題解：
https://files.cnblogs.com/files/clrs97/2023hangzhou_tutorials-2-22.pdf
Code：
A. Submissions
#include <bits/stdc++.h>
using namespace std;
using Submission = tuple<string, char, int, string>;
using Score = pair<int, int>;
Score operator+(const Score &s0, const Score &s1) {
return Score(s0.first + s1.first, s0.second + s1.second);
}
Score operator-(const Score &s0, const Score &s1) {
return Score(s0.first - s1.first, s0.second - s1.second);
}
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
int T;
cin >> T;
for (int ti = 0; ti < T; ti += 1) {
int n = 0, m;
cin >> m;
vector<Submission> submissions(m);
unordered_map<string, int> mp;
vector<string> names;
vector<array<vector<pair<int, bool>>, 26>> tp;
for (auto &[c, p, t, s] : submissions) {
cin >> c >> p >> t >> s;
if (not mp.count(c)) {
mp[c] = n++;
names.push_back(c);
tp.emplace_back();
}
tp[mp[c]][p - 'A'].emplace_back(t, s == "accepted");
}
auto print = [&](string s) {
cout << count(s.begin(), s.end(), '1') << "\n";
for (int i = 0; i < n; i += 1) {
if (s[i] == '1') { cout << names[i] << " "; }
}
cout << "\n";
};
auto score = [&](const vector<pair<int, bool>> &vp) -> Score {
int p = 0;
for (auto [t, s] : vp) {
if (s) { return Score(1, -t - p); }
p += 20;
}
return Score(0, 0);
};
vector<Score> s(n), bs(n), ws(n);
for (int i = 0; i < n; i += 1) {
for (int j = 0; j < 26; j += 1) { s[i] = s[i] + score(tp[i][j]); }
bs[i] = ws[i] = s[i];
for (int j = 0; j < 26; j += 1) {
auto vp = tp[i][j];
if (not vp.empty()) { vp[0].second = true; }
bs[i] = max(bs[i], s[i] - score(tp[i][j]) + score(vp));
}
for (int j = 0; j < 26; j += 1) {
auto vp = tp[i][j];
for (auto &[t, s] : vp) {
if (s) {
s = false;
break;
}
}
ws[i] = min(ws[i], s[i] - score(tp[i][j]) + score(vp));
}
}
int k = n - count(s.begin(), s.end(), Score(0, 0));
int r = min((k + 9) / 10, 35);
auto ss = s;
sort(ss.begin(), ss.end());
string ans(n, '0');
if (k == 0) { ss.emplace_back(1, numeric_limits<int>::min()); }
for (int i = 0; i < n; i += 1) {
if (bs[i] >= ss[n - r]) { ans[i] = '1'; }
if (bs[i].first and not s[i].first and min(k / 10 + 1, 35) > r and
bs[i] >= ss[n - r - 1]) {
ans[i] = '1';
}
}
if (r == n or ss[n - r - 1] == ss[n - r]) {
print(ans);
continue;
}
int ok = 0;
for (int i = 0; i < n; i += 1) {
if (s[i] >= ss[n - r]) {
if (ws[i] <= ss[n - r - 1]) {
if (ws[i].first or min((k + 8) / 10, 35) == r) { ok = 1; }
}
}
if (s[i].first == 0) {
int m = -1;
for (auto &p : tp[i]) {
if (not p.empty()) {
m = max(m, p.back().first + ((int)p.size() - 1) * 20);
}
}
if (m != -1 and Score(1, -m) <= ss[n - r - 1] and
min(k / 10 + 1, 35) > r) {
ok = 1;
}
}
}
if (ok) {
for (int i = 0; i < n; i += 1) {
if (s[i] == ss[n - r - 1]) { ans[i] = '1'; }
}
}
print(ans);
}
}
B. Festival Decorating
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
typedef double ld;
const int N=550001,LIM=1028;
const ld pi=acosl(-1.0);
int n,q,mx,i,j,k,x,c,loc[N],col[N],val[N],l,r,ans[N],pos[N];
struct comp{
ld r,i;comp(ld _r=0,ld _i=0){r=_r,i=_i;}
void clear(){r=i=0;}
comp operator+(const comp&x)const{return comp(r+x.r,i+x.i);}
comp operator-(const comp&x)const{return comp(r-x.r,i-x.i);}
comp operator*(const comp&x)const{return comp(r*x.r-i*x.i,r*x.i+i*x.r);}
}A0[N],A1[N],A2[N],B0[N],B1[N],B2[N],F[N],w[N],ww[N];
inline void FFT(comp a[],int n,int o){
for(int i=1;i<n;i++)if(i<pos[i])swap(a[i],a[pos[i]]);
for(int d=0,k=__builtin_ctz(n);(1<<d)<n;d++){
int m=1<<d,m2=m<<1;
for(int i=0;i<n;i+=m2)for(int j=0;j<m;j++){
comp&A=a[i+j+m],&B=a[i+j],t=(o==1?w[j<<(k-d)]:ww[j<<(k-d)])*A;
A=B-t;B=B+t;
}
}
if(o==-1)for(int i=0;i<n;i++)a[i].r/=n;
}
inline void solve(int x,int l,int r){
for(;l<=r;l++)if(val[loc[l]+x]&&col[l]!=val[loc[l]+x]){
ans[x]=l;
break;
}
}
int main(){
scanf("%d%d",&n,&q);
for(i=1;i<=n;i++){
scanf("%d%d",&loc[i],&col[i]);
val[loc[i]]=col[i];
if(loc[i]>mx)mx=loc[i];
}
for(k=1;k<mx*2;k<<=1);
j=__builtin_ctz(k)-1;
for(i=0;i<k;i++)pos[i]=pos[i>>1]>>1|((i&1)<<j);
for(i=0;i<k;i++)w[i]=comp(cosl(pi*i/k),sinl(pi*i/k));
for(i=0;i<k;i++)ww[i]=w[i],ww[i].i*=-1;
for(i=1;i<=n;i++){
x=loc[i],c=col[i];
B0[x].r=1;
B1[x].r=-2*c;
B2[x].r=((ld)c)*((ld)c);
}
FFT(B0,k,1);
FFT(B1,k,1);
FFT(B2,k,1);
l=min(n,LIM);
for(i=1;i<mx;i++)solve(i,1,l);
l++;
while(l<=n){
r=l*3;
if(r&1)r--;
r=min(r,n);
for(i=0;i<k;i++){
A0[i].clear();
A1[i].clear();
A2[i].clear();
}
for(i=l;i<=r;i++){
x=mx-loc[i],c=col[i];
A0[x].r=((ld)c)*((ld)c);
A1[x].r=c;
A2[x].r=1;
}
FFT(A0,k,1);
FFT(A1,k,1);
FFT(A2,k,1);
for(i=0;i<k;i++)F[i]=A0[i]*B0[i]+A1[i]*B1[i]+A2[i]*B2[i];
FFT(F,k,-1);
for(i=1;i<mx;i++){
if(ans[i])continue;
if(F[mx+i].r>0.5)ans[i]=r/2;
}
l=r+1;
}
while(q--)scanf("%d",&x),printf("%d\n",ans[x]);
}
/*
[l,3l]
1.5l
*/
C. Yet Another Shortest Path Query
#include<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
typedef pair<int,int>P;
const int BUF=50000000;
char Buf[BUF],*buf=Buf;
inline void read(int&a){for(a=0;*buf<48;buf++);while(*buf>47)a=a*10+*buf++-48;}
const int OUT=13000000;
char Out[OUT],*ou=Out;int Outn[15],Outcnt;
inline void write(int x){
if(x==-1){
*ou++='-';
*ou++='1';
return;
}
if(!x)*ou++=48;
else{
for(Outcnt=0;x;x/=10)Outn[++Outcnt]=x%10+48;
while(Outcnt)*ou++=Outn[Outcnt--];
}
}
inline void writeln(int x){write(x);*ou++='\n';}
const int N=1000005,M=N*3,Q=1000005,inf=500000000;
int n,m,cq,i,x,y,z,ans[Q],e[M][3],deg[N],g[N],v[M<<1],nxt[M<<1],ed;
int q[N],h,t,ord[N];bool vis[N];
vector<P>ga[N],gr[N];
inline void add(int x,int y){deg[x]++;v[++ed]=y;nxt[ed]=g[x];g[x]=ed;}
inline void ext(int x){if(deg[x]<=5&&!vis[x])vis[q[++t]=x]=1;}
inline void up(int&a,int b){a>b?(a=b):0;}
struct E{int o,x,y,z;E(){}E(int _o,int _x,int _y,int _z){o=_o,x=_x,y=_y,z=_z;}};
int cur,val[N],last[N];
inline void update(int x,int y){if(last[x]!=cur)last[x]=cur,val[x]=y;else up(val[x],y);}
namespace TWO{
const int MAXQ=Q*20;
int ce,cnt[N],pool[MAXQ];E e[MAXQ];
inline void solve(int o,int x,int y,int z){
if(x==y){up(ans[o],z);return;}
e[++ce]=E(o,x,y,z);
cnt[x]++;
e[++ce]=E(o,y,x,z);
cnt[y]++;
}
inline void single(int x){
if(x==cur)return;
cur=x;
for(const auto&A:ga[x]){
update(A.first,A.second);
for(const auto&B:gr[A.first])update(B.first,A.second+B.second);
}
}
void run(){
int i,u;
for(i=1;i<=n;i++)cnt[i]+=cnt[i-1];
for(i=1;i<=ce;i++)pool[cnt[e[i].x]--]=i;
for(cur=0,i=1;i<=n;i++)last[i]=0;
for(i=1;i<=ce;i++){
u=pool[i];
single(e[u].x);
if(last[e[u].y]==cur)up(ans[e[u].o],val[e[u].y]+e[u].z);
}
}
}
namespace THREE{
const int MAXQ=Q*2;
int ce,cnt[N],pool[MAXQ];E e[MAXQ];
inline void solve(int o,int x,int y){
for(const auto&A:gr[x])TWO::solve(o,y,A.first,A.second);
for(const auto&A:gr[y])TWO::solve(o,x,A.first,A.second);
e[++ce]=E(o,x,y,0);
cnt[x]++;
e[++ce]=E(o,y,x,0);
cnt[y]++;
}
inline void single(int x){
if(x==cur)return;
cur=x;
for(const auto&A:ga[x])for(const auto&B:gr[A.first]){
int w=A.second+B.second;
update(B.first,w);
for(const auto&C:gr[B.first])update(C.first,w+C.second);
}
}
void run(){
int i,u;
for(i=1;i<=n;i++)cnt[i]+=cnt[i-1];
for(i=1;i<=ce;i++)pool[cnt[e[i].x]--]=i;
for(cur=0,i=1;i<=n;i++)last[i]=0;
for(i=1;i<=ce;i++){
u=pool[i];
single(e[u].x);
if(last[e[u].y]==cur)up(ans[e[u].o],val[e[u].y]);
}
}
}
int main(){
fread(Buf,1,BUF,stdin);read(n);read(m);
for(i=1;i<=m;i++){
read(x);read(y);read(z);
e[i][0]=x,e[i][1]=y,e[i][2]=z;
add(x,y),add(y,x);
}
for(h=i=1;i<=n;i++){
ext(i);
ga[i].reserve(deg[i]);
gr[i].reserve(5);
}
while(h<=t)for(i=g[x=q[h++]];i;i=nxt[i]){
y=v[i];
if(vis[y])continue;
deg[y]--;
ext(y);
}
for(i=1;i<=n;i++)ord[q[i]]=i;
for(i=1;i<=m;i++){
x=e[i][0],y=e[i][1],z=e[i][2];
if(ord[x]>ord[y])swap(x,y);
gr[x].emplace_back(P(y,z));
ga[x].emplace_back(P(y,z));
ga[y].emplace_back(P(x,z));
}
read(cq);
for(i=1;i<=cq;i++){
read(x);read(y);
ans[i]=inf;
THREE::solve(i,x,y);
}
TWO::run();
THREE::run();
for(i=1;i<=cq;i++){
x=ans[i];
if(x==inf)x=-1;
writeln(x);
}
fwrite(Out,1,ou-Out,stdout);
}
D. Operator Precedence
#include "bits/stdc++.h"
using namespace std;
int main()
{
ios::sync_with_stdio(0); cin.tie(0);
int T; cin>>T;
while (T--)
{
int n,i;
cin>>n;
cout<<2*n-3;
for (i=1; i<n; i++) cout<<" 2 -1";
cout<<" 1\n";
}
}
E. Period of a String
#include<bits/stdc++.h>
using namespace std;
int n ;
string s[100005];
struct my_list {
int num[26] , id;
my_list() {
memset(num,0,sizeof(num)) ;
}
}p[100005];
int L[100005];
bool operator < (const my_list &A,const my_list &B) {
return A.id < B.id;
}
void solv() {
cin >> n;
for(int i = 1;i <= n;i++) {
cin >> s[i] ;
memset(p[i].num,0,sizeof(p[i].num)) ;
L[i] = s[i].size() ;
for(int j = 0;j < s[i].size();j++) {
p[i].num[s[i][j] - 'a']++;
}
p[i].id = i;
}
set<pair<int,my_list> > st;
bool ok = 1;
for(int i = n;i >= 1 && ok;i--) {
while(st.size() && (--st.end())->first >= L[i] && ok) {
auto it = st.end() ; it-- ;
int len = it->first ;
my_list k = it->second ;
st.erase(it) ;
int pr = len / L[i] ; len %= L[i] ;
for(int j = 0;j < 26;j++) {
if(k.num[j] < 1LL * p[i].num[j] * pr) {ok = 0 ; break ;} ///有可能爆int，記得卡
k.num[j] -= p[i].num[j] * pr;
}
if(len) st.insert({len , k}) ;
}
st.insert({L[i] , p[i]}) ;
}
if(!ok) {
cout << "NO\n" ; return ;
}
vector<pair<int,my_list> > v(st.begin() , st.end()) ;
string s1 ;
my_list cur ;
for(int i = 0;i < v.size() && ok;i++) {
// printf("%d : " , v[i].first) ;
for(int j = 0;j < 26;j++) {
// printf("%d ",v[i].second.num[j]) ;
if(v[i].second.num[j] >= cur.num[j]) {
for(int k = cur.num[j] + 1 ; k <= v[i].second.num[j] ; k++) s1 += (j + 'a') ;
cur.num[j] = v[i].second.num[j] ;
}
else {ok = 0 ; break ;}
}
// printf("\n") ;
}
if(!ok) {
cout << "NO\n" ; return ;
}
cout << "YES\n" ;
for(int i = 1 ; i <= n;i++) {
cout << s1 << '\n' ;
if(i == n) break ;
if(L[i + 1] < s1.size()) s1.resize(L[i + 1]) ;
else {
int d = s1.size() ;
for(int j = s1.size() ; j < L[i + 1] ; j++) s1 += (s1[j % d]) ;
}
}
return ;
}
int main() {
//freopen("in.txt","r",stdin) ;
ios::sync_with_stdio(false) ; cin.tie(0) ; cout.tie(0) ;
int t;cin >> t;
while(t--) solv() ;
}
F. Top Cluster
#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=500005,K=21;
const int BUF=30000000;
char Buf[BUF],*buf=Buf;
inline void read(int&a){for(a=0;*buf<48;buf++);while(*buf>47)a=a*10+*buf++-48;}
inline void readll(ll&a){for(a=0;*buf<48;buf++);while(*buf>47)a=a*10+*buf++-48;}
const int OUT=7000000;
char Out[OUT],*ou=Out;int Outn[15],Outcnt;
inline void write(int x){
if(!x)*ou++=48;
else{
for(Outcnt=0;x;x/=10)Outn[++Outcnt]=x%10+48;
while(Outcnt)*ou++=Outn[Outcnt--];
}
}
inline void writeln(ll x){write(x);*ou++='\n';}
int n,m,mx,i,j,x,y,z,id[N];
int g[N],v[N<<1],w[N<<1],nxt[N<<1],ed,dfn,loc[N],Log[N<<1];
ll d[N],q[K][N<<1],k;
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){
q[0][loc[x]=++dfn]=d[x];
for(int i=g[x];i;i=nxt[i])if(v[i]!=y){
d[v[i]]=d[x]+w[i];
dfs(v[i],x);
q[0][++dfn]=d[x];
}
}
inline ll lca(int x,int y){
x=loc[x],y=loc[y];
if(x>y)swap(x,y);
int k=Log[y-x+1];
return min(q[k][x],q[k][y-(1<<k)+1]);
}
inline ll dis(int x,int y){return x==y?0:d[x]+d[y]-lca(x,y)*2;}
struct P{
int a,b;ll d;
P(){}
P(int x){a=b=x,d=0;}
void add(int x){
ll now=dis(x,a);
int na=a,nb=b;
if(now>d)d=now,na=a,nb=x;
now=dis(x,b);
if(now>d)d=now,na=b,nb=x;
a=na,b=nb;
}
}dia[N];
inline int ask(int x,ll k){
int ret=mx+1,l=0,r=mx,mid;
while(l<=r){
mid=(l+r)>>1;
if(dis(x,dia[mid].a)>k||dis(x,dia[mid].b)>k)r=(ret=mid)-1;else l=mid+1;
}
return ret;
}
int main(){
fread(Buf,1,BUF,stdin);
read(n);read(m);
for(i=1;i<=n;i++){
read(x);
if(x<n)id[x]=i;
}
for(i=1;i<n;i++){
read(x);read(y);read(z);
add(x,y,z);
add(y,x,z);
}
dfs(1,0);
for(i=2;i<=dfn;i++)Log[i]=Log[i>>1]+1;
for(i=1;i<K;i++)for(j=1;j+(1<<i)-1<=dfn;j++)q[i][j]=min(q[i-1][j],q[i-1][j+(1<<(i-1))]);
for(i=0;i<n;i++){
x=id[i];
if(!x)break;
if(!i)dia[i]=P(x);
else{
dia[i]=dia[i-1];
dia[i].add(x);
}
mx=i;
}
while(m--){
read(x);readll(k);
writeln(ask(x,k));
}
fwrite(Out,1,ou-Out,stdout);
}
G. Snake Move
#include<cstdio>
typedef unsigned long long ull;
const int N=3005,K=100005,inf=~0U>>1;
int n,m,k,i,j,x,y,sx,sy;
int pos[K][2],lim[N][N],f[N][N],h,t,q[N*N][2];
char a[N][N];
inline void ext(int x,int y,int z){
if(x<1||x>n||y<1||y>m)return;
if(a[x][y]=='#')return;
if(z<lim[x][y]){
z=lim[x][y];
if(z<f[x][y])f[x][y]=z;
return;
}
if(z>=f[x][y])return;
f[x][y]=z;
q[++t][0]=x;
q[t][1]=y;
}
inline void branch(int x,int y,int z){
if(f[x][y]!=z)return;
z++;
ext(x-1,y,z);
ext(x+1,y,z);
ext(x,y-1,z);
ext(x,y+1,z);
}
int main(){
scanf("%d%d%d",&n,&m,&k);
scanf("%d%d",&sx,&sy);
for(i=k-1;i;i--){
scanf("%d%d",&x,&y);
lim[x][y]=i;
pos[i][0]=x;
pos[i][1]=y;
}
for(i=1;i<=n;i++)scanf("%s",a[i]+1);
for(i=1;i<=n;i++)for(j=1;j<=m;j++)f[i][j]=inf;
ext(sx,sy,0);
i=1;
while(1){
int f1=inf;
if(h<=t){
x=q[h][0];
y=q[h][1];
f1=f[x][y];
}
int f2=i<k?i:inf;
if(f1==inf&&f2==inf)break;
if(f1<f2){
branch(x,y,f1);
h++;
}else{
branch(pos[i][0],pos[i][1],i);
i++;
}
}
ull ans=0;
for(i=1;i<=n;i++)for(j=1;j<=m;j++){
ull tmp=f[i][j];
//printf("%d%c",f[i][j]==inf?-1:f[i][j],j<m?' ':'\n');
if(tmp==inf)continue;
ans+=tmp*tmp;
}
printf("%llu",ans);
}
H. Sugar Sweet II
#include <bits/stdc++.h>
using namespace std;
int n;
int a[500005] , b[500005] , w[500005];
vector<int> E[500005];
int len[500005];
int st[500005];
bool vis[500005];
void dfs(int u , int d) {
vis[u] = 1; len[u] = d;
for(auto v : E[u]) {
if(!vis[v] && st[v] == 1) dfs(v , d + 1) ;
}
}
int t[500005];
const int mod = 1e9 + 7;
int fpow(int a,int b) {
int ans = 1;
while(b) {
if(b & 1) ans = 1LL * ans * a % mod;
a = 1LL*a*a%mod;b >>= 1;
}
return ans;
}
void solv() {
cin >> n;
for(int i = 1;i <= n;i++) E[i].clear() , len[i] = vis[i] = 0;
for(int i = 1;i <= n;i++) cin >> a[i];
for(int i = 1;i <= n;i++) {
cin >> b[i];
E[b[i]].push_back(i) ;
}
for(int i = 1;i <= n;i++) cin >> w[i];
for(int i = 1;i <= n;i++) {
if(i == b[i] || a[i] >= a[b[i]] + w[b[i]]) st[i] = 0 ; ///不會發生
else if(a[i] >= a[b[i]] && a[i] < a[b[i]] + w[b[i]]) st[i] = 1 ; ///只有父親發生了才能發生
else st[i] = 2 ; ///一定發生
}
for(int i = 1;i <= n;i++) {
if(st[i] == 2) dfs(i , 1) ;
}
t[0] = 1; t[1] = 1;
for(int i = 2;i <= n;i++) t[i] = 1LL * (mod - mod / i) * t[mod % i] % mod;
for(int i = 1;i <= n;i++) t[i] = 1LL * t[i] * t[i - 1] % mod;
for(int i = 1;i <= n;i++) {
if(len[i]) cout << (a[i] + 1LL * t[len[i]] * w[i]) % mod <<' ';
else cout << a[i] <<' ';
}
cout << '\n' ;
}
int main() {
// freopen("in.txt","r",stdin);
ios::sync_with_stdio(false) ; cin.tie(0) ;cout.tie(0) ;
int t ; cin >> t;
while(t--) solv() ;
}
I. Dreamy Putata
#include<cstdio>
#include<algorithm>
using namespace std;
const int N=100005,K=5,M=K*2+3,P=1000000007;
int n,m,cnt,q,i,j,op,sx,sy,ex,ey,inv[101];
int pos[N],pl[N][K],pr[N][K],pu[N][K],pd[N][K];
int val[262155][K*2][M],A[K*2][M],B[K*2][M],C[K*2][M],g[M][M],e[M];
bool flag;
const int BUF=30000000;
char Buf[BUF],*buf=Buf;
inline void read(int&a){for(a=0;*buf<48;buf++);while(*buf>47)a=a*10+*buf++-48;}
inline int po(int a,int b){int t=1;for(;b;b>>=1,a=1LL*a*a%P)if(b&1)t=1LL*t*a%P;return t;}
inline void init(int v[][M],int x){
for(int i=0;i<m;i++){
v[i][i+m]=1;
/*
E[x,i]=(pl[x][i]*E[x,i-1]+pr[x][i]*E[x,i+1]+pu[x][i]*E[x-1,i]+pd[x][i]*E[x+1,i])/100+1
100*E[x,i]=pl[x][i]*E[x,i-1]+pr[x][i]*E[x,i+1]+pu[x][i]*E[x-1,i]+pd[x][i]*E[x+1,i]+100
pd[x][i]*E[x+1,i]=100*E[x,i]-pl[x][i]*E[x,i-1]-pr[x][i]*E[x,i+1]-pu[x][i]*E[x-1,i]-100
pd[x][i]*E[x+1,i]=100*v[i]-pl[x][i]*E[x,i-1]-pr[x][i]*E[x,i+1]-pu[x][i]*E[x-1,i]-100
*/
int _inv=inv[pd[x][i]];
v[i+m][i+m]=100LL*_inv%P;
v[i+m][(i-1+m)%m+m]=1LL*(P-pl[x][i])*_inv%P;
v[i+m][(i+1)%m+m]=1LL*(P-pr[x][i])*_inv%P;
v[i+m][i]=1LL*(P-1LL*pu[x][i])*_inv%P;
v[i+m][cnt+1]=1LL*(P-100)*_inv%P;
}
}
inline void copy(int a[][M],int b[][M]){
for(int i=0;i<cnt;i++)for(int j=0;j<=cnt+1;j++)a[i][j]=b[i][j];
}
inline void merge(int f[][M],int a[][M],int b[][M]){
static int c[K*2][M];
for(int i=0;i<cnt;i++){
for(int j=0;j<=cnt+1;j++)c[i][j]=0;
c[i][cnt+1]=b[i][cnt+1];
for(int j=0;j<cnt;j++)for(int k=0;k<=cnt+1;k++)c[i][k]=(1LL*b[i][j]*a[j][k]+c[i][k])%P;
}
copy(f,c);
}
void build(int x,int a,int b){
if(a==b){
pos[a]=x;
init(val[x],a);
return;
}
int mid=(a+b)>>1;
build(x<<1,a,mid);
build(x<<1|1,mid+1,b);
merge(val[x],val[x<<1],val[x<<1|1]);
}
inline void change(int o){
int x=pos[o];
init(val[x],o);
for(x>>=1;x;x>>=1)merge(val[x],val[x<<1],val[x<<1|1]);
}
void ask(int x,int a,int b,int c,int d){
if(c<=a&&b<=d){
if(!flag)flag=1,copy(B,val[x]);else merge(B,B,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);
}
inline void mul(int v[][M]){
static int f[M];
for(int i=0;i<cnt;i++){
int w=v[i][cnt+1];
for(int j=0;j<=cnt;j++)w=(1LL*v[i][j]*e[j]+w)%P;
f[i]=w;
}
for(int i=0;i<cnt;i++)e[i]=f[i];
}
void cal(int x,int a,int b,int c,int d){
if(c<=a&&b<=d){mul(val[x]);return;}
int mid=(a+b)>>1;
if(c<=mid)cal(x<<1,a,mid,c,d);
if(d>mid)cal(x<<1|1,mid+1,b,c,d);
}
inline void gauss(){
int i,j,k;
for(i=0;i<=cnt;i++){
for(j=i;j<=cnt;j++)if(g[j][i])break;
if(j!=i)for(k=i;k<=cnt+1;k++)swap(g[i][k],g[j][k]);
int inv=po(g[i][i],P-2);
for(j=i+1;j<=cnt;j++){
int t=1LL*g[j][i]*inv%P;
for(k=i;k<=cnt+1;k++)g[j][k]=(g[j][k]-1LL*g[i][k]*t)%P;
}
}
for(i=cnt;~i;i--){
e[i]=g[i][cnt+1];
for(j=i+1;j<=cnt;j++)e[i]=(e[i]-1LL*g[i][j]*e[j])%P;
e[i]=1LL*e[i]*po(g[i][i],P-2)%P;
}
}
inline int query(int sx,int sy,int ex,int ey){
/*
0<=ex<n-1
ask A=[0,ex]
ask B=[ex+1,n-1]
in A:
we know E(ex,ey)=0
but E(ex+1,ey) is not right, set it into itself
then merge C=A+B
in C:
we know the last row, it equals to the first m variables
we know the row after the last row, it equals to the next m variables
then we know the first row, the last row and row ex, row ex+1
if sx<=ex, ask[0,sx], use row first&last to get answer
if sx>ex, ask[ex+1,sx] use row ex..ex+1 to get answer
*/
/*
ex==n-1
ask A=[0,n-1]
we know the last row, it equals to the first m variables
we know the row after the last row, it equals to the next m variables, except the ty-th
we know E(ex,ey)=0
ask[0,sx], use row first&last to get answer
*/
flag=0;
ask(1,0,n-1,0,ex);
copy(A,B);
for(int i=0;i<=cnt+1;i++)A[ey+m][i]=0;
A[ey+m][cnt]=1;
if(ex<n-1){
flag=0;
ask(1,0,n-1,ex+1,n-1);
merge(C,A,B);
}else copy(C,A);
for(int i=0;i<cnt;i++){
for(int j=0;j<=cnt;j++)g[i][j]=C[i][j];
g[i][i]=(g[i][i]-1+P)%P;
g[i][cnt+1]=(P-C[i][cnt+1])%P;
}
for(int i=0;i<=cnt;i++)g[cnt][i]=A[ey][i];
g[cnt][cnt+1]=(P-A[ey][cnt+1])%P;
gauss();
if(sx<=ex)cal(1,0,n-1,0,sx);
else{
static int w[M];
for(int i=0;i<cnt;i++){
w[i]=A[i][cnt+1];
for(int j=0;j<=cnt;j++)w[i]=(1LL*A[i][j]*e[j]+w[i])%P;
}
for(int i=0;i<cnt;i++)e[i]=w[i];
cal(1,0,n-1,ex+1,sx);
}
return (e[sy]%P+P)%P;
}
int main(){
for(inv[0]=inv[1]=1,i=2;i<=100;i++)inv[i]=1LL*(P-inv[P%i])*(P/i)%P;
fread(Buf,1,BUF,stdin);read(n);read(m);
for(i=0;i<n;i++)for(j=0;j<m;j++)read(pl[i][j]);//(i,j-1)
for(i=0;i<n;i++)for(j=0;j<m;j++)read(pr[i][j]);//(i,j+1)
for(i=0;i<n;i++)for(j=0;j<m;j++)read(pu[i][j]);//(i-1,j)
for(i=0;i<n;i++)for(j=0;j<m;j++)read(pd[i][j]);//(i+1,j)
cnt=m*2;
build(1,0,n-1);
read(q);
while(q--){
read(op);read(sx);read(sy);
if(op==1){
read(pl[sx][sy]);read(pr[sx][sy]);read(pu[sx][sy]);read(pd[sx][sy]);
change(sx);
}else{
read(ex);read(ey);
printf("%d\n",query(sx,sy,ex,ey));
}
}
}
J. Mysterious Tree
#include<bits/stdc++.h>
using namespace std;
int n;
int ask(int u,int v) {
cout << "? " << u <<' ' << v << endl ;
int x ; cin >> x;
return x;
}
void solv() {
cin >> n;
int u = -1, v = -1;
for(int i = 1;i + 1 <= n;i += 2) {
if(ask(i , i + 1) == 1) {
u = i ; v = i + 1 ; break ;
}
}
if(n & 1) {
if(ask(n , n - 1)== 1) {
u = n ; v = n - 1;
}
}
if(u == -1) {
cout << "! 1" << endl ; return ;
}
vector<int> vec;
for(int i = 1;i <= n;i++) {
if(i != u && i != v) vec.push_back(i) ;
}
if(!ask(u , vec[0])) {
if(!ask(v , vec[0])) {
cout << "! 1" << endl ; return ;
}
swap(u , v);
}
if(ask(u , vec[1])) {
cout << "! 2" << endl ; return ;
}
cout << "! 1" << endl ; return ;
}
int main () {
int t ; cin >> t;
while(t--) solv() ;
}
K. Card Game
#include<bits/stdc++.h>
using namespace std;
const int N = 3e5 + 5;
int a[N] ;
int ch[N * 60][2] ;
int tag[N * 60] ;
int cnt = 0;
int n , q;
int rt[N] ;
int build(int l,int r) {
int c = ++cnt ;
tag[c] = 0;
if(l == r) return c;
ch[c][0] = build(l , (l + r >> 1)) ;
ch[c][1] = build((l + r >> 1) + 1, r);
return c;
}
int modify(int x,int y,int ql,int qr,int l,int r,int tagx,int tagy) { /// [ql,qr]繼承x , ++ , < ql繼承x ， >qr繼承y
if(ql <= l && r <= qr) {
int c = ++cnt ;
ch[c][0] = ch[x][0];
ch[c][1] = ch[x][1] ;
tag[c] = tag[x] + tagx + 1;
// printf("on %d %d , tag %d\n",l,r,tag[c]) ;
return c;
}
else if(r < ql) {
int c = ++cnt ;
ch[c][0] = ch[x][0];
ch[c][1] = ch[x][1];
tag[c] = tagx + tag[x];
return c;
}
else if(l > qr) {
int c = ++cnt ;
ch[c][0] = ch[y][0];
ch[c][1] = ch[y][1];
tag[c] = tagy + tag[y];
return c;
}
else {
int md = (l + r >> 1) ;
int c = ++cnt ;
ch[c][0] = modify(ch[x][0] , ch[y][0] , ql , qr , l , md , tagx + tag[x] , tagy + tag[y]) ;
ch[c][1] = modify(ch[x][1] , ch[y][1] , ql , qr , md + 1 , r , tagx + tag[x] , tagy + tag[y]) ;
return c;
}
}
int qval(int rt,int pos,int l,int r) {
if(l == r) return tag[rt] ;
int md = (l + r >> 1) ;
if(pos <= md) return tag[rt] + qval(ch[rt][0] , pos , l , md) ;
else return tag[rt] + qval(ch[rt][1] , pos , md + 1, r) ;
}
int nxt[N] ;
int main() {
// freopen("in.txt","r",stdin) ;
// freopen("out2.txt","w",stdout) ;
ios::sync_with_stdio(false) ; cin.tie(0) ;
cin >> n >> q;
for(int i = 1;i <= n;i++) cin >> a[i] ;
for(int i = 1;i <= n;i++) nxt[i] = n + 1;
rt[n + 1] = build(1 , n) ;
for(int i = n;i >= 1;i--) {
// printf("on %d\n" , i) ;
rt[i] = modify(rt[i + 1] , rt[min(n+1 , nxt[a[i]] + 1)] , i , nxt[a[i]] - 1, 1 , n , 0 , 0) ;
nxt[a[i]] = i;
}
// cout << qval(rt[3] , 4 , 1 , n) << '\n' ;
int lans = 0;
while(q--) {
int l , r;
cin >> l >> r;
l ^= lans ; r ^= lans;
cout << (lans = qval(rt[l] , r , 1 , n)) << '\n' ;
}
return 0;
}
L. Master of Both V
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
#define fs first
#define sd second
const int N=5e5+1e3+7;
struct P {
int x,y;
}a[N],b[N];
bool operator <(const P &a,const P &b)
{
return a.x<b.x||(a.x==b.x&&a.y<b.y);
}
bool operator ==(const P &a,const P &b)
{
return !(a<b)&&!(b<a);
}
P operator -(const P &a,const P &b)
{
return {a.x-b.x,a.y-b.y};
}
ll operator *(const P &a,const P &b)
{
return 1ll*a.x*b.y-1ll*a.y*b.x;
}
ll operator ^(const P &a,const P &b)
{
return 1ll*a.x*b.x+1ll*a.y*b.y;
}
using L=pair<P,P>;
int T,n;
L mod[N];
tuple<int,int,int> e[N];
int to[N];
int phase(const P &a)
{
if(a.y!=0)
return a.y<0;
return a.x<0;
}
bool cmp(const P &a,const P &b)
{
int pa=phase(a),pb=phase(b);
if(pa!=pb)
return pa<pb;
return a*b>0;
}
struct T{
L lv,rv;
int ok,cnt;
}t[N*4+1];
bool chk(const L &a,const L &b)
{
if(a==b)
return 1;
P u=a.sd-a.fs,v=b.sd-b.fs,w=b.fs-a.sd;
if(w.x==0&&w.y==0)
return u*v>0;
return (u*w>0||(u*w==0&&(u^w)>0))&&(w*v>0||(w*v==0&&(w^v)>0));
}
void update(int x)
{
if(!t[x<<1].cnt)
t[x]=t[x<<1|1];
else if(!t[x<<1|1].cnt)
t[x]=t[x<<1];
else
{
t[x].lv=t[x<<1].lv,t[x].rv=t[x<<1|1].rv;
t[x].ok=t[x<<1].ok&&t[x<<1|1].ok&&chk(t[x<<1].rv,t[x<<1|1].lv);
t[x].cnt=t[x<<1].cnt+t[x<<1|1].cnt;
}
}
int id[N];
int st[N];
multiset<P> seg[N];
void adj(L &a,L b)
{
ll f=(a.sd-a.fs)*(b.fs-a.fs);
if(f)
{
if(f<0)
swap(a.fs,a.sd);
}
else
{
f=(a.sd-a.fs)*(b.sd-a.fs);
if(f<0)
swap(a.fs,a.sd);
}
}
int m;
void modify(int p,L u)
{
int x=p+m-1;
if(u.fs==u.sd)
t[x].cnt=0;
else
t[x].ok=1,t[x].cnt=1,t[x].lv=t[x].rv=u;
x>>=1;
while(x)
{
update(x);
x>>=1;
}
}
struct MODIFY{
int r;
L u;
int c;
};
vector<MODIFY> ch[N],rch[N];
signed main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cin>>T;
while(T--)
{
cin>>n;
vector<tuple<int,int,int> >X;
for(int i=1;i<=n;i++)
{
string op;
cin>>op;
if(op=="+")
{
cin>>a[i].x>>a[i].y>>b[i].x>>b[i].y;
ll A=a[i].y-b[i].y,B=b[i].x-a[i].x,C=-1ll*b[i].y*a[i].x+1ll*a[i].y*b[i].x;
ll g=__gcd(__gcd(A,B),C);
A/=g,B/=g,C/=g;
if(A<0||(A==0&&B<0))
A*=-1,B*=-1,C*=-1;
g=abs(__gcd(A,B));
e[i]={A,B,C};
X.push_back(e[i]);
}
else
{
cin>>a[i].x;
a[i].y=0;
b[i]=a[i];
}
}
sort(X.begin(),X.end());
X.erase(unique(X.begin(),X.end()),X.end());
for(int i=1;i<=X.size();i++)
seg[i].clear(),st[i]=0;
for(int i=1;i<=n;i++)
ch[i].clear(),rch[i].clear();
for(int i=1;i<=n;i++)
{
if(a[i]==b[i])
{
int x=id[a[i].x];
id[i]=x;
int j=a[i].x;
seg[x].erase(seg[x].find(a[j]));
seg[x].erase(seg[x].find(b[j]));
ch[st[x]].push_back({i-1,mod[st[x]],x});
if(!seg[x].size())
st[x]=0;
else
st[x]=i,mod[i]={*seg[x].begin(),*--seg[x].end()};
}
else
{
id[i]=lower_bound(X.begin(),X.end(),e[i])-X.begin()+1;
int x=id[i];
seg[x].insert(a[i]),seg[x].insert(b[i]);
mod[i]={*seg[x].begin(),*--seg[x].end()};
if(st[x])
ch[st[x]].push_back({i-1,mod[st[x]],x});
st[x]=i;
}
}
for(int i=1;i<=X.size();i++)
if(st[i])
{
ch[st[i]].push_back({n,mod[st[i]],i});
mod[n+1]=mod[st[i]];
}
MODIFY mx,smx,rem;
mx.r=smx.r=-1;
rem.c=-1;
for(int i=1;i<=n;i++)
{
if(!ch[i].size())
continue;
if(rem.c!=-1)
{
if(rem.r>=i)
ch[i].push_back(rem);
rem.c=-1;
}
sort(ch[i].begin(),ch[i].end(),[&](const MODIFY &u,const MODIFY &v){return u.r>v.r;});
for(auto [r,u,c]:ch[i])
{
MODIFY v={r,u,c};
if(v.r>mx.r)
swap(mx,v);
if(v.r>smx.r)
swap(smx,v);
if(mx.c==smx.c)
swap(v,smx);
}
for(auto [r,u,c]:ch[i])
{
MODIFY dir;
if(mx.c!=c)
dir=mx;
else if(smx.c!=c)
dir=smx;
else
dir.c=-1;
if(dir.c==-1||dir.r<i)
rem={r,u,c};
else
{
adj(u,dir.u);
rch[i].push_back({min(dir.r,r),u,c});
if(dir.r<r)
ch[dir.r+1].push_back({r,u,c});
}
}
}
vector<P> v;
for(int i=1;i<=n;i++)
for(auto [r,u,c]:rch[i])
v.push_back({u.sd-u.fs});
sort(v.begin(),v.end(),cmp);
vector<int> ct(v.size());
for(int i=1;i<=n;i++)
ch[i].clear();
for(int i=1;i<=n;i++)
for(auto [r,u,c]:rch[i])
{
int p=lower_bound(v.begin(),v.end(),u.sd-u.fs,cmp)-v.begin();
++ct[p];
ch[i].push_back({p+ct[p],u,c});
ch[r+1].push_back({-(p+ct[p]),u,c});
}
m=1;
while(m<v.size())
m<<=1;
for(int i=1;i<=m*2-1;i++)
t[i].cnt=0,t[i].ok=1;
for(int i=1;i<=n;i++)
{
for(auto [r,u,c]:ch[i])
{
if(r>0)
modify(r,u);
else
modify(-r,{{0,0},{0,0}});
}
if(t[1].cnt<=1||(t[1].ok&&chk(t[1].rv,t[1].lv)))
cout<<1;
else
cout<<0;
}
cout<<"\n";
}
}
M. V-Diagram
#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
using f64 = double_t;
int main() {
cin.tie(nullptr)->sync_with_stdio(0);
cout << fixed << setprecision(20);
int t;
cin >> t;
for (int ti = 0; ti < t; ti += 1) {
int n;
cin >> n;
vector<i64> a(n);
for (i64& ai : a) { cin >> ai; }
int m = min_element(a.begin(), a.end()) - a.begin();
for (int i = 1; i < n; i += 1) { a[i] += a[i - 1]; }
f64 ans = 0;
ans = max(ans, (f64)a.back() / n);
ans = max(ans, ((f64)a.back() - (m > 1 ? a[m - 2] : 0)) / (n - m + 1));
ans = max(ans, (f64)a[m + 1] / (m + 2));
cout << ans << "\n";
}
}