51nod 1297 管理二叉树 (树分治)

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <queue>
#include <cstdlib>
#include <vector>
#include <set>
#include <assert.h>
using namespace std;

#define N 200020
#define M 500200
#define inf 0x3f3f3f3f
#define mod 110119
#define LL long long
#define ls (i << 1)
#define rs (ls | 1)
#define md (ll + rr >> 1)
#define lson ll, md, ls
#define rson md + 1, rr, rs
#define MP make_pair
#define pii pair<int, int>
#define ui unsigned int
#define fi first
#define se second
#define pll pair<LL, LL>

int n, a
;
int fa
;
int fst
, nxt[M], vv[M], e;

int dep
, sz
, mx
;
int q
, qh, qt;
bool vis
, tvis
;
LL sum[N * 20];
int cnt[N * 20];
int bk_cnt;

struct node {
int x, y, d;
node() {}
node(int x, int y, int d):x(x), y(y), d(d) {}
};
vector<node> vt
;

void init() {
memset(fst, -1, sizeof fst);
e = 0;
}
void add(int u, int v) {
vv[e] = v, nxt[e] = fst[u], fst[u] = e++;
}

struct bst {
int tag[N << 2];

int x
, y
, xx
, yy
;

void push_down(int i) {
if(tag[i]) {
tag[ls] = tag[rs] = tag[i];
tag[i] = 0;
}
}
void update(int l, int r, int v, int ll, int rr, int i) {
if(ll == l && rr == r) {
tag[i] = v;
return;
}
push_down(i);
if(r <= md) update(l, r, v, lson);
else if(l > md) update(l, r, v,rson);
else update(l, md, v, lson), update(md + 1, r, v, rson);
}
int query(int x, int ll, int rr, int i) {
if(tag[i]) return tag[i];
if(ll == rr) return 0;
if(x <= md) return query(x, lson);
return query(x, rson);
}

void insert(int v) {
if(v == 1) {
x[1] = 1, y[1] = n;
}
else {
int p = query(a[v], 1, n, 1);
if(a[v] < a[p]) {
x[v] = x[p], y[v] = y[p];
}
else
x[v] = xx[p], y[v] = yy[p];
fa[v] = p;
}
yy[v] = y[v];
y[v] = a[v] - 1;
xx[v] = a[v] + 1;
if(x[v] <= y[v]) update(x[v], y[v], v, 1, n, 1);
if(xx[v] <= yy[v]) update(xx[v], yy[v], v, 1, n, 1);
}

}BST;

void bfs(int s) {

qh = qt = 0;
q[qt++] = s;
tvis[s] = 1;
dep[s] = 0;

while(qh < qt) {
int u = q[qh++];
for(int i = fst[u]; ~i; i = nxt[i]) {
int v = vv[i];
if(vis[v] || tvis[v]) continue;
tvis[v] = 1;
dep[v] = dep[u] + 1;
q[qt++] = v;
}
}
for(int i = 0; i < qt; ++i) tvis[q[i]] = 0;

}

void divide(int s) {
bfs(s);
int rt = 0, tmp = inf;
for(int i = qt - 1; i >= 0; --i) {
int u = q[i];
sz[u] = 1;
mx[u] = 0;
for(int j = fst[u]; ~j; j = nxt[j]) {
int v = vv[j];
if(dep[v] < dep[u] || vis[v]) continue;
sz[u] += sz[v];
mx[u] = max(mx[u], sz[v]);
}
}
for(int i = 0; i < qt; ++i) {
int u = q[i];
mx[u] = max(mx[u], qt - sz[u]);
if(mx[u] < tmp) tmp = mx[u], rt = u;
}

vis[rt] = 1;
bfs(rt);
int k = ++bk_cnt;
vt[rt].push_back(node(k, -1, 0));
for(int i = fst[rt]; ~i; i = nxt[i]) {
int v = vv[i];
if(vis[v]) continue;
bfs(v);
++bk_cnt;
for(int j = 0; j < qt; ++j) {
int u = q[j];
vt[u].push_back(node(k, bk_cnt, dep[u] + 1));
}
}
for(int i = fst[rt]; ~i; i = nxt[i]) {
int v = vv[i];
if(!vis[v]) divide(v);
}

}
LL query(int u) {
LL ret = 0;
for(int i = 0; i < vt[u].size(); ++i) {
int x = vt[u][i].x;
int y = vt[u][i].y;
int d = vt[u][i].d;
ret += 1LL * cnt[x] * d + sum[x];
if(y != -1) ret -= 1LL * cnt[y] * d + sum[y];
}
return ret;
}

void upd(int u) {
for(int i = 0; i < vt[u].size(); ++i) {
int x = vt[u][i].x;
int y = vt[u][i].y;
int d = vt[u][i].d;
sum[x] += d;
cnt[x] ++;
if(y != -1) cnt[y] ++, sum[y] += d;
}
}

int main() {
scanf("%d", &n);
for(int i = 1; i <= n; ++i) {
scanf("%d", &a[i]);
}
for(int i = 1; i <= n; ++i) {
BST.insert(i);
}
init();
for(int i = 2; i <= n; ++i) {
add(fa[i], i);
add(i, fa[i]);
}
memset(vis, 0, sizeof vis);
bk_cnt = 0;

divide(1);
LL ans = 0;
for(int i = 1; i <= n; ++i) {
if(i > 1) {
ans += query(i);
}
upd(i);
printf("%lld\n", ans);
}
return 0;
}