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157 | #include <algorithm>
#include <cstring>
#include <iostream>
using namespace std;
constexpr int MAXN = 500010;
constexpr int INF = 0x3f3f3f3f;
int Begin[MAXN], Next[MAXN], To[MAXN], e, n, m;
int sz[MAXN], son[MAXN], top[MAXN], fa[MAXN], dis[MAXN], p[MAXN], id[MAXN],
End[MAXN];
// p[i]表示i树剖后的编号，id[p[i]] = i
int cnt, tot, a[MAXN], f[MAXN][2];
struct matrix {
int g[2][2];
matrix() { memset(g, 0, sizeof(g)); }
matrix operator*(const matrix &b) const // 重载矩阵乘
{
matrix c;
for (int i = 0; i <= 1; i++)
for (int j = 0; j <= 1; j++)
for (int k = 0; k <= 1; k++)
c.g[i][j] = max(c.g[i][j], g[i][k] + b.g[k][j]);
return c;
}
} Tree[MAXN], g[MAXN]; // Tree[]是建出来的线段树，g[]是维护的每个点的矩阵
void PushUp(int root) { Tree[root] = Tree[root << 1] * Tree[root << 1 | 1]; }
void Build(int root, int l, int r) {
if (l == r) {
Tree[root] = g[id[l]];
return;
}
int Mid = (l + r) >> 1;
Build(root << 1, l, Mid);
Build(root << 1 | 1, Mid + 1, r);
PushUp(root);
}
matrix Query(int root, int l, int r, int L, int R) {
if (L <= l && r <= R) return Tree[root];
int Mid = (l + r) >> 1;
if (R <= Mid) return Query(root << 1, l, Mid, L, R);
if (Mid < L) return Query(root << 1 | 1, Mid + 1, r, L, R);
return Query(root << 1, l, Mid, L, R) *
Query(root << 1 | 1, Mid + 1, r, L, R);
// 注意查询操作的书写
}
void Modify(int root, int l, int r, int pos) {
if (l == r) {
Tree[root] = g[id[l]];
return;
}
int Mid = (l + r) >> 1;
if (pos <= Mid)
Modify(root << 1, l, Mid, pos);
else
Modify(root << 1 | 1, Mid + 1, r, pos);
PushUp(root);
}
void Update(int x, int val) {
g[x].g[1][0] += val - a[x];
a[x] = val;
// 首先修改x的g矩阵
while (x) {
matrix last = Query(1, 1, n, p[top[x]], End[top[x]]);
// 查询top[x]的原本g矩阵
Modify(1, 1, n,
p[x]); // 进行修改(x点的g矩阵已经进行修改但线段树上的未进行修改)
matrix now = Query(1, 1, n, p[top[x]], End[top[x]]);
// 查询top[x]的新g矩阵
x = fa[top[x]];
g[x].g[0][0] +=
max(now.g[0][0], now.g[1][0]) - max(last.g[0][0], last.g[1][0]);
g[x].g[0][1] = g[x].g[0][0];
g[x].g[1][0] += now.g[0][0] - last.g[0][0];
// 根据变化量修改fa[top[x]]的g矩阵
}
}
void add(int u, int v) {
To[++e] = v;
Next[e] = Begin[u];
Begin[u] = e;
}
void DFS1(int u) {
sz[u] = 1;
int Max = 0;
f[u][1] = a[u];
for (int i = Begin[u]; i; i = Next[i]) {
int v = To[i];
if (v == fa[u]) continue;
dis[v] = dis[u] + 1;
fa[v] = u;
DFS1(v);
sz[u] += sz[v];
if (sz[v] > Max) {
Max = sz[v];
son[u] = v;
}
f[u][1] += f[v][0];
f[u][0] += max(f[v][0], f[v][1]);
// DFS1过程中同时求出f[i][0/1]
}
}
void DFS2(int u, int t) {
top[u] = t;
p[u] = ++cnt;
id[cnt] = u;
End[t] = cnt;
g[u].g[1][0] = a[u];
g[u].g[1][1] = -INF;
if (!son[u]) return;
DFS2(son[u], t);
for (int i = Begin[u]; i; i = Next[i]) {
int v = To[i];
if (v == fa[u] || v == son[u]) continue;
DFS2(v, v);
g[u].g[0][0] += max(f[v][0], f[v][1]);
g[u].g[1][0] += f[v][0];
// g矩阵根据f[i][0/1]求出
}
g[u].g[0][1] = g[u].g[0][0];
}
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
cin >> n >> m;
for (int i = 1; i <= n; i++) cin >> a[i];
for (int i = 1; i <= n - 1; i++) {
int u, v;
cin >> u >> v;
add(u, v);
add(v, u);
}
dis[1] = 1;
DFS1(1);
DFS2(1, 1);
Build(1, 1, n);
for (int i = 1; i <= m; i++) {
int x, val;
cin >> x >> val;
Update(x, val);
matrix ans = Query(1, 1, n, 1, End[1]); // 查询1所在重链的矩阵乘
cout << max(ans.g[0][0], ans.g[1][0]) << '\n';
}
return 0;
}
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