动态DP
神仙芝士= =
恐怕讲不好，还是挂别人 dalao 的 blog 吧！
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147// luogu4719
using namespace std;
const int N = 1e5 + 10, inf = 1e9;
int n, m, dfn;
int f[N][2], g[N][2];
int w[N], w2[N], sz[N], top[N], ed[N], bel[N];
int dep[N], fa[N], son[N], id[N];
int to[N << 1], nxt[N << 1], lnk[N], cnt;
struct tree {
int l, r;
}tr[N << 2];
struct node {
int m[5][5];
void cl() {
for (int i = 0; i <= 2; i++)
for (int j = 0; j <= 2; j++) m[i][j] = -inf;
}
}ans[N << 2], val[N << 2];
void add(int x, int y) {
to[++cnt] = y, nxt[cnt] = lnk[x], lnk[x] = cnt;
}
void dfs1(int x, int f) {
sz[x] = 1;
dep[x] = dep[f] + 1;
fa[x] = f;
int Mx = -1;
for (int i = lnk[x]; i; i = nxt[i]) {
int y = to[i];
if (y == f) continue;
dfs1(y, x);
sz[x] += sz[y];
if (sz[y] > Mx) Mx = sz[y], son[x] = y;
}
}
void dfs2(int x, int f) {
top[x] = f;
id[x] = ++dfn;
bel[dfn] = x, ed[f] = x;
if (son[x]) dfs2(son[x], f);
for (int i = lnk[x]; i; i = nxt[i]) {
int y = to[i];
if (y == fa[x] || y == son[x]) continue;
dfs2(y, y);
}
ed[x] = ed[f]; // !!!!!!!!
}
void dfs3(int x) {
g[x][1] = w[x];
for (int i = lnk[x]; i; i = nxt[i]) {
int y = to[i];
if (y == son[x] || y == fa[x]) continue;
dfs3(y);
g[x][0] += max(f[y][0], f[y][1]);
g[x][1] += f[y][0];
}
f[x][0] += g[x][0], f[x][1] += g[x][1];
if (son[x]) {
dfs3(son[x]);
f[x][0] += max(f[son[x]][1], f[son[x]][0]);
f[x][1] += f[son[x]][0];
}
}
// ----------------------------------------------------------------
node mul(node x, node y) {
node res;
res.cl();
for (int i = 0; i <= 1; i++)
for (int j = 0; j <= 1; j++)
for (int k = 0; k <= 1; k++)
res.m[i][j] = max(res.m[i][j], x.m[i][k] + y.m[k][j]);
return res;
}
void build(int x, int l, int r) {
tr[x].l = l, tr[x].r = r;
if (l == r) {
val[bel[l]].m[0][0] = g[bel[l]][0], val[bel[l]].m[0][1] = g[bel[l]][0];
val[bel[l]].m[1][0] = g[bel[l]][1], val[bel[l]].m[1][1] = -inf;
ans[x] = val[bel[l]];
return;
}
int mid = (l + r) >> 1;
build(x << 1, l, mid), build(x << 1 | 1, mid + 1, r);
ans[x] = mul(ans[x << 1], ans[x << 1 | 1]);
}
node query(int x, int l, int r) {
if (l <= tr[x].l && tr[x].r <= r) return ans[x];
int mid = (tr[x].l + tr[x].r) >> 1;
if (mid >= r) return query(x << 1, l, r);
if (mid < l) return query(x << 1 | 1, l, r);
return mul(query(x << 1, l, r), query(x << 1 | 1, l, r));
}
void upd(int x, int pos) {
if (tr[x].l == tr[x].r && tr[x].l == pos) {
ans[x] = val[bel[pos]];
return;
}
int mid = (tr[x].l + tr[x].r) >> 1;
if (pos <= mid) upd(x << 1, pos);
else upd(x << 1 | 1, pos);
ans[x] = mul(ans[x << 1], ans[x << 1 | 1]);
}
void modify(int x, int f) {
val[x].m[1][0] += f - w[x];
w[x] = f;
while (x != 0) {
int y = top[x];
node lst = query(1, id[y], id[ed[y]]);
upd(1, id[x]);
node now = query(1, id[y], id[ed[y]]);
x = fa[y];
val[x].m[0][0] += max(now.m[0][0], now.m[1][0]) - max(lst.m[0][0], lst.m[1][0]);
val[x].m[0][1] = val[x].m[0][0];
val[x].m[1][0] += now.m[0][0] - lst.m[0][0];
}
}
int main() {
scanf("%d%d", &n, &m);
for (int i = 1; i <= n; i++) scanf("%d", &w[i]);
for (int i = 1; i < n; i++) {
int x, y; scanf("%d%d", &x, &y);
add(x, y), add(y, x);
}
dfs1(1, 0);
dfs2(1, 0);
dfs3(1);
build(1, 1, n);
while (m--) {
int x, y; scanf("%d%d", &x, &y);
modify(x, y);
node res = query(1, id[1], id[ed[1]]);
printf("%d\n", max(res.m[0][0], res.m[1][0]));
}
return 0;
}