题解：
https://files.cnblogs.com/files/clrs97/2024_Hong_Kong_Tutorial.pdf
Code：
A. General Symmetry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 | // 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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | #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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | #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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 | #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; else t[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); else ins(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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 | #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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 | #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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | #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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 | #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 <= j pre[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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 | #include<bits/stdc++.h>using namespace std;#define int long longnamespace 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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 | #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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 | #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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 | #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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 | #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]); }} |
