i=X+1;i<=cb;i++)up(ret,mi[i]);
return ret;
}
struct Layer{
int g[Base+2],vx[N],vy[N],nxt[N],ed;
int rad;
vector<int>pool[N];
int st[N],size[N];
int head;
int ask(int x,int y){
if(x<0||y<0)return 0;
U val=((((U)x)<<8)^y)&Base;
for(int i=g[val];i;i=nxt[i])if(vx[i]==x&&vy[i]==y)return i;
return 0;
}
int ins(int x,int y){
U val=((((U)x)<<8)^y)&Base;
for(int i=g[val];i;i=nxt[i])if(vx[i]==x&&vy[i]==y)return i;
vx[++ed]=x;
vy[ed]=y;
nxt[ed]=g[val];
g[val]=ed;
return ed;
}
void insert(int o){pool[ins(a[o].x>>rad,a[o].y>>rad)].push_back(o);}
void init(){
for(int i=1;i<=ed;i++)st[i]=pool[i].size()-1;
head=1;
}
void search(int o){
int A=a[o].x>>rad,B=a[o].y>>rad;
for(int X=A-1;X<=A+1;X++)for(int Y=B-1;Y<=B+1;Y++){
int O=ask(X,Y);
if(!O)continue;
int i=st[O];
while(i>=0&&pool[O][i]<head)i--;
for(st[O]=i;i>=0;i--){
int who=pool[O][i];
if(who>=o)break;
ll now=dis(a[o],a[who]);
if(now>>(rad*2))continue;
if(!(now>>((rad-1)*2))){
if(head<=who)head=who+1;
continue;
}
modify(who,now);
}
}
}
}layer[K];
int main(){
scanf("%d%d",&n,&m);
for(i=1;i<=n;i++)scanf("%d%d",&a[i].x,&a[i].y);
for(i=1;i<=m;i++){
scanf("%d%d",&x,&y);
v[i]=x;
nxt[i]=g[y];
g[y]=i;
}
cb=n>>BLK;
for(i=0;i<=cb;i++)mi[i]=inf;
for(i=1;i<=n;i++)val[i]=inf;
for(i=0;i<K;i++)layer[i].rad=i+1;
for(i=n;i;i--)for(j=0;j<K;j++)layer[j].insert(i);
for(i=0;i<K;i++)layer[i].init();
for(i=1;i<=n;i++){
for(j=0;j<K;j++){
if(j&&layer[j-1].head>layer[j].head)layer[j].head=layer[j-1].head;
layer[j].search(i);
}
for(j=g[i];j;j=nxt[j]){
x=v[j];
if(x<layer[0].head)ans[j]=0;else ans[j]=query(x);
}
}
for(i=1;i<=m;i++)printf("%lld\n",ans[i]);
}
J. Dice Game
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int P=998244353;
typedef pair<int,int> pii;
#define fs first
#define sd second
#define mp make_pair
int qpow(int a,int b)
{
int ret=1;
while(b)
{
if(b&1)
ret=ret*a%P;
b>>=1;
a=a*a%P;
}
return ret;
}
int n;
int val[31],L,R;
pii operator +(const pii &a,const pii &b)
{
return {max(a.fs,b.fs),min(a.sd,b.sd)};
}
pii f[2][2][31];
int vis[2][2][31];
pii dp(int p,int up,int dw)
{
if(p==-1)
return mp(0,0);
if(vis[up][dw][p])
return f[up][dw][p];
vis[up][dw][p]=1;
pii ret(-1e18,1e18);
for(int i=dw?L>>p&1:0;i<=(up?R>>p&1:1);i++)
{
auto nxt=dp(p-1,up&&i==(R>>p&1),dw&&i==(L>>p&1));
nxt.first+=(i?-val[p]:val[p]);
nxt.second+=(i?-val[p]:val[p]);
ret=ret+nxt;
}
return f[up][dw][p]=ret;
}
int c1(int N,int i)
{
return N/(1<<i+1)*(1<<i)+max(0ll,N%(1<<i+1)-(1<<i));
}
pii getv(int l,int r)
{
memset(vis,0,sizeof(vis));
L=l,R=r;
return dp(30,1,1);
}
int sgn(int x)
{
return x>=0?1:-1;
}
int ans=0,ivn;
void solve(int l,int r)
{
pii res=getv(l,r);
if(sgn(res.fs)==sgn(res.sd))
{
if(sgn(res.fs)>=0)
{
int sum=0;
for(int i=30;i>=0;i--)
{
int x1=val[i]/(1<<i),x0=(n-x1),y1=c1(r+1,i)-c1(l,i),y0=r-l+1-y1;
sum=(sum+(x1*y0%P+x0*y1%P)*(1<<i))%P;
}
ans=(ans+sum*ivn)%P;
}
else
ans=(ans+(l+r)*(r-l+1)/2)%P;
return;
}
int mid=(l+r)>>1;
solve(l,mid);
solve(mid+1,r);
}
signed main()
{
ios::sync_with_stdio(false);
cin.tie(0);
int T;
cin>>T;
while(T--)
{
cin>>n;
ivn=qpow(n,P-2);
for(int i=0;i<=30;i++)
val[i]=c1(n,i)*(1<<i);
ans=0;
solve(0,n-1);
ans=ans*ivn%P;
cout<<ans<<"\n";
}
}
K. Maximum GCD
#include<bits/stdc++.h>
using namespace std;
const int N=1e6+1e3+7;
set<int>s;
int n;
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cin>>n;
for(int i=1;i<=n;i++)
{
int x;
cin>>x;
s.insert(x);
}
int ans=s.size()==1?*s.begin():(*s.begin())/2;
if(s.size()>1)
{
if((*next(s.begin()))/2>=*s.begin())
ans=*s.begin();
}
cout<<ans<<endl;
}
L. Permutation Compression
#include<bits/stdc++.h>
using namespace std;
const int N=2e5+1e3+7;
int T,n,m,k,p[N],q[N],l[N],pos[N],del[N];
int c[N];
void add(int x,int v)
{
while(x<=n)
{
c[x]+=v;
x+=x&-x;
}
}
int qry(int x)
{
int ret=0;
while(x)
{
ret+=c[x];
x-=x&-x;
}
return ret;
}
int main()
{
scanf("%d",&T);
while(T--)
{
scanf("%d%d%d",&n,&m,&k);
for(int i=1;i<=n;i++)
scanf("%d",&p[i]),pos[p[i]]=i,del[i]=1,c[i]=0;
for(int i=1;i<=m;i++)
scanf("%d",&q[i]),del[q[i]]=0;
for(int i=1;i<=k;i++)
scanf("%d",&l[i]);
bool ok=1;
for(int i=1;i<m;i++)
if(pos[q[i]]>pos[q[i+1]])
ok=0;
if(!ok)
{
puts("NO");
continue;
}
set<int>s;
vector<int>nd;
for(int i=n;i>=1;i--)
{
int x=pos[i];
if(!del[i])
s.insert(x);
else
{
auto it=s.lower_bound(x);
int r=it==s.end()?n:*it-1;
int l=it==s.begin()?1:*prev(it)+1;
nd.push_back((r-l+1)-(qry(r)-qry(l-1)));
add(x,1);
}
}
sort(nd.begin(),nd.end());
sort(l+1,l+k+1);
int p=k;
while(nd.size())
{
int x=nd.back();
nd.pop_back();
while(p>0&&l[p]>x)
p--;
if(!p)
{
ok=0;
break;
}
p--;
}
puts(ok?"YES":"NO");
}
}
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