poj 3237 Tree(树链拆分)

题目链接：poj 3237 Tree

题目大意：给定一棵树，三种操作：

CHANGE i v：将i节点权值变为v
NEGATE a b：将ab路径上全部节点的权值变为相反数
QUERY a b：查询ab路径上节点权值的最大值。

解题思路：树链剖分。然后用线段树维护节点权值，成端更新查询。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 10005;
const int INF = 0x3f3f3f3f;

int id, far[maxn], son[maxn], cnt[maxn], idx[maxn], top[maxn], dep[maxn];

int N, en, first[maxn], jump[maxn * 2], val[maxn];
struct Edge {
int u, v, w;
void set (int u, int v, int w) {
this->u = u;
this->v = v;
this->w = w;
}
}ed[maxn * 2];

void dfs_fir (int u, int pre, int d) {
dep[u] = d;
far[u] = pre;
cnt[u] = 1;
son[u] = 0;

for (int i = first[u]; i + 1; i = jump[i]) {
int v = ed[i].v;
if (v == pre)
continue;
dfs_fir(v, u, d + 1);
cnt[u] += cnt[v];
if (cnt[son[u]] < cnt[v])
son[u] = v;
}
}

void dfs_sec(int u, int rot) {
idx[u] = id++;
top[u] = rot;

if (son[u])
dfs_sec(son[u], rot);

for (int i = first[u]; i + 1; i = jump[i]) {
int v = ed[i].v;
if (v == far[u] || v == son[u])
continue;
dfs_sec(v, v);
}
}

#define lson(x) ((x)<<1)
#define rson(x) (((x)<<1)|1)

int lc[maxn << 2], rc[maxn << 2], filp[maxn << 2], Ma[maxn << 2], Mi[maxn << 2];

inline void maintain (int u) {
filp[u] ^= 1;
swap(Ma[u], Mi[u]);
Ma[u] = -Ma[u];
Mi[u] = -Mi[u];
}

inline void pushup(int u) {
Ma[u] = max(Ma[lson(u)], Ma[rson(u)]);
Mi[u] = min(Mi[lson(u)], Mi[rson(u)]);
}

inline void pushdown (int u) {
if (filp[u]) {
maintain(lson(u));
maintain(rson(u));
filp[u] = 0;
}
}

void build (int u, int l, int r) {
lc[u] = l;
rc[u] = r;
filp[u] = 0;

if (l == r) {
Ma[u] = Mi[u] = val[l];
return;
}

int mid = (l + r) / 2;
build(lson(u), l, mid);
build(rson(u), mid + 1, r);
pushup(u);
}

void modify (int u, int x, int w) {
if (lc[u] == x && rc[u] == x) {
Ma[u] = Mi[u] = w;
return;
}

pushdown(u);
int mid = (lc[u] + rc[u]) / 2;
if (x <= mid)
modify(lson(u), x, w);
else
modify(rson(u), x, w);
pushup(u);
}

void splay(int u, int l, int r) {
if (l <= lc[u] && rc[u] <= r) {
maintain(u);
return;
}

pushdown(u);
int mid = (lc[u] + rc[u]) / 2;
if (l <= mid)
splay(lson(u), l, r);
if (r > mid)
splay(rson(u), l, r);
pushup(u);
}

int query (int u, int l, int r) {
if (l <= lc[u] && rc[u] <= r)
return Ma[u];

pushdown(u);
int mid = (lc[u] + rc[u]) / 2, ret = -INF;
if (l <= mid)
ret = max(ret, query(lson(u), l, r));
if (r > mid)
ret = max(ret, query(rson(u), l, r));
pushup(u);
return ret;
}

inline void add_Edge(int u, int v, int w) {
ed[en].set(u, v, w);
jump[en] = first[u];
first[u] = en++;
}

void init () {
en = 0;
id = 1;
memset(first, -1, sizeof(first));

scanf("%d", &N);

int u, v, w;
for (int i = 0; i  < N - 1; i++) {
scanf("%d%d%d", &u, &v, &w);
add_Edge(u, v, w);
add_Edge(v, u, w);
}

dfs_fir(1, 0, 0);
dfs_sec(1, 1);

for (int i = 0; i < N - 1; i++) {
int t = i * 2;
if (dep[ed[t].u] < dep[ed[t].v])
swap(ed[t].u, ed[t].v);
val[idx[ed[t].u]] = ed[t].w;
}
build(1, 1, N);
}

int query (int u, int v) {
int p = top[u], q = top[v], ret = -INF;
while (p != q) {
if (dep[p] < dep[q]) {
swap(p, q);
swap(u, v);
}
ret = max(ret, query(1, idx[p], idx[u]));
u = far[p];
p = top[u];
}
//printf("%d %d\n", u, v);

if (u == v)
return ret;

if (dep[u] > dep[v])
swap(u, v);
ret = max(ret, query(1, idx[son[u]], idx[v]));
return ret;
}

void modify (int u, int v) {
int p = top[u], q = top[v];
while (p != q) {
if (dep[p] < dep[q]) {
swap(p, q);
swap(u, v);
}
splay(1, idx[p], idx[u]);
u = far[p];
p = top[u];
}

if (u == v)
return;

if (dep[u] > dep[v])
swap(u, v);
splay(1, idx[son[u]], idx[v]);
}

void solve () {
int u, v;
char op[20];
while (scanf("%s", op), strcmp(op, "DONE") != 0) {
scanf("%d%d", &u, &v);
if (op[0] == 'C')
modify(1, idx[ed[u*2-2].u], v);
else if (op[0] == 'Q')
printf("%d\n", query(u, v));
else
modify(u, v);
}
}

int main () {
int cas;
scanf("%d", &cas);
while (cas--) {
init();
solve();
}
return 0;
}