1 /* // 图论模板 // */ 2 //----------------------------------------------------------------------------- 3 /*卡常小技巧*/ 4 #define re register 5 #define max(x,y) ((x)>(y)?(x):(y)) 6 #define min(x,y) ((x)<(y)?(x):(y)) 7 #define swap(x,y) ((x)^=(y)^=(x)^=(y)) 8 #define abs(x) ((x)<0?-(x):(x)) 9 inline + 函数（非递归） 10 static 相当于全局变量，防止爆栈，且不用重复申请空间，初值为0 11 //----------------------------------------------------------------------------- 12 /*前向星邻接表*/ 13 //单向链表 14 int tot,first[100010]; 15 struct node{int u,v,w,next;}edge[200010]; 16 inline void add(re int x,re int y,re int w){ 17 edge[++tot].u=x; 18 edge[tot].v=y; 19 edge[tot].w=w; 20 edge[tot].next=first[x]; 21 first[x]=tot; 22 } 23 //双向链表 24 int tot,head[100010],tail[100010]; 25 struct node{int u,v,next,last;}edge[200010]; 26 inline void add(re int x,re int y){ 27 edge[++tot].u=x; 28 edge[tot].v=y; 29 edge[tot].w=w; 30 edge[tot].next=0; 31 edge[tot].last=tail[x]; 32 edge[tail[x]].next=tot;tail[x]=tot; 33 if(!head[x]) head[x]=tot; 34 } 35 //----------------------------------------------------------------------------- 36 /*遍历（dfs，bfs)*/ 37 //dfs 38 void dfs(re int x,re int fa){ 39 for(re int i=first[x];i;i=edge[i].next){ 40 re int y=edge[i].v; 41 if(y==fa) continue; 42 dfs(y,x); 43 } 44 } 45 //bfs 46 inline void bfs(re int s){ 47 static queue<int> q; 48 q.push(s);ins[s]=1; 49 while(!q.empty()){ 50 re int x=q.front();q.pop(),ins[x]=0; 51 for(re int i=first[x];i;i=edge[i].next){ 52 re int y=edge[i].v; 53 if(ins[y]) continue; 54 q.push(y);ins[y]=1; 55 } 56 } 57 } 58 //----------------------------------------------------------------------------- 59 /*最短路*/ 60 //Floyd 61 for(re int k=1;k<=n;++k) 62 for(re int i=1;i<=n;++i) 63 for(re int j=1;j<=n;++j) 64 if(f[i][k]+f[k][j]<f[i][j]) 65 f[i][j]=f[i][k]+f[k][j]; 66 //堆优化Dijkstra 67 inline void Dijkstra(re int s){ 68 static priority_queue<pair<int,int> > q; 69 memset(dis,0x3f,sizeof(dis));dis[s]=0; 70 q.push(make_pair(dis[s],s)); 71 while(!q.empty()){ 72 re int x=q.top();q.pop(); 73 if(vis[x]) continue;vis[x]=1; 74 for(re int i=first[x];i;i=edge[i].next){ 75 re int y=edge[i].v,w=edge[i].w; 76 if(dis[x]+w<dis[y]){ 77 dis[y]=dis[x]+w; 78 q.push(make_pair(dis[y],y)); 79 } 80 } 81 } 82 } 83 //spfa 84 inline void spfa(re int s){ 85 static queue<int> q; 86 memset(dis,0x3f,sizeof(dis)); 87 dis[s]=0;q.push(s);ins[s]=1; 88 while(!q.empty()){ 89 re int x=q.front();q.pop();ins[x]=0; 90 for(re int i=first[x];i;i=edge[i].next){ 91 re int y=edge[i].v,w=edge[i].w; 92 if(dis[x]+w<dis[y]){ 93 dis[y]=dis[x]+w; 94 if(!ins[y]) q.push(y),ins[y]=1; 95 } 96 } 97 } 98 } 99 //----------------------------------------------------------------------------- 100 /*拓扑排序*/ 101 inline void topsort(){ 102 static queue<int> q; 103 for(re int i=1;i<=n;++i) 104 if(!in[i]) q.push(i); 105 while(!q.empty()){ 106 re int x=q.front();q.pop(); 107 for(re int i=first[x];i;i=edge[i].next){ 108 re int y=edge[i].v; --in[y]; 109 if(!in[y]) q.push(y); 110 } 111 } 112 } 113 //----------------------------------------------------------------------------- 114 /*并查集*/ 115 //普通并查集 116 int find(re int x){return fa[x]==x?x:find(fa[x]);} 117 inline void merge(re int x,re int y){ 118 x=find(x),y=find(y); 119 if(x!=y) fa[x]=y; 120 } 121 //路径压缩 122 int find(re int x){return fa[x]==x?x:fa[x]=find(fa[x]);} 123 //按秩合并 124 inline void merge(re int x,re int y){ 125 x=find(x),y=find(y); 126 if(x==y) return ; 127 if(rk[x]<=rk[y]) fa[x]=y,rk[y]=max(rk[y],rk[x]+1); 128 else fa[y]=x,rk[x]=max(rk[x],rk[y]+1); 129 } 130 //----------------------------------------------------------------------------- 131 /*最小生成树*/ 132 //Kruskal 133 inline bool cmp(node x,node y){ 134 return x.w<y.w; 135 } 136 inline void Kruskal(){ 137 sort(a+1,a+m+1,cmp); 138 for(re int i=1;i<=m;i++){ 139 re int x=a[i].x,y=a[i].y; 140 x=find(x),y=find(y); 141 if(x==y) continue; 142 fa[x]=y,++cnt,ans+=a[i].w; 143 if(cnt==n-1) break; 144 } 145 } 146 //prim 147 inline void init(){ 148 for(re int i=1;i<=n;++i) 149 for(re int j=1;j<=n;++j) 150 w[i][j]=inf; 151 for(re int i=1,u,v,w;i<=m;++i){ 152 u=read(),v=read(),w=read(); 153 if(w[u][v]>w) w[u][v]=w[v][u]=w; 154 } 155 for(re int i=1;i<=n;++i) to[i]=w[1][i]; 156 fm[1]=1; 157 } 158 inline int prim(){ 159 while(tot<n){ 160 re int minn=inf,now;++tot; 161 for(re int i=1;i<=n;++i) 162 if(!fm[i]&&to[i]<minn)minn=to[i],now=i; 163 ans+=minn; 164 for(re int i=1;i<=n;++i) 165 if(to[i]>w[now][i]&&!fm[i]) to[i]=w[now][i]; 166 fm[now]=1; 167 } 168 return ans; 169 } 170 //----------------------------------------------------------------------------- 171 /*树的直径*/ 172 //树形DP 173 void dfs(re int x){ 174 vis[x]=1; 175 for(re int i=first[x];i;i=edge[i].next){ 176 re int y=edge[i].v;if(vis[y]) continue; 177 dfs(y);ans=max(ans,dep[x]+dep[y]+edge[i].w); 178 dep[x]=max(dep[x],dep[y]+edge[i].w); 179 } 180 } 181 //两遍dfs 182 void dfs(re int x,re int fa){ 183 for(re int i=first[x];i;i=edge[i].next){ 184 re int y=edge[i].v; 185 if(y==fa) continue; 186 dis[y]=dis[x]+1,pre[y]=x; dfs(y,x); 187 } 188 } 189 re int st=0,ed=0,len=0; 190 dis[1]=0;dfs(1,0); 191 for(re int i=1;i<=n;++i) 192 if(dis[i]>dis[st]) st=i; 193 dis[st]=0;dfs(st,0); 194 for(re int i=1;i<=n;++i) 195 if(dis[i]>dis[ed]) len=dis[ed],ed=i; 196 //----------------------------------------------------------------------------- 197 /*tarjan*/ 198 //有向图强联通分量+缩点重建 199 void tarjan(re int x){ 200 dfn[x]=low[x]=++cnt; 201 stk[++top]=x,ins[x]=1; 202 for(re int i=first[x];i;i=edge[i].next){ 203 re int y=edge[i].v; 204 if(!dfn[y]){ 205 tarjan(y); 206 low[x]=min(low[x],low[y]); 207 } 208 else if(ins[y]) low[x]=min(low[x],dfn[y]); 209 } 210 if(dfn[x]==low[x]){ 211 ++cnt;re int dat; 212 do{ 213 dat=stk[top--],ins[dat]=0; 214 bel[y]=cnt,scc[cnt].push_back(dat); 215 }while(dat!=x); 216 } 217 } 218 for(re int i=1;i<=n;++i) 219 if(!dfn[i]) tarjan(i); 220 for(re int x=1;x<=n;++x){ 221 for(re int i=first[x];i;i=edge[i].next){ 222 re int y=edge[i].v; 223 if(bel[x]==bel[y]) continue; 224 readd(bel[x],bel[y]); 225 } 226 } 227 //割点(无向图） 228 void tarjan(re int x){ 229 dfn[x]=low[x]=++cnt;re int flag=0; 230 for(re int i=first[x];i;i=edge[i].next){ 231 re int y=edge[i].v; 232 if(!dfn[y]){ 233 tarjan(y); 234 low[x]=min(low[x],low[y]); 235 if(low[y]>=dfn[x]) { 236 ++flag; 237 if(x!=root||flag>1) cut[x]=1; 238 } 239 } 240 else low[x]=min(low[x],dfn[y]); 241 } 242 } 243 for(re int i=1;i<=n;++i) 244 if(!dfn[i]) root=i,tarjan(i); 245 //割边(无向图） 246 void tarjan(re int x,re int ed){ 247 dfn[x]=low[x]=++cnt; 248 for(re int i=first[x];i;i=edge[i].next){ 249 re int y=edge[i].v; 250 if(dfn[y]){ 251 if(i!=(ed^1)) 252 low[x]=min(low[x],dfn[y]); 253 continue; 254 } 255 tarjan(y,i); 256 low[x]=min(low[x],low[y]); 257 if(low[y]>dfn[x]) bridge[i]=bridge[i^1]=1; 258 } 259 } 260 for(re int i=1;i<=n;++i) 261 if(!dfn[i]) tarjan(i,0); 262 //点双+缩点重建 263 void tarjan(re int x){ 264 dfn[x]=low[x]=++num; 265 stk[++top]=x; 266 if(x==root&&first[x]==0){ 267 dcc[++cnt].push_back(x); 268 return ; 269 } 270 re int flag=0; 271 for(re int i=first[x];i;i=edge[i].next){ 272 re int y=edge[i].v; 273 if(!dfn[y]){ 274 tarjan(y); 275 low[x]=min(low[x],low[y]); 276 if(low[y]>=dfn[x]){ 277 ++flag; 278 if(x!=root||flag>1) cut[x]=1; 279 cnt++;re int dat; 280 do{ 281 dat=stk[top--]; 282 dcc[cnt].push_back(dat); 283 }while(dat!=y); 284 dcc[cnt].push_back(x); 285 } 286 } 287 else low[x]=min(low[x],dfn[y]); 288 } 289 } 290 for(re int i=1;i<=n;++i) 291 if(!dfn[i]) root=i,tarjan(i); 292 num=cnt; 293 for(re int i=1;i<=n;++i) 294 if(cut[i]) id[i]=++num; 295 retot=1; 296 for(re int i=1;i<=cnt;++i){ 297 for(re int j=0;j<dcc[i].size();++j){ 298 re int x=dcc[i][j]; 299 if(cut[x]) 300 readd(i,id[x]),readd(id[x],i); 301 else bel[x]=i; 302 } 303 } 304 //边双(即删除割边)(无向图)+缩点重建 305 void tarjan(re int x,re int ed){ 306 dfn[x]=low[x]=++cnt; 307 for(re int i=first[x];i;i=edge[i].next){ 308 re int y=edge[i].v; 309 if(dfn[y]){ 310 if(i!=(ed^1)) 311 low[x]=min(low[x],dfn[y]); 312 continue; 313 } 314 tarjan(y,i); 315 low[x]=min(low[x],low[y]); 316 if(low[y]>dfn[x]) bridge[i]=bridge[i^1]=1; 317 } 318 } 319 void dfs(re int x){ 320 id[x]=dcc; 321 for(re int i=first[x];i;i=edge[i].next){ 322 re int y=edge[i].v; 323 if(id[y]||bridge[i]) continue; 324 dfs(y); 325 } 326 } 327 for(re int i=1;i<=n;++i) 328 if(!dfn[i]) tarjan(i,0); 329 for(re int i=1;i<=n;++i){ 330 if(!id[i]) ++dcc,dfs(i); 331 } 332 for(re int i=1;i<=tot;++i){ 333 re int x=edge[i].v,y=edge[i^1].v; 334 if(id[x]==id[y]) continue; 335 readd(id[x],id[y]); 336 } 337 //----------------------------------------------------------------------------- 338 /*二分图*/ 339 //匈牙利算法（增广路算法） 340 bool dfs(re int x){ 341 for(re int i=first[x];i;i=edge[i].next){ 342 re int y=edge[i].v; 343 if(!vis[y]){ 344 vis[y]=1; 345 if(!match[y]||dfs(match[y])){ 346 match[y]=x;return 1; 347 } 348 } 349 } 350 return 0; 351 } 352 for(re int i=1;i<=n;++i){ 353 memset(vis,0,sizeof(vis)); 354 if(dfs(i)) ++ans; 355 } 356 //----------------------------------------------------------------------------- 357 /*lca*/ 358 //倍增lca 359 void dfs(re int x,re int fa){ 360 dep[x]=dep[fa]+1; 361 for(re int i=1;i<=20;++i) 362 f[x][i]=f[f[x][i-1]][i-1]; 363 for(re int i=first[x];i;i=edge[i].next){ 364 re int y=edge[i].v; 365 if(y==fa) continue; 366 f[y][0]=x;dfs(y,x); 367 } 368 } 369 inline int lca(re int x,re int y){ 370 if(dep[x]<dep[y]) x^=y^=x^=y; 371 re int dat=dep[x]-dep[y]; 372 for(re int i=0;i<=20;++i) if(dat>>i&1) x=f[x][i]; 373 if(x==y) return x; 374 for(re int i=20;~i;--i) 375 if(f[x][i]!=f[y][i]) x=f[x][i],y=f[y][i]; 376 return f[x][0]; 377 } 378 //ST表lca 379 void dfs(re int x,re int fa){ 380 dep[x]=dep[fa]+1,id[x]=++cnt,euler[cnt]=x; 381 for(re int i=first[x];i;i=edge[i].next){ 382 re int y=edge[i].v; 383 if(y==fa) continue; 384 dfs(y,x),euler[++cnt]=x; 385 } 386 } 387 inline void ST(){ 388 for(re int i=1;i<=cnt;++i) f[i][0]=euler[i]; 389 for(re int j=1;j<20;++j){ 390 for(re int i=1;i<=cnt;++i){ 391 if(i+(1<<j)>cnt) break; 392 if(dep[f[i][j-1]]<dep[f[i+(1<<(j-1))][j-1]]) 393 f[i][j]=f[i][j-1]; 394 else f[i][j]=f[i+(1<<(j-1))][j-1]; 395 } 396 } 397 } 398 inline int lca(re int x,re int y){ 399 if(x>y) x^=y^=x^=y; 400 re int pos=(int)(log(y-x+1)/log(2)); 401 re int res=f[x][pos]; 402 re int k=f[y-(1<<pos)+1][pos]; 403 if(dep[res]>dep[k]) res=k; return res; 404 } 405 LCA(x,y)=lca(id[x],id[y]); 406 //树链剖分lca 407 void dfs1(re int x){ 408 siz[x]++; 409 for(re int i=first[x];i;i=edge[i].next){ 410 re int y=edge[i].v; 411 if(dep[y]) continue; 412 dep[y]=dep[x]+1,fa[y]=x; 413 dfs1(y);siz[x]+=siz[y]; 414 } 415 } 416 void dfs2(re int x,re int pt){ 417 top[x]=pt;re int sz=0,pos=0; 418 for(re int i=first[x];i;i=edge[i].next){ 419 re int y=edge[i].v; 420 if(fa[y]==x) continue; 421 if(siz[y]>sz) 422 pos=y,sz=siz[y]; 423 } 424 dfs2(pos,pt); 425 for(re int i=first[x];i;i=edge[i].next){ 426 re int y=edge[i].v; 427 if(y==pos||fa[y]==x) continue; 428 dfs2(y,y); 429 } 430 } 431 inline int lca(re int x,re int y){ 432 while(top[x]!=top[y]){ 433 if(dep[top[x]]<dep[top[y]]) x^=y^=x^=y; 434 x=fa[top[x]]; 435 } 436 return dep[x]<dep[y]?x:y; 437 } 438 //----------------------------------------------------------------------------- 439 /*欧拉回路*/ 440 inline void euler(){ 441 stk[++top]=1; 442 while(top){ 443 re int x=stk[top],i=first[x]; 444 while(i&&vis[i]) i=edge[i].next; 445 if(i){ 446 stk[++top]=edge[i].v; 447 vis[i]=vis[i^1]=1; 448 first[x]=edge[i].next; 449 } 450 else top--,ans[++cnt]=x; 451 } 452 } 453 for(re int i=cnt;i;--i) printf("%d ",ans[i]); 454 //----------------------------------------------------------------------------- 455 /*网络流*/ 456 //最大流EK 457 int tot=1;//!!! 458 struct node{int u,v,next,w,c,eg}edge[200010];//w:流量 c:容量 459 inline void add(re int x,re int y,re int w){ 460 edge[tot]=(node){x,y,first[x],0,w,cnt+1}; 461 first[x]=tot++; 462 edge[tot]=(node){y,x,first[y],0,0,cnt-1}; 463 first[y]=tot++; 464 } 465 inline void EK(){ 466 re int ans=0;static queue<int> q; 467 while(1){ 468 for(re int i=1;i<=n;++i) a[i]=0; 469 while(!q.empty()) q.pop(); 470 q.push(S);pre[S]=0;a[S]=inf; 471 while(!q.empty()){ 472 re int x=q.front();q.pop(); 473 for(re int i=first[x];i;i=edge[i].next){ 474 re int y=edge[i].v; 475 if(!a[y]&&edge[i].c>edge[i].w){ 476 a[y]=min(a[x],edge[i].c-edge[i].w); 477 pre[y]=i,q.push(y); 478 } 479 } 480 if(a[T]) break; 481 } 482 if(!a[T]) break; 483 for(re int u=T;u!=S;u=edge[pre[u]].u){ 484 edge[pre[u]].w+=a[T]; 485 edge[edge[pre[u]].eg].w-=a[T]; 486 } 487 ans+=a[T]; 488 } 489 } 490 //最大流dinic 491 int tot=1;//!!! 492 struct node{int v,next,w,eg}edge[200010]; 493 inline void add(re int x,re int y,re int w){ 494 edge[tot]=(node){x,y,first[x],w,cnt+1}; 495 first[x]=tot++; 496 edge[tot]=(node){y,x,first[y],0,cnt-1}; 497 first[y]=tot++; 498 } 499 inline bool bfs(){ 500 for(re int i=1;i<=n;++i) bel[i]=0; 501 bel[S]=1;static queue<int> q; 502 while(!q.empty()) q.pop(); 503 q.push(S); 504 while(!q.empty()){ 505 re int x=q.front();q.pop(); 506 for(re int i=first[x];i;i=edge[i].next){ 507 re int y=edge[i].v; 508 if(edge[i].w&&!bel[y]) 509 bel[y]=bel[x]+1,q.push(y); 510 } 511 } 512 return bel[T]; 513 } 514 int dfs(re int s,re int t,re int flow){ 515 if(s==t||flow==0) return flow; 516 re int res=0; 517 for(re int i=first[u];i;i=edge[i].next){ 518 re int y=edge[i].v; 519 if(edge[i].w&&bel[y]==bel[u]+1){ 520 re int dat=dfs(y,T,min(flow,edge[i].w)); 521 res+=dat; flow-=dat; 522 edge[i].w-=dat;edge[edge[i].eg].w+=dat; 523 } 524 } 525 return res; 526 } 527 inline int dinic(){ 528 re int res=0; 529 while(bfs()) res+=dfs(S,T,inf); 530 return res; 531 }