BZOJ 4568 [Scoi2016]幸运数字(树链剖分 + 异或线性基)

题目链接  BZOJ 4568

考虑树链剖分+线段树维护每一段区域的异或线性基

对于每个询问,求出该点集的异或线性基。然后求一下这个线性基里面能异或出的最大值即可。

#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b)	for (int i(a); i <= (b); ++i)
#define dec(i, a, b) for (int i(a); i >= (b); --i)
#define ls i << 1
#define rs i << 1 | 1
#define lson i << 1, L, mid
#define rson i << 1 | 1, mid + 1, R typedef long long LL; const int N = 2e4 + 10; struct lb{
LL d[70];
int cnt;
void clear(){
memset(d, 0, sizeof d);
cnt = 0;
}
bool ins(LL val){
dec(i, 62, 0) if (val & (1LL << i)){
if (!d[i]){ d[i] = val; break; }
val ^= d[i];
}
return val > 0;
}
LL qmax(){
LL ret = 0;
dec(i, 62, 0) if ((ret ^ d[i]) > ret) ret ^= d[i];
return ret;
}
LL qmin(){
rep(i, 0, 62) if (d[i]) return d[i];
return 0;
}
}; lb t[N << 3]; int f[N], fp[N], son[N], deep[N], father[N], sz[N], top[N];
int q, tot, n;
LL a[N];
vector <int> v[N]; lb merge(const lb &n1, const lb &n2){
lb ret = n1;
dec(i, 60, 0) if (n2.d[i]) ret.ins(n2.d[i]);
return ret;
} void dfs1(int x, int fa, int dep){
deep[x] = dep;
father[x] = fa;
son[x] = 0;
sz[x] = 1;
int ct = (int)v[x].size();
rep(i, 0, ct - 1){
int u = v[x][i];
if (u == fa) continue;
dfs1(u, x, dep + 1);
sz[x] += sz[u];
if (sz[son[x]] < sz[u]) son[x] = u;
}
} void dfs2(int x, int tp){
top[x] = tp;
f[x] = ++tot;
fp[f[x]] = x;
if (son[x]) dfs2(son[x], tp);
int ct = (int)v[x].size();
rep(i, 0, ct - 1){
int u = v[x][i];
if (u == father[x] || u == son[x]) continue;
dfs2(u, u);
}
} void build(int i, int L, int R){
if (L == R){
t[i].ins(a[fp[L]]);
return;
} int mid = (L + R) >> 1;
build(lson);
build(rson);
t[i] = merge(t[ls], t[rs]);
} lb query(int i, int L, int R, int l, int r){
if (L == l && R == r) return t[i];
int mid = (L + R) >> 1;
if (r <= mid) return query(lson, l, r);
else if (l > mid) return query(rson, l, r);
else return merge(query(lson, l, mid), query(rson, mid + 1, r));
} lb work(int x, int y){
lb ret;
ret.clear();
int f1 = top[x], f2 = top[y];
for (; f1 != f2; ){
if (deep[f1] < deep[f2]) swap(f1, f2), swap(x, y);
ret = merge(ret, query(1, 1, n, f[f1], f[x]));
x = father[f1], f1 = top[x];
} if (x == y) return merge(ret, query(1, 1, n, f[x], f[y]));
if (deep[x] > deep[y]) swap(x, y);
return merge(ret, query(1, 1, n, f[x], f[y]));
} int main(){ scanf("%d%d", &n, &q);
rep(i, 1, n) scanf("%lld", a + i); rep(i, 2, n){
int x, y;
scanf("%d%d", &x, &y);
v[x].push_back(y);
v[y].push_back(x);
} dfs1(1, 0, 0);
dfs2(1, 1);
build(1, 1, n); while (q--){
int x, y;
scanf("%d%d", &x, &y);
lb cnt = work(x, y);
printf("%lld\n", cnt.qmax());
} return 0;
}

  

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