# World Codesprint 10: Maximum Disjoint Subtree Product

### 解法

#include <iostream>
#include <cstdio>
#include <vector>
#include <functional>
#include <algorithm>

// add :: T -> T -> T
//     {v1,v2,...,vm}+vm+1
// bundle :: T -> T
//     u->{v1,v2,v3,...,vm}
template<class T, class F1, class F2>
std::vector<T> freeTreeDP(const std::vector<std::vector<int>> &g, F1 add, F2 bundle) {
const int n = g.size();
std::vector<T> dp(n);
std::function<void(int, int)> dfs = [&](int u, int p) {
for (int v : g[u]) {
if (v != p) {
dfs(v, u);
}
}
dp[u] = bundle(dp[u], u);
};
dfs(0, -1);
std::function<void(int, int)> dfs2 = [&](int u, int p) {
const int m = g[u].size();
T l;
std::vector<T> r(m);
for (int i = m - 2; i >= 0; i--) {
r[i] = add(dp[g[u][i + 1]], r[i + 1]);
}
for (int i = 0; i < m; i++) {
const int v = g[u][i];
if (v != p) {
dfs2(v, u);
}
}
dp[u] = bundle(l, u);
};
dfs2(0, -1);
return dp;
}

int main() {
const long long INF = 1e18;
struct foo {
long long max = -INF;
long long min = INF;
long long maxc = -INF;
long long minc = INF;
long long maxp;
long long minp;
};

int n;
std::cin >> n;

std::vector<long long> w(n);
for (int i = 0; i < n; i++) {
scanf("%lld", &w[i]);
}

std::vector<std::vector<int>> tree(2 * n - 1);
for (int i = 0; i < n - 1; i++) {
int u, v;
scanf("%d %d", &u, &v);
u--;
v--;
tree[u].push_back(i + n);
tree[i + n].push_back(u);
tree[v].push_back(i + n);
tree[i + n].push_back(v);
}

auto add = [&](const foo &a, const foo &b) {
foo c;
c.max = std::max(a.max, b.max);
c.min = std::min(a.min, b.min);
c.maxc = std::max(0LL, a.maxc) + std::max(0LL, b.maxc);
c.minc = std::min(0LL, a.minc) + std::min(0LL, b.minc);
c.maxp = a.max * b.max;
c.minp = a.min * b.min;
return c;
};

auto bundle = [&](const foo &a, int id) {
foo c;
if (id < n) {
c.maxc = std::max(a.maxc + w[id], w[id]);
c.minc = std::min(a.minc + w[id], w[id]);
c.max = std::max(a.max, c.maxc);
c.min = std::min(a.min, c.minc);
} else {
c = a;
}
return c;
};

auto dp = freeTreeDP<foo>(tree, add, bundle);

long long ans = -1e18;
for (int i = n; i < 2 * n - 1; i++) {
ans = std::max(ans, std::max(dp[i].maxp, dp[i].minp));
}
std::cout << ans << std::endl;
}