题解：
https://files.cnblogs.com/files/clrs97/2024_Hong_Kong_Tutorial.pdf
Code：
A. General Symmetry
// floating point errors
#pragma GCC optimize("Ofast,unroll-loops")// safe
// #pragma GCC optimize("O3,unroll-loops")// doesn't work in yandex
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")// doesn't work in some judges
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt,tune=native")// safe
// #pragma GCC target("sse4.2,bmi,bmi2,lzcnt,popcnt")
#include<iostream>
#include<bitset>
#include<algorithm>
using namespace std;
const int N=200005,V=1000,K=5;
int n,m,k,i,l,r,a[N];
struct BIT{unsigned long long v[(N>>6)+1];bool get(int x)const{return v[x>>6]>>(x&63)&1;}void set(int x){v[x>>6]|=1ULL<<(x&63);}void operator^=(const BIT&o){for(int i=0;i<=m;i++)v[i]^=o.v[i];}void operator=(const BIT&o){for(int i=0;i<=m;i++)v[i]=o.v[i];}void shiftand(const BIT&o){for(int i=0;i<m;i++)v[i]=((v[i]>>1)+((v[i+1]&1)<<63))&o.v[i];v[m]=(v[m]>>1)&o.v[m];}
}occ[V+1],mask[V+1],f,save[(N>>K)+1];
inline int myabs(int x){return x>0?x:-x;}
inline bool check(int l,int r){return myabs(a[l]-a[r])<=k;}
inline int ask(int A,int B){if(!check(A,B))return 0;int l=((B-1)>>K)+1,r=n>>K,mid,t=0;while(l<=r){mid=(l+r)>>1;int d=(mid<<K)-B;if(A-d>=1&&save[mid].get(A-d))l=mid+1,t=d;else r=mid-1;}A-=t,B+=t;while(A>1&&B<n&&check(A-1,B+1))A--,B++;return B-A+1;
}
int main(){ios_base::sync_with_stdio(0);cin.tie(0);cin>>n>>k;m=n>>6;for(i=1;i<=n;i++)cin>>a[i];for(i=1;i<=n;i++)occ[a[i]].set(i);for(i=2;i<=V;i++)occ[i]^=occ[i-1];for(i=1;i<=V;i++){l=max(i-k,1);r=min(i+k,V);mask[i]=occ[r];mask[i]^=occ[l-1];}for(i=1;i<=n;i++){m=i>>6;f.shiftand(mask[a[i]]);f.set(i);if(i>1&&check(i-1,i))f.set(i-1);if(!(i&((1<<K)-1)))save[i>>K]=f;}for(i=1;i<=n;i++){cout<<ask(i,i);if(i<n)cout<<" ";else cout<<"\n";}for(i=1;i<n;i++){cout<<ask(i,i+1);if(i+1<n)cout<<" ";else cout<<"\n";}
}
B. Defeat the Enemies
#include <bits/stdc++.h>
using namespace std;
int n , m;
int a[500005] , b[500005];
const int mod = 998244353;
typedef long long ll;
void upd(int &x,int y) {((x += y) >= mod ? (x -= mod) : 0) ;
}
int c[105] , k;
void solv() {cin >> n >> m;int mx = 0;for(int i = 1;i <= n;i++) cin >> a[i]; for(int i = 1;i <= n;i++) cin >> b[i]; cin >> k;for(int i = 1;i <= k;i++) cin >> c[i];for(int i = 1;i <= n;i++) mx = max(mx , a[i] + b[i]) ;vector<int> h(mx + k*2 + 1 , 1e9) ;for(int i = 1;i <= n;i++) {int x = mx - (a[i] + b[i]) ;h[b[i] - 1] = min(h[b[i] - 1] , b[i] + x) ;}for(int i = mx + k*2 - 1; i >= 0;i--) h[i] = min(h[i] , h[i + 1]) ;vector<ll> f(mx + k*2 + 1) ;vector<int> g(mx + k*2 + 1) ;ll ans = 1e18;int cnt = 0;for(int d = 0 ; d <= k * 2 - 2 ; d++) {for(auto &x : f) x = 1e18;for(auto &x : g) x = 0;f[0] = 0; g[0] = 1;for(int i = 0 ;i < mx + d ; i++) {for(int j = 1 ; j <= k && i + j <= mx + d && i + j <= h[i] + d ; j++) {if(f[i + j] > f[i] + c[j]) {f[i + j] = f[i] + c[j] ;g[i + j] = g[i] ;}else if(f[i + j] == f[i] + c[j]) {upd(g[i + j] , g[i]) ;}}}if(f[mx + d] < ans) {ans = f[mx + d]; cnt = g[mx + d] ;}else if(f[mx + d] == ans) upd(cnt , g[mx + d]) ;}cout << ans <<' ' << cnt << '\n' ;return ;
}
int main() {ios::sync_with_stdio(false) ; cin.tie(0) ;int t ; cin >> t;while(t--) solv() ;
}
C. The Story of Emperor Bie
#include <bits/stdc++.h>
using namespace std;
int p[500005];
int n ;
void solv() {cin >> n;for(int i = 1;i <= n;i++) cin >> p[i] ;int mx = *max_element(p + 1 , p + n + 1) ;for(int i = 1;i <= n;i++) {if(p[i] == mx) cout << i <<' ' ;}cout << '\n';
}
int main() {ios::sync_with_stdio(false) ; cin.tie(0) ;int t ; cin >> t;while(t--) solv() ;
}
D. Master of Both VI
#include<bits/stdc++.h>
using namespace std;using ll=int;const int N=5e5+1e3+7,Q=3e5+1e3+7;int n,q,fa[N];vector<int> g[N];struct Mat {ll f00,f01,f10,f11;
};struct Vec {ll f0,f1;ll gmn(){return min(f0,f1);}
};Vec operator *(const Mat &a,const Vec &b)
{return {min(a.f00+b.f0,a.f01+b.f1),min(a.f10+b.f0,a.f11+b.f1)};
}Mat operator *(const Mat &a,const Mat &b)
{return {min(a.f00+b.f00,a.f01+b.f10),min(a.f00+b.f01,a.f01+b.f11),min(a.f10+b.f00,a.f11+b.f10),min(a.f10+b.f01,a.f11+b.f11)};
}struct T {int ls,rs,cnt;Mat v;
}t[Q*2*19];int st[20][N],dfn[N],dc;void dfs(int x,int f)
{fa[x]=f;st[0][dc]=f;dfn[x]=++dc;for(auto v:g[x]){if(v==f)continue;dfs(v,x);}
}int mn(int x,int y)
{return dfn[x]<dfn[y]?x:y;
}int lca(int x,int y)
{if(dfn[x]>dfn[y])swap(x,y);int k=__lg(dfn[y]-dfn[x]);return x!=y?mn(st[k][dfn[x]],st[k][dfn[y]-(1<<k)]):x;
}vector<int> add[N],qr[N];int rt[N],cnt;ll w[Q];void update(int x)
{t[x].cnt=t[t[x].ls].cnt+t[t[x].rs].cnt;if(!t[x].cnt)return;else if(!t[t[x].ls].cnt)t[x].v=t[t[x].rs].v;else if(!t[t[x].rs].cnt)t[x].v=t[t[x].ls].v;elset[x].v=t[t[x].ls].v*t[t[x].rs].v;
}Mat Z={0,(ll)1e9,(ll)1e9,0};void ins(int &x,int l,int r,int p,int v)
{if(!x)x=++cnt;if(l==r){if(v>0){t[x].cnt=1;t[x].v={w[l]*2,w[l],w[l]*2,w[l]*2};}else{t[x].cnt=0;t[x].v=Z;}return;}int mid=(l+r)>>1;if(p<=mid)ins(t[x].ls,l,mid,p,v);elseins(t[x].rs,mid+1,r,p,v);update(x);
}int merge(int x,int y,int l,int r)
{if(!x||!y)return x+y;if(l==r)return t[x].cnt?x:y;int mid=(l+r)>>1;t[x].ls=merge(t[x].ls,t[y].ls,l,mid);t[x].rs=merge(t[x].rs,t[y].rs,mid+1,r);update(x);return x;
}int fd;int qry(int x,int l,int r,int p,Vec &u,ll h)
{if(r<=p){auto ru=t[x].v*u;if(ru.gmn()<h){u=ru;return t[x].cnt;}}if(l==r){fd=1;return 0;}int mid=(l+r)>>1;int ret=0;if(p>mid&&t[t[x].rs].cnt)ret=qry(t[x].rs,mid+1,r,p,u,h);if(!t[t[x].ls].cnt||fd)return ret;ret+=qry(t[x].ls,l,mid,p,u,h);return ret;
}int ans[Q];void getans(int x)
{for(auto v:g[x]){if(v==fa[x])continue;getans(v);rt[x]=merge(rt[x],rt[v],1,q);}for(auto id:add[x])ins(rt[x],1,q,abs(id),id);for(auto id:qr[x]){Vec u={0,0};fd=0;ans[id]=qry(rt[x],1,q,id,u,w[id]*2);}
}signed main()
{ios::sync_with_stdio(false);cin.tie(0);t[0].v=Z;cin>>n>>q;for(int i=1;i<n;i++){int u,v;cin>>u>>v;g[u].push_back(v);g[v].push_back(u);}dfs(1,0);for(int i=1;i<20;i++)for(int j=1;j+(1<<i)-1<n;j++)st[i][j]=mn(st[i-1][j],st[i-1][j+(1<<i-1)]);memset(ans,-1,sizeof(ans));for(int i=1;i<=q;i++){string op;cin>>op;if(op[0]=='A'){int u,v;cin>>u>>v>>w[i];int p=lca(u,v);add[u].push_back(i);add[v].push_back(i);add[fa[p]].push_back(-i);}else{int x;cin>>x>>w[i];qr[x].push_back(i);}}getans(1);for(int i=1;i<=q;i++)if(ans[i]!=-1)cout<<ans[i]<<"\n";
}
E. Concave Hull
#include<bits/stdc++.h>
using namespace std;
const int N=2505;
typedef long long ll;
const int mod=1e9+7;
int n,ans;
bool on[N];
struct Point{int x,y,id;Point(int _x=0,int _y=0,int _id=-1):x(_x),y(_y),id(_id){}friend Point operator - (const Point &a,const Point &b){return Point(a.x-b.x,a.y-b.y);}friend Point operator + (const Point &a,const Point &b){return Point(a.x+b.x,a.y+b.y);}friend ll operator % (const Point &a,const Point &b){return 1LL*a.x*b.y-1LL*a.y*b.x;}friend bool operator < (const Point &a,const Point &b){return a.y==b.y?a.x<b.x:a.y<b.y;}inline ll len2(){return 1LL*x*x+1LL*y*y;}inline int Quad(){return y>0||(y==0&&x>0);}
};
typedef vector<Point> poly;
inline bool Left(Point a,Point b){return b%a>0;
}
poly A;
int Area(poly A){int m=A.size();int tot=0;for(int i=0;i<m;++i){tot=(tot+(A[i]%A[(i+1)%m]))%mod;}tot=(tot+mod)%mod;return tot;
}
void calc(poly B){sort(B.begin(),B.end(),[&](Point a,Point b){return a.Quad()^b.Quad()?a.Quad()>b.Quad():Left(b,a);});for(int i=0;i<(int)B.size();++i){if(on[B[i].id]){rotate(B.begin(),B.begin()+i,B.end());break;}}B.push_back(B[0]);int cnt=0;poly st;ll now=0;for(auto &p:B){while(st.size()>1&&Left(st.back()-st[st.size()-2],p-st[st.size()-2])){now=(now-(st[st.size()-2]%st.back()))%mod;st.pop_back();}if(st.size()>0){now=(now+(st.back()%p))%mod;}st.push_back(p);++cnt;if(on[p.id]){if(st.size()>1){ans=(ans+cnt*((st[st.size()-2]%st.back())%mod))%mod;}cnt=0;now=0;}ans=(ans-now)%mod;}reverse(B.begin(),B.end());now=0;for(auto &p:B){while(st.size()>1&&Left(p-st[st.size()-2],st.back()-st[st.size()-2])){now=(now-(st.back()%st[st.size()-2]))%mod;st.pop_back();}if(st.size()>0){now=(now+(p%st.back()))%mod;}st.push_back(p);if(on[p.id]){now=0;}ans=(ans-now)%mod;}
}
int main(){ios::sync_with_stdio(false);cin.tie(0);cin>>n;A.resize(n);for(int i=0;i<n;++i){cin>>A[i].x>>A[i].y;A[i].id=i;}Point LTL=*min_element(A.begin(),A.end());sort(A.begin(),A.end(),[&](Point a,Point b){a=a-LTL;b=b-LTL;if((a%b)==0)return a.len2()<b.len2();return Left(b,a);});poly st;for(auto &p:A){while(st.size()>1&&Left(st.back()-st[st.size()-2],p-st[st.size()-2])){st.pop_back();}st.push_back(p);}for(auto &p:st){on[p.id]=1;}for(auto &t:A){if(on[t.id])continue;poly B;for(auto &p:A){if(p.id!=t.id){B.push_back(p-t);B.back().id=p.id;}}calc(B);}ans=(ans+mod)%mod;ans=(1LL*(n-1)*(n-((int)st.size()))%mod*Area(st)%mod-ans+mod)%mod;cout<<ans<<'\n';return 0;
}
F. Money Game 2
#include<bits/stdc++.h>
using namespace std;using pii=pair<int,int>;const int N=5e5+1e3+7;int T,n,a[N];vector<pii> L[N],R[N];int chk(int a,int b,int c,int d)
{if(a>b)return chk(a,n-1,c,d)&&chk(0,b,c,d);if(c>d)return chk(a,b,c,n-1)&&chk(a,b,0,d);return a>d||c>b;
}int main()
{ios::sync_with_stdio(false);cin.tie(0);cin>>T;while(T--){cin>>n;for(int i=0;i<n;i++)cin>>a[i],L[i].clear(),R[i].clear();if(n==1){cout<<a[0]<<"\n";continue;}for(int r=0;r<n*2;r++){int i=r%n;auto tmp=L[(i+n-1)%n];if(tmp.size()&&tmp.begin()->second==i)tmp.erase(tmp.begin());tmp.push_back({0,i});L[i].clear();reverse(tmp.begin(),tmp.end());for(auto [x,y]:tmp){if(!L[i].size()||x/2+a[i]!=L[i].back().first)L[i].push_back({x/2+a[i],y});}reverse(L[i].begin(),L[i].end());}for(int r=n*2-1;r>=0;r--){int i=r%n;auto tmp=R[(i+1)%n];if(tmp.size()&&tmp.begin()->second==i)tmp.erase(tmp.begin());tmp.push_back({0,i});R[i].clear();reverse(tmp.begin(),tmp.end());for(auto [x,y]:tmp){if(!R[i].size()||x/2+a[i]!=R[i].back().first)R[i].push_back({x/2+a[i],y});}reverse(R[i].begin(),R[i].end());}for(int i=0;i<n;i++){long long ans=0;ans=max(ans,1ll*R[i][0].first);for(int j=0,k=(int)R[i].size()-1;j+1<L[i].size();j++){while(k>0&&chk(L[i][j].second,(i+n-1)%n,(i+1)%n,R[i][k-1].second))k--;ans=max(ans,1ll*R[i][k].first+L[i][j].first-a[i]);}cout<<ans<<" \n"[i+1==n];}}
}
G. Yelkrab
#include<bits/stdc++.h>
using namespace std;const int N=1e6+1e3+7;int T,n,sz[N];vector<int> fac[N];int son[N][26],ans[N];string s[N];int t;int main()
{ios::sync_with_stdio(false);cin.tie(0);for(int i=1;i<=500000;i++)for(int j=i;j<=500000;j+=i)fac[j].push_back(i);cin>>T;while(T--){cin>>n;memset(son[0],-1,sizeof(son[0]));t=0;for(int i=1;i<=n;i++)ans[i]=0;int ANS=0;for(int i=1;i<=n;i++){string s;cin>>s;int x=0;for(auto c:s){c-='a';if(son[x][c]==-1){son[x][c]=++t;sz[t]=0;memset(son[t],-1,sizeof(son[t]));}x=son[x][c];sz[x]++;for(auto p:fac[sz[x]]){ANS^=ans[p]*p;ans[p]++;ANS^=ans[p]*p;}}cout<<ANS<<" \n"[i==n];}}
}
H. Mah-jong
#include <bits/stdc++.h>
using namespace std;
const int D = 8;
vector<int> g(D - 2) ;
typedef vector<int> vi;
typedef long long ll;vector<pair<vi,vi> > t;
void dfs(int u) {if(u == D - 2) {vector<int> v(D) , lm(D);for(int i = 0;i < D - 2;i++) {v[i] += g[i];v[i + 1] += g[i];v[i + 2] += g[i];}for(int i = 0;i < D;i++) {lm[i] = v[i] ;v[i] %= 3;}t.push_back({v , lm}) ;return ;}for(int i = 0;i < 3;i++) {g[u] = i;dfs(u + 1);}
}
int n;
int a[100005];
int pre[100005][D];
int fir[D][100005];
const int D3 = 6561;
typedef pair<int,int> pii;
vector<int> tr(D);
void solv() {cin >> n;for(int i = 1;i <= n;i++) {cin >> a[i] ; a[i]-- ;}for(int i = 1;i <= n;i++ ) {for(int j = 0;j < D;j++) {pre[i][j] = pre[i - 1][j];}fir[a[i]][pre[i][a[i]]] = i - 1; /// for num ai , the last one with <= jpre[i][a[i]]++ ;}for(int j = 0;j < D;j++) fir[j][pre[n][j]] = n;ll ans = 0;for(auto &[v,lm] : t) {vector<int> pre(D) , pv(D);for(int j = 0;j < D;j++) pre[j] = ::pre[n][j] ;int d = 0;for(int j = 0;j < D;j++) {pv[j] = (pre[j] - v[j] + 3) % 3;d += pv[j] * tr[j] ;}vector<pii> qry;int r = n + 1;for(int j = 0;j < D;j++) {if(pre[j] < lm[j]) r = -1;else r = min(r , fir[j][pre[j] - lm[j]]) ;}if(r == -1) continue ;for(int i = n;i >= 1;i--) {r = min(r , i - 1);if(r != -1) {qry.push_back({r , d}) ;}d -= pv[a[i]] * tr[a[i]] ;pv[a[i]]-- ;if(pv[a[i]] < 0) pv[a[i]] += 3;d += pv[a[i]] * tr[a[i]] ;pre[a[i]]-- ;if(pre[a[i]] < lm[a[i]]) {r = -1; break ;}else r = min(r , fir[a[i]][pre[a[i]] - lm[a[i]]]) ;}reverse(qry.begin() , qry.end()) ;vector<int> sum(D) , num(D3);int hs = 0;int nxt = 0;for(int i = 0;i <= n;i++) {if(i) {hs -= sum[a[i]] * tr[a[i]] ;sum[a[i]] = (sum[a[i]] + 1) % 3;hs += sum[a[i]] * tr[a[i]] ;}num[hs]++ ;while(nxt < qry.size() && qry[nxt].first <= i) {ans += num[qry[nxt].second] ;nxt++ ;}}}cout << ans << '\n';return ;
}
int main() {ios::sync_with_stdio(false) ; cin.tie(0) ;dfs(0) ;tr[0] = 1;for(int i = 1;i < D;i++) tr[i] = tr[i - 1] * 3;int t ; cin >> t;while(t--) solv() ;
}
I. Ma Meilleure Ennemie
#include<bits/stdc++.h>
using namespace std;
#define int long long
namespace Pollard_Rho {mt19937 rd(time(0));inline int A(int x, int p) { return x >= p ? x - p : x; }inline int D(int x, int p) { return x < 0 ? x + p : x; }inline int Mul(int x, int y, int p) {return D(A(x * y - (int)((long double)x * y / p) * p, p), p);}inline int Qpow(int x, int y, int p) {int ans = 1;for (; y; y >>= 1, x = Mul(x, x, p)) if (y & 1) ans = Mul(ans, x, p);return ans;}inline bool Mr(int x, int b) {int k = x - 1;while (k) {int cur = Qpow(b % x, k, x);if (cur != 1 && cur != x - 1) return 0;if ((k & 1) || cur == x - 1) return 1;k >>= 1;}return 1;}int p[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};inline bool IsPrime(int n) {if (n <= 1 || n == 46856248255981ll) return 0;for(int i = 0; i < 7; i++) {if(p[i] % n == 0)continue;if(n == p[i])return 1;if(!Mr(n, p[i]))return 0;}return 1;// if (n == 2 || n == 61) return 1;// return Mr(n, 2) && Mr(n, 61);}inline int Pr(int x) {int s = 0, t = 0, c = rd() % (x - 1) + 1;int stp = 0, goal = 1;int val = 1;for (goal = 1; ; goal <<= 1, s = t, val = 1) {for (stp = 1; stp <= goal; ++stp) {t = A(Mul(t, t, x) + c, x);val = Mul(val, abs(t - s), x);if ((stp & 127) == 0) {int d = __gcd(val, x);if (d > 1) return d;}}int d = __gcd(val, x);if (d > 1) return d;}}inline void Divide(int n, map<int, int> &ans) {if (n <= 1) return;if (IsPrime(n)) return void(++ans[n]);int x = n;while (x == n) x = Pr(n);Divide(x, ans); Divide(n / x, ans);}inline map<int, int> Factor(int x) {map<int, int> ans;Divide(x, ans);return ans;}
}int n, m;vector<int> fac, id, wid;const int P = 998244353;vector<int> prod;int qpow(int a, int b) {b %= P - 1;int ret = 1;while(b) {if(b & 1)ret = ret * a % P;b >>= 1; a = a * a % P;}return ret;
}signed main() {cin >> n >> m;if(n == 1) {cout << m % P << "\n";return 0;}auto tmp = Pollard_Rho::Factor(n);for(auto [x, y] : tmp)fac.push_back(x);prod.resize(1 << fac.size(), 1);wid.resize(prod.size());id.resize(fac.size());id[0] = 1;for(int i = 1; i < fac.size(); i += 1)id[i] = id[i - 1] * (tmp[fac[i - 1]] + 1);for(int S = 0; S < (1 << fac.size()); S += 1) for(int i = 0; i < fac.size(); i += 1)if(S >> i & 1)prod[S] *= fac[i], wid[S] += id[i];int ID = 0;for(int i = 0; i < fac.size(); i += 1)ID += id[i] * tmp[fac[i]];vector<int> dp(ID + 1, 0), wn(ID + 1, 0), wm(ID + 1, 0);wn[ID] = n, wm[ID] = m;for(int i = ID; i >= 0; i -= 1) {for(int j = 0; j < fac.size(); j += 1) {if(wn[i] % fac[j] == 0) {wn[i - id[j]] = wn[i] / fac[j];wm[i - id[j]] = wm[i] / fac[j];}}}for(int i = 0; i <= ID; i += 1) {int T = 0;for(int j = 0; j < fac.size(); j += 1)if(wn[i] % fac[j] == 0)T ^= 1 << j;int ret = 0;for(int S = T;;S = (S - 1) & T) {int mu = __builtin_parity(S) ? -1 : 1;int e = prod[S];ret += mu * (wm[i] / e);if(S) {ret -= mu * qpow(dp[i - wid[S]], e);}if(!S)break;}dp[i] = (ret % P + P) % P;}cout << dp[ID] << "\n";return 0;
}
J. Reconstruction
#include<bits/stdc++.h>
using namespace std;
const int N=500050;
int n,ok[N];
vector<int> G[N],H[N];
struct Union_Set{int f[N];void init(int n){for(int i=1;i<=n;++i){f[i]=i;}}inline int getf(int x){return f[x]==x?x:f[x]=getf(f[x]);}
}S;
int vis[N];
int dfs(int u,int fa){for(auto v:H[u]){if(v==fa)continue;int x=dfs(v,u);if(x)return x;}for(auto v:G[u]){vis[S.getf(v)]=u;}for(auto v:H[u]){if(v==fa)continue;if(vis[v]!=u)return v;S.f[S.getf(v)]=u;}return 0;
}
int main(){ios::sync_with_stdio(false);cin.tie(0);cin>>n;for(int i=1;i<n;++i){int u,v;cin>>u>>v;G[u].push_back(v);G[v].push_back(u);}for(int i=1;i<n;++i){int u,v;cin>>u>>v;H[u].push_back(v);H[v].push_back(u);}S.init(n);int rt=dfs(1,0),OK=0;if(!rt)rt=1,OK=1;memset(vis,0,sizeof(vis));S.init(n);if(OK||!dfs(rt,0)){memset(vis,0,sizeof(vis));queue<int> q;q.push(rt);ok[rt]=1;while(!q.empty()){int u=q.front();q.pop();for(auto v:G[u]){vis[v]=u;}for(auto v:H[u]){if(vis[v]&&!ok[v]){ok[v]=1;q.push(v);}}}}for(int i=1;i<=n;++i){cout<<ok[i];}cout<<'\n';return 0;
}
K. LR String
#include <bits/stdc++.h>
using namespace std;
string s ;
int q;
const int N = 5e5 + 5;
int nxt[N][2];
const int inf = 1e9;
void solv() {cin >> s >> q;int c[2] = {inf , inf} ;for(int i= s.size() - 1;i >= 0;i--) {nxt[i][0] = c[0];nxt[i][1] = c[1];if(s[i] == 'L') c[0] = i;else c[1] = i;}while(q--) {string t ; cin >> t;if(s[0] == 'L' && t[0] != 'L') {cout << "NO\n"; continue ;}if(s.back() == 'R' && t.back() != 'R') {cout << "NO\n" ; continue ;}bool ff = 1;int u = (t[0] == 'L' ? c[0] : c[1]);for(int i = 1;i < t.size();i++) {if(u >= s.size()) {ff = 0 ; break ;}if(t[i] == 'L') u = nxt[u][0];else u = nxt[u][1] ;if(u >= s.size()) {ff = 0 ; break ;}}cout << (ff ? "YES\n" : "NO\n") ;}return ;
}
int main() {ios::sync_with_stdio(false) ; cin.tie(0) ;int t ; cin >> t;while(t--) solv() ;
}
L. Flipping Paths
#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;vector<string> s(n+5);for(int i=1;i<=n;i++){string t;cin>>t;s[i]=' '+t;}if(n==1 and m==1){cout<<"YES\n0\n";continue;}if(n==3 and m==3 and s[1]==" WBB" and s[2]==" BWB" and s[3]==" BBW"){cout<<"YES\n2\nRRDD\nDDRR\n";continue;}if(n==2 and m==2 and s[1]==" BB" and s[2]==" BB"){cout<<"YES\n0\n";continue;}if(n==1 and m==5 and s[1]==" WWWWW"){cout<<"YES\n0\n";continue;}vector<string> ans;int ok=0;auto tmp=s;auto flip=[&](char &ch){ch='B'+'W'-ch;};for(auto ch:"BW"){s=tmp;ans.clear();for(int diag=m-2;diag>=1-n;diag--)//y-x{string op;int x=1,y=1;while(y-x<diag)flip(s[x][y]),y++,op+='R';while(y-x>diag)flip(s[x][y]),x++,op+='D';while(x<n and y<m){if(s[x][y+1]!=ch){flip(s[x][y]),y++,op+='R';flip(s[x][y]),x++,op+='D';}else{flip(s[x][y]),x++,op+='D';flip(s[x][y]),y++,op+='R';}}while(y<m)flip(s[x][y]),y++,op+='R';while(x<n)flip(s[x][y]),x++,op+='D';flip(s[x][y]);ans.push_back(op);if(diag<=2-n){int done=1;for(int i=1;i<=n;i++){for(int j=1;j<=m;j++){if(s[i][j]!=ch)done=0;}}if(done){ok=1;break;}}}if(ok)break;}if(ok){cout<<"YES\n"<<ans.size()<<endl;for(auto row:ans)cout<<row<<endl;}else{cout<<"NO\n";}}return 0;
}
M. Godzilla
#include<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
typedef pair<int,int>P;
typedef unsigned short U;
const int N=77,M=N*2,K=8,CE=N*N;
int n,m,ce,i,j,optd,optv,opt[4],f[M];
int maxd[4],two[4],twoedges[4],edge[3][3][4][2],extra[3][4];
struct E{int x,y,d,v;bool ban;}e[CE];
struct Basis{int f,s,d,v;bool oncircle,del;
}basis[M];
vector<int>adj[M];
int dfn,st[M],en[M],ccom,at[M],root[M],cir[M],delid[3];
struct Ranges{vector<P>seg;int r,nxt;void init(int _l,int _r){seg.clear();r=_r;nxt=_l;}void append(int l,int r){if(nxt<l)seg.emplace_back(P(nxt,l-1));nxt=r+1;}void finish(){if(nxt>r)return;seg.emplace_back(P(nxt,r));}bool find(int x)const{for(const auto&it:seg)if(it.first<=x&&x<=it.second)return 1;return 0;}void addtotree(vector<P>&v){for(const auto&it:seg)v.emplace_back(it);}
};
U top[4],top2[4][2];int Log[M];
inline void upu(U&a,U b){a<b?(a=b):0;}
struct RMQ{U f[K][M][4][2];void init(){for(int i=1;i<=n;i++)for(int j=0;j<4;j++)for(int k=0;k<2;k++)f[0][i][j][k]=0;}void build(){for(int i=1;(1<<i)<=n;i++)for(int j=1;j+(1<<i)-1<=n;j++)for(int k=0;k<4;k++){const auto&A=f[i-1][j][k];const auto&B=f[i-1][j+(1<<(i-1))][k];auto&C=f[i][j][k];if(A[0]>B[0]){C[0]=A[0];C[1]=max(A[1],B[0]);}else if(A[0]<B[0]){C[0]=B[0];C[1]=max(A[0],B[1]);}else{C[0]=A[0];C[1]=max(A[1],B[1]);}}}void fetchtop(const P&seg)const{int k=Log[seg.second-seg.first+1];const auto&L=f[k][seg.first];const auto&R=f[k][seg.second-(1<<k)+1];for(int i=0;i<4;i++){upu(top[i],L[i][0]);upu(top[i],R[i][0]);}}void fetchtop2(const P&seg)const{int k=Log[seg.second-seg.first+1];const auto&L=f[k][seg.first];const auto&R=f[k][seg.second-(1<<k)+1];for(int i=0;i<4;i++){const auto&A=L[i];const auto&B=R[i];auto&C=top2[i];if(C[0]>=A[0]&&C[0]>=B[0]){upu(C[1],A[A[0]==C[0]]);upu(C[1],B[B[0]==C[0]]);}else if(C[0]>=A[0]){C[1]=max(C[0],B[1]);C[0]=B[0];}else if(C[0]>=B[0]){C[1]=max(C[0],A[1]);C[0]=A[0];}else if(A[0]>B[0]){C[1]=max(C[0],A[1]);upu(C[1],B[0]);C[0]=A[0];}else if(A[0]<B[0]){C[1]=max(C[0],B[1]);upu(C[1],A[0]);C[0]=B[0];}else{C[1]=max(C[0],A[1]);upu(C[1],B[1]);C[0]=A[0];}}}
};
vector<RMQ>rmq[M];
inline bool cmpe(const E&a,const E&b){return a.d<b.d;}
int F(int x){return f[x]==x?x:f[x]=F(f[x]);}
inline void up(int&a,int b){a<b?(a=b):0;}
inline void solve2edges(int A,int B){int i,j;for(i=0;i<4;i++)twoedges[i]=0;for(i=0;i<4;i++)if(edge[A][B][i][0])for(j=0;j<=i;j++)if(edge[A][B][j][i==j])up(twoedges[(i+j)&3],edge[A][B][i][0]+edge[A][B][j][i==j]);
}
inline void solve2components(int A,int B){int i,j;solve2edges(A,B);static int one[4];for(i=0;i<4;i++){one[i]=max(extra[A][i],extra[B][i]);two[i]=twoedges[i];}for(i=0;i<4;i++)if(extra[A][i])for(j=0;j<4;j++)if(extra[B][j])up(two[(i+j)&3],extra[A][i]+extra[B][j]);for(i=0;i<4;i++)if(edge[A][B][i][0])for(j=0;j<4;j++)if(one[j])up(two[(i+j)&3],edge[A][B][i][0]+one[j]);
}
inline bool cmpv(int x,int y){return st[x]<st[y];}
inline void solve(int cntdel){int i,j,k,x,y;static int T,lastcom[M];T++;static vector<int>poolcom;poolcom.clear();for(i=0;i<cntdel;i++){int o=delid[i];x=basis[o].s;y=at[x];if(lastcom[y]!=T){lastcom[y]=T;poolcom.emplace_back(y);}}int ctree=0;static vector<P>tree[3];for(i=0;i<cntdel;i++)tree[i].clear();for(const auto&x:poolcom){int S=root[x];int L=st[S],R=en[S];int pos=cir[x]?st[basis[cir[x]].s]:0;static int pool[4];pool[0]=S;int cp=1;for(j=0;j<cntdel;j++)if(!basis[delid[j]].oncircle){y=basis[delid[j]].s;if(at[y]==x)pool[cp++]=y;}sort(pool,pool+cp,cmpv);static int q[4];int top=0;q[0]=0;static Ranges ranges[4];ranges[0].init(L,R);for(i=1;i<cp;i++){y=pool[i];while(en[pool[q[top]]]<st[y])top--;ranges[q[top]].append(st[y],en[y]);q[++top]=i;ranges[i].init(st[y],en[y]);}for(i=0;i<cp;i++)ranges[i].finish();if(pos&&!basis[cir[x]].del){for(i=0;i<cp;i++)if(ranges[i].find(pos))break;if(!i)for(j=1;j<cp;j++)ranges[j].addtotree(tree[ctree++]);else{ranges[0].addtotree(tree[ctree]);ranges[i].addtotree(tree[ctree]);sort(tree[ctree].begin(),tree[ctree].end());ctree++;for(j=1;j<cp;j++)if(j!=i)ranges[j].addtotree(tree[ctree++]);}}else for(j=0;j<cp;j++)ranges[j].addtotree(tree[ctree++]);}static vector<P>all,outer;all.clear();outer.clear();for(i=0;i<ctree;i++)for(const auto&it:tree[i])all.emplace_back(it);sort(all.begin(),all.end());int r=0;for(const auto&it:all){if(r+1<it.first)outer.emplace_back(P(r+1,it.first-1));up(r,it.second);}if(r<n)outer.emplace_back(P(r+1,n));for(i=0;i<ctree;i++){for(j=0;j<4;j++)top[j]=0;for(const auto&A:tree[i]){const auto&ds=rmq[A.second][A.first];for(const auto&B:tree[i]){ds.fetchtop(B);if(B.first==A.first)break;}for(const auto&B:outer)ds.fetchtop(B);}for(j=0;j<4;j++)extra[i][j]=e[top[j]].d;for(j=i+1;j<ctree;j++){for(k=0;k<4;k++)for(x=0;x<2;x++)top2[k][x]=0;for(const auto&A:tree[i]){const auto&ds=rmq[A.second][A.first];for(const auto&B:tree[j])ds.fetchtop2(B);}for(k=0;k<4;k++)for(x=0;x<2;x++){int id=top2[k][x];edge[i][j][k][x]=edge[j][i][k][x]=e[id].d;}}}if(ctree==1){for(i=0;i<4;i++)maxd[i]=extra[0][i];return;}if(ctree==2){solve2components(0,1);for(i=0;i<4;i++)maxd[i]=two[i];return;}for(i=0;i<4;i++)maxd[i]=0;for(i=0;i<4;i++)if(edge[0][1][i][0])for(j=0;j<4;j++)if(edge[0][2][j][0])for(k=0;k<4;k++)if(edge[1][2][k][0])up(maxd[(i+j+k)&3],edge[0][1][i][0]+edge[0][2][j][0]+edge[1][2][k][0]);static int common[4];for(i=0;i<4;i++){common[i]=0;for(j=0;j<3;j++)up(common[i],extra[j][i]);}for(int S=0;S<3;S++){int A=(S+1)%3,B=(S+2)%3;solve2components(A,B);for(i=0;i<4;i++)if(two[i])for(j=0;j<4;j++)if(extra[S][j])up(maxd[(i+j)&3],two[i]+extra[S][j]);for(i=0;i<4;i++)if(edge[S][A][i][0])for(j=0;j<4;j++)if(edge[S][B][j][0])for(k=0;k<4;k++)if(common[k])up(maxd[(i+j+k)&3],edge[S][A][i][0]+edge[S][B][j][0]+common[k]);for(int _=0;_<2;_++){solve2edges(S,A);for(i=0;i<4;i++)if(twoedges[i])for(j=0;j<4;j++)if(edge[S][B][j][0])up(maxd[(i+j)&3],twoedges[i]+edge[S][B][j][0]);swap(A,B);}}
}
void dfs(int x,int y){at[x]=ccom;st[x]=++dfn;for(const auto&id:adj[x]){int u=basis[id].f^basis[id].s^x;if(u==y)continue;if(u!=basis[id].s)swap(basis[id].f,basis[id].s);dfs(u,x);}en[x]=dfn;
}
inline void newcom(int S){root[++ccom]=S;dfs(S,0);
}
void search(int o,int x){if(o){solve(o);for(int i=0;i<4;i++)if(maxd[i])up(opt[(optv+i)&3],optd+maxd[i]);}if(o==3)return;for(;x<=n;x++){optd-=basis[x].d;(optv+=4-basis[x].v)&=3;basis[x].del=1;delid[o]=x;search(o+1,x+1);optd+=basis[x].d;(optv+=basis[x].v)&=3;basis[x].del=0;}
}
int main(){scanf("%d%d",&n,&m);for(i=1;i<=n;i++)for(j=1;j<=m;j++){e[++ce].x=i;e[ce].y=j+n;scanf("%d",&e[ce].d);}ce=0;for(i=1;i<=n;i++)for(j=1;j<=m;j++){scanf("%d",&e[++ce].v);e[ce].v&=3;}n+=m;sort(e+1,e+ce+1,cmpe);static bool g[M];for(i=1;i<=n;i++)f[i]=i;m=0;for(i=ce;i;i--){int x=F(e[i].x),y=F(e[i].y);if(g[x]&&g[y])continue;++m;basis[m].f=e[i].x;basis[m].s=e[i].y;basis[m].d=e[i].d;basis[m].v=e[i].v;e[i].ban=1;optd+=e[i].d;(optv+=e[i].v)&=3;if(x==y){g[x]=1;basis[m].oncircle=1;}else{f[x]=y;g[y]|=g[x];adj[e[i].x].emplace_back(m);adj[e[i].y].emplace_back(m);}}opt[optv]=optd;for(i=1;i<=n;i++)if(basis[i].oncircle){newcom(basis[i].f);cir[ccom]=i;}for(i=1;i<=n;i++)if(!st[i])newcom(i);for(i=2;i<=n;i++)Log[i]=Log[i>>1]+1;for(i=1;i<=n;i++){rmq[i].resize(i+1);for(j=1;j<=i;j++)rmq[i][j].init();}for(i=ce;i;i--)if(!e[i].ban){int x=st[e[i].x],y=st[e[i].y],val=e[i].v;for(int _=0;_<2;_++){for(int r=x;r<=n;r++)for(int l=x;l;l--){auto&f=rmq[r][l].f[0][y][val];if(!f[0])f[0]=i;else if(f[0]!=i&&!f[1])f[1]=i;else break;}swap(x,y);}}for(i=1;i<=n;i++)for(j=1;j<=i;j++)rmq[i][j].build();search(0,1);for(i=0;i<4;i++){if(!opt[i])opt[i]=-1;printf("%d\n",opt[i]);}
}
