Bzoj4568: [Scoi2016]幸运数字
题面
Sol
裸的线性基
当然是选择\(log^3\)的\(st\)表+树剖辣
# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(2e4 + 5);
IL ll Input(){
RG ll x = 0, z = 1; RG char c = getchar();
for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
return x * z;
}
int n, q, lg[_], first[_], cnt;
struct Edge{
int to, next;
} edge[_ << 1];
ll pw[63] = {1}, w[_];
struct Bac{
ll b[63];
int num;
IL void Init(){
Fill(b, 0);
}
IL void Insert(RG ll x){
if(num == 63) return;
for(RG int i = 62; ~i; --i){
if(~x & pw[i]) continue;
if(!x) break;
if(!b[i]){
b[i] = x, ++num;
break;
}
x ^= b[i];
}
}
IL ll Calc(){
RG ll x = 0;
for(RG int i = 62; ~i; --i) x = max(x, x ^ b[i]);
return x;
}
} st[20][_], Ans;
IL Bac operator +(RG Bac A, RG Bac B){
for(RG int i = 62; ~i; --i)
if(A.b[i]) B.Insert(A.b[i]);
return B;
}
IL void Add(RG int u, RG int v){
edge[cnt] = (Edge){v, first[u]}, first[u] = cnt++;
}
int dfn[_], fa[_], top[_], size[_], son[_], idx, deep[_];
IL void Dfs1(RG int u){
size[u] = 1;
for(RG int e = first[u]; e != -1; e = edge[e].next){
RG int v = edge[e].to;
if(size[v]) continue;
deep[v] = deep[u] + 1, fa[v] = u;
Dfs1(v);
size[u] += size[v];
if(size[v] > size[son[u]]) son[u] = v;
}
}
IL void Dfs2(RG int u, RG int Top){
top[u] = Top, dfn[u] = ++idx;
if(son[u]) Dfs2(son[u], Top);
for(RG int e = first[u]; e != -1; e = edge[e].next)
if(!dfn[edge[e].to]) Dfs2(edge[e].to, edge[e].to);
}
IL void Build(){
for(RG int i = 2; i <= n; ++i) lg[i] = lg[i >> 1] + 1;
Dfs1(1), Dfs2(1, 1);
for(RG int i = 1; i <= n; ++i) st[0][dfn[i]].Insert(w[i]);
for(RG int j = 1; j <= lg[n]; ++j)
for(RG int i = 1; i + (1 << j) - 1 <= n; ++i)
st[j][i] = st[j - 1][i] + st[j - 1][i + (1 << (j - 1))];
}
IL Bac Query(RG int l, RG int r){
RG int lg2 = lg[r - l + 1];
return st[lg2][l] + st[lg2][r - (1 << lg2) + 1];
}
IL Bac LCA(RG int u, RG int v){
Ans.Init();
while(top[u] ^ top[v]){
if(deep[top[u]] < deep[top[v]]) swap(u, v);
Ans = Ans + Query(dfn[top[u]], dfn[u]);
u = fa[top[u]];
}
if(deep[u] > deep[v]) swap(u, v);
return Ans + Query(dfn[u], dfn[v]);
}
int main(RG int argc, RG char *argv[]){
for(RG int i = 1; i < 63; ++i) pw[i] = pw[i - 1] << 1;
n = Input(), q = Input();
for(RG int i = 1; i <= n; ++i) w[i] = Input(), first[i] = -1;
for(RG int i = 1; i < n; ++i){
RG int u = Input(), v = Input();
Add(u, v), Add(v, u);
}
Build();
for(RG int i = 1; i <= q; ++i){
RG int u = Input(), v = Input();
printf("%lld\n", LCA(u, v).Calc());
}
return 0;
}
