[BZOJ4568][SCOI2016]幸运数字(倍增LCA,点分治+线性基)

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 #define rep(i,l,r) for (int i=l; i<=r; i++)
 5 typedef long long ll;
 6 using namespace std;
 7 
 8 const int N=20100,M=62;
 9 ll g[N][16][M],Ans[M],a[N];
10 int n,Q,u,v,cnt,to[N<<1],nxt[N<<1],h[N],d[N],fa[N][16];
11 
12 void add(int u,int v){ to[++cnt]=v; nxt[cnt]=h[u]; h[u]=cnt; }
13 void ins(ll p[],ll x){
14     for (int i=61; ~i; i--) if (x&(1ll<<i)){
15         if (!p[i]) { p[i]=x; break; } else x^=p[i];
16     }
17 }
18 void merge(ll g[],ll f1[],ll f2[]){
19     rep(i,0,61) g[i]=f1[i];
20     rep(i,0,61) if (f2[i]) ins(g,f2[i]);
21 }
22 void dfs(int x){
23     ins(g[x][0],a[x]);
24     rep(i,1,15){
25         fa[x][i]=fa[fa[x][i-1]][i-1];
26         merge(g[x][i],g[x][i-1],g[fa[x][i-1]][i-1]);
27     }
28     for (int i=h[x],k; i; i=nxt[i])
29         if ((k=to[i])!=fa[x][0]) fa[k][0]=x,d[k]=d[x]+1,dfs(k);
30 }
31 
32 void lca(int u,int v){
33     memset(Ans,0,sizeof(Ans));
34     if (d[u]<d[v]) swap(u,v);
35     int t=d[u]-d[v];
36     for (int i=15; ~i; i--)
37         if (t&(1<<i)) merge(Ans,Ans,g[u][i]),u=fa[u][i];
38     if (u==v){ merge(Ans,Ans,g[u][0]); return; }
39     for (int i=15; ~i; i--)
40         if (fa[u][i]!=fa[v][i])
41             merge(Ans,Ans,g[u][i]),merge(Ans,Ans,g[v][i]),
42             u=fa[u][i],v=fa[v][i];
43     merge(Ans,Ans,g[u][0]); merge(Ans,Ans,g[v][0]);
44     merge(Ans,Ans,g[fa[u][0]][0]);
45 }
46 
47 ll get(ll p[]){
48     ll res=0;
49     for (int i=61; ~i; i--) res=max(res,res^p[i]);
50     return res;
51 }
52 
53 int main(){
54      freopen("bzoj4568.in","r",stdin);
55      freopen("bzoj45682.out","w",stdout);
56     scanf("%d%d",&n,&Q);
57     rep(i,1,n) scanf("%lld",&a[i]);
58     rep(i,2,n) scanf("%d%d",&u,&v),add(u,v),add(v,u);
59     dfs(1);
60     while (Q--) scanf("%d%d",&u,&v),lca(u,v),printf("%lld\n",get(Ans));
61     return 0;
62 }

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<vector>
 4 #include<algorithm>
 5 #define rep(i,l,r) for (int i=l; i<=r; i++)
 6 #define For(i,x) for (int i=h[x],k; i; i=nxt[i])
 7 typedef long long ll;
 8 using namespace std;
 9 
10 const int N=20010,M=200010,inf=1000000000;
11 int n,Q,u,v,cnt,S,rt,tim,pos[N],f[N],b[N],sz[N],vis[N],d[N];
12 int fa[N][16],h[N],to[N<<1],nxt[N<<1];
13 ll a[N],g[N][65],Ans[65],ans[M];
14 struct P{ int u,v; }s[M];
15 vector<int>V[N];
16 void add(int u,int v){ to[++cnt]=v; nxt[cnt]=h[u]; h[u]=cnt; }
17 
18 void ins(ll p[],ll x){
19     for (int i=60; ~i; i--) if (x&(1ll<<i)){
20         if (!p[i]) { p[i]=x; break; } else x^=p[i];
21     }
22 }
23 
24 void merge(ll g[],ll f1[],ll f2[]){
25     rep(i,0,60) g[i]=f1[i];
26     rep(i,0,60) if (f2[i]) ins(g,f2[i]);
27 }
28 
29 ll get(ll p[]){
30     ll res=0;
31     for (int i=60; ~i; i--) res=max(res,res^p[i]);
32     return res;
33 }
34 
35 void find(int x,int fa){
36     f[x]=0; sz[x]=1;
37     For(i,x) if ((k=to[i])!=fa && !vis[k])
38         find(k,x),sz[x]+=sz[k],f[x]=max(f[x],sz[k]);
39     f[x]=max(f[x],S-sz[x]);
40     if (f[x]<f[rt]) rt=x;
41 }
42 
43 void work(int x,int fa,int bel){
44     pos[x]=bel; b[x]=tim;
45     rep(i,0,60) g[x][i]=g[fa][i]; ins(g[x],a[x]);
46     For(i,x) if ((k=to[i])!=fa && !vis[k]) work(k,x,bel);
47 }
48 
49 void work1(int x,int fa){
50     for (vector<int>::iterator it=V[x].begin(); it!=V[x].end(); it++){
51         int k=*it; if (ans[k]) continue;
52         int u=s[k].u; if (u==x) u=s[k].v;
53         if (b[u]==tim && (pos[u]!=pos[x] || !pos[u]))
54             merge(Ans,g[u],g[x]),ans[k]=get(Ans);
55     }
56     For(i,x) if ((k=to[i])!=fa && !vis[k]) work1(k,x);
57 }
58 
59 void solve(int x){
60     vis[x]=1; b[x]=++tim; pos[x]=0;
61     rep(i,0,60) g[x][i]=0; ins(g[x],a[x]);
62     For(i,x) if (!vis[k=to[i]]) work(k,x,k); work1(x,0);
63     For(i,x) if (!vis[k=to[i]]) S=sz[k],f[rt=0]=inf,find(k,x),solve(k);
64 }
65 
66 int main(){
67     freopen("bzoj4568.in","r",stdin);
68     freopen("bzoj4568.out","w",stdout);
69     scanf("%d%d",&n,&Q);
70     rep(i,1,n) scanf("%lld",&a[i]);
71     rep(i,2,n) scanf("%d%d",&u,&v),add(u,v),add(v,u);
72     rep(i,1,Q) scanf("%d%d",&s[i].u,&s[i].v),V[s[i].u].push_back(i),V[s[i].v].push_back(i);
73     f[rt=0]=inf; S=n; find(1,0); solve(rt);
74     rep(i,1,Q) printf("%lld\n",ans[i]);
75     return 0;
76 }