BZOJ 4539: [Hnoi2016]树 [主席树 lca]
4539: [Hnoi2016]树
题意：不想写。复制模板树的子树，查询两点间距离。
终于有一道会做的题了......
画一画发现可以把每次复制的子树看成一个大点来建一棵树，两点的lca一定在大点的lca里
然后每个大点维护一坨信息：节点编号的区间范围，到根的距离，大点对应子树的根，大点是接在了模板树里哪个点下面
然后做就行了
给出大树上一个点的编号，找到对应的大点可以二分；再找到对应模板树上的点，因为编号是按原大小来的，就是子树k大值，可以用主席树
求距离的时候我分了三种情况：
- 同一个大点
- 大点在一条链上
- 普通情况
第一次写这么长的代码...(以前我压行是有多厉害)
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
#define fir first
#define sec second
#define lc(x) t[x].l
#define rc(x) t[x].r
typedef long long ll;
const int N=2e5+5;
inline ll read() {
char c=getchar(); ll x=0,f=1;
while(c<'0' || c>'9') {if(c=='-')f=-1; c=getchar();}
while(c>='0' && c<='9') {x=x*10+c-'0'; c=getchar();}
return x*f;
}
int n, m, Q; ll x, y;
namespace temT {
struct edge{int v, ne;} e[N<<1];
int cnt=1, h[N];
inline void ins(int u, int v) {
e[++cnt] = (edge){v, h[u]}; h[u] = cnt;
e[++cnt] = (edge){u, h[v]}; h[v] = cnt;
}
int deep[N], size[N], fa[N][18];
pair<int, int> dfn[N]; int dfc, ver[N];
void dfs(int u) {
for(int i=1; (1<<i) <= deep[u]; i++)
fa[u][i] = fa[ fa[u][i-1] ][i-1];
dfn[u].fir = ++dfc; ver[dfc] = u;
size[u] = 1;
for(int i=h[u];i;i=e[i].ne)
if(e[i].v != fa[u][0]) {
fa[e[i].v][0] = u;
deep[e[i].v] = deep[u]+1;
dfs(e[i].v);
size[u] += size[e[i].v];
}
dfn[u].sec = dfc;
}
inline int lca(int x, int y) {
if(deep[x] < deep[y]) swap(x, y);
int bin = deep[x] - deep[y];
for(int i=16; i>=0; i--) if((1<<i) & bin) x = fa[x][i];
if(x == y) return x;
for(int i=16; i>=0; i--) if(fa[x][i] != fa[y][i]) x = fa[x][i], y = fa[y][i];
return fa[x][0];
}
inline int dis(int x, int y) {return abs(deep[x] - deep[y]);}
struct meow{int l, r, size;} t[N*20];
int sz, root[N];
void insert(int &x, int l, int r, int p) {
t[++sz] = t[x]; x = sz;
t[x].size++;
if(l==r) return;
int mid = (l+r)>>1;
if(p <= mid) insert(t[x].l, l, mid, p);
else insert(t[x].r, mid+1, r, p);
}
int kth(int id, int k) {
int x = root[ dfn[id].fir - 1 ], y = root[ dfn[id].sec ], l=1, r=n;
//printf("kth %d %d %d %d\n", id, x, y, k);
while(l != r) {
int mid = (l+r)>>1, lsize = t[lc(y)].size - t[lc(x)].size;
if(k <= lsize) x = lc(x), y = lc(y), r = mid;
else k -= lsize, x = rc(x), y = rc(y), l = mid+1;
}
return l;
}
void build() {
dfs(1);
for(int i=1; i<=dfc; i++) root[i]=root[i-1], insert(root[i], 1, n, ver[i]);
}
}
namespace bigT {
struct edge{int v, ne;} e[N];
int cnt=1, h[N];
inline void ins(int u, int v) {
e[++cnt] = (edge){v, h[u]};
}
int fa[N][17], deep[N];
inline void update(int u) {
for(int i=1; (1<<i) <= deep[u]; i++)
fa[u][i] = fa[ fa[u][i-1] ][i-1];
}
inline int lca(int x, int y) {
if(deep[x] < deep[y]) swap(x, y);
int bin = deep[x] - deep[y];
for(int i=16; i>=0; i--) if((1<<i) & bin) x = fa[x][i];
if(x == y) return x;
for(int i=16; i>=0; i--) if(fa[x][i] != fa[y][i]) x = fa[x][i], y = fa[y][i];
return fa[x][0];
}
struct info{
ll l, r, dis, root, in;
//void print() {printf("[%d, %d] %d %d %d\n", l, r, dis, root, in);}
} li[N];
int tot; ll size;
void init() {
tot=1; size=n;
li[1] = (info){1, n, 0, 1, 0};
}
inline int find(ll x) {
int l=1, r=tot;
while(l <= r) {
int mid = (l+r)>>1;
if(li[mid].l <= x && x <= li[mid].r) return mid;
else if(x < li[mid].l) r = mid-1;
else l = mid+1;
}
return -1;
}
void move(ll x, ll y) { //printf("\nmove %d --> %d\n", x, y);
int by = find(y);
y = temT::kth(li[by].root, y - li[by].l + 1); //printf("by %d %d\n", by, y);
int bx = ++tot;
li[bx] = (info){size+1, size + temT::size[x], li[by].dis + temT::dis(y, li[by].root) + 1, x, y};
size = li[bx].r;
fa[bx][0] = by;
deep[bx] = deep[by]+1;
update(bx);
}
void quer(ll x, ll y) { //printf("\nquer %d --- %d\n", x, y);
int bx = find(x); x = temT::kth(li[bx].root, x - li[bx].l + 1); //printf("bx %d %d\n", bx, x);
int by = find(y); y = temT::kth(li[by].root, y - li[by].l + 1); //printf("by %d %d\n", by, y);
ll ans=0;
if(bx == by) {
int p = temT::lca(x, y);
ans = temT::dis(x, p) + temT::dis(y, p);
} else {
int bp = lca(bx, by); //printf("bp %d\n", bp);
if(bp == by) swap(bx, by), swap(x, y);
if(bp == bx) {
ans += li[by].dis - li[bx].dis + temT::dis(y, li[by].root) + temT::dis(x, li[bx].root);
//printf("ans %d\n", ans);
//for(int i=16; i>=0; i--) printf("fa %d %d %d %d\n", by, i, fa[by][i], deep[fa[by][i]]);
for(int i=16; i>=0; i--)
if(fa[by][i] && deep[ fa[by][i] ] > deep[bx]) by = fa[by][i];
y = li[by].in;
//printf("iny %d %d\n", by, y);
int p = temT::lca(x, y);
if(p != li[bx].root) ans += temT::dis(x, p) + temT::dis(y, p) - temT::dis(x, li[bx].root) - temT::dis(y, li[bx].root);
} else {
ans = li[bx].dis + li[by].dis - (li[bp].dis << 1); //printf("ans %d %d %d %d\n", ans, li[bx].dis, li[by].dis, li[bp].dis);
ans += temT::dis(x, li[bx].root) + temT::dis(y, li[by].root); //printf("ans %d\n", ans);
for(int i=16; i>=0; i--) {
if(fa[bx][i] && deep[ fa[bx][i] ] > deep[bp]) bx = fa[bx][i];
if(fa[by][i] && deep[ fa[by][i] ] > deep[bp]) by = fa[by][i];
}
x = li[bx].in, y = li[by].in; //printf("in %d %d %d %d\n", bx, x, by, y);
int p = temT::lca(x, y);
if(p != li[bp].root)
ans += temT::dis(x, p) + temT::dis(y, p) - temT::dis(x, li[bp].root) - temT::dis(y, li[bp].root);
}
}
printf("%lld\n", ans);
}
}
int main() {
//freopen("in", "r", stdin);
freopen("tree_tenderRun.in", "r", stdin);
freopen("tree_tenderRun.out", "w", stdout);
n=read(); m=read(); Q=read();
for(int i=1; i<n; i++) temT::ins(read(), read());
temT::build();
bigT::init();
for(int i=1; i<=m; i++) x=read(), y=read(), bigT::move(x, y);
for(int i=1; i<=Q; i++) x=read(), y=read(), bigT::quer(x, y);
}
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