new file: P17437.cpp

P17437.cpp

@@ -0,0 +1,127 @@
+#include <bits/stdc++.h>
+#define int long long
+using namespace std;
+int n; // 5e5
+vector<int> fri[500005];
+int dep[500005];
+int fa[500005];
+long long sum[500005];
+long long dmin[500005], dmax[500005]; // down max / min
+long long umin[500005], umax[500005]; // up 反向的 max和min
+int ord[500005], stk[500005];
+const long long INF = LLONG_MAX;
+const long long _INF = LLONG_MIN;
+long long median(long long x, long long y, long long z) {
+    long long a[3] = {x, y, z};
+    sort(a, a + 3);
+    return a[1];
+}
+int noword;
+void dfs(int u) {
+    dep[u] = dep[fa[u]] + 1;
+    ord[++noword] = u;
+    for (int v : fri[u]) {
+        if (v == fa[u]) continue;
+        fa[v] = u;
+        dfs(v);
+    }
+}
+void pre() {
+    noword = 0;
+    dfs(1);
+    int cnt = noword;
+    for (int i = cnt; i >= 1; --i) {
+        int now = ord[i];
+        dmin[now] = INF;
+        dmax[now] = _INF;
+        for (int v : fri[now]) {
+            if (v == fa[now]) continue;
+            sum[now] += sum[v];
+            if (sum[v] < dmin[now]) dmin[now] = sum[v];
+            if (sum[v] > dmax[now]) dmax[now] = sum[v];
+            if (dmin[v] < dmin[now]) dmin[now] = dmin[v];
+            if (dmax[v] > dmax[now]) dmax[now] = dmax[v];
+        }
+    }
+    umin[1] = INF;
+    umax[1] = _INF;
+    for (int i = 1; i <= cnt; ++i) {
+        int u = ord[i];
+        long long min1 = INF, min2 = INF;
+        long long max1 = _INF, max2 = _INF;
+        int minid = 0, maxid = 0;
+        for (int v : fri[u]) {
+            if (v == fa[u]) continue;
+            long long mn = sum[v];
+            if (dmin[v] < mn) mn = dmin[v];
+            long long mx = sum[v];
+            if (dmax[v] > mx) mx = dmax[v];
+            if (mn < min1) {
+                min2 = min1;
+                min1 = mn;
+                minid = v;
+            } else if (mn < min2) {
+                min2 = mn;
+            }
+            if (mx > max1) {
+                max2 = max1;
+                max1 = mx;
+                maxid = v;
+            } else if (mx > max2) {
+                max2 = mx;
+            }
+        }
+        long long pmin = INF, pmax = _INF;
+        if (u != 1) {
+            pmin = sum[1] - sum[u];
+            if (umin[u] < pmin) pmin = umin[u];
+            pmax = sum[1] - sum[u];
+            if (umax[u] > pmax) pmax = umax[u];
+        }
+        for (int v : fri[u]) {
+            if (v == fa[u]) continue;
+            long long amin = (v == minid ? min2 : min1);
+            long long amax = (v == maxid ? max2 : max1);
+            umin[v] = pmin < amin ? pmin : amin;
+            umax[v] = pmax > amax ? pmax : amax;
+        }
+    }
+}
+signed main() {
+    // freopen("young.in", "r", stdin);
+    // freopen("young.out", "w", stdout);
+    scanf("%lld", &n);
+    for (int i = 1; i <= n; ++i)
+        scanf("%lld", &sum[i]);
+    for (int i = 1, u, v; i < n; ++i)
+        scanf("%lld%lld", &u, &v), fri[u].push_back(v), fri[v].push_back(u);
+    pre();
+    long long ans = _INF;
+    for (int v = 2; v <= n; ++v) {
+        long long B = sum[1] - sum[v];
+        if (dmin[v] != INF)
+            ans = max(ans, median(dmin[v], sum[v] - dmin[v], B));
+        if (dmax[v] != _INF)
+            ans = max(ans, median(dmax[v], sum[v] - dmax[v], B));
+        if (umin[v] != INF)
+            ans = max(ans, median(umin[v], B - umin[v], sum[v]));
+        if (umax[v] != _INF)
+            ans = max(ans, median(umax[v], B - umax[v], sum[v]));
+    }
+    printf("%lld\n", ans);
+    return 0;
+}
+/*
+让三块里排在中间的那块尽可能大
+先枚举第一条断边
+令1为根，用id代表节点id头顶的边
+枚举第一个切割，分为两部分 一部分是id的子树 另一部分为sum[1]-sum[id]
+第二刀切在id内部或id外部
+
+以 1 为根。求出
+S_u 以 u 为根的子树权值和
+dmin[u] u 内切，最小连通块权值
+dmax[u] u 内切，最大连通块权值
+
+可以直接求（max/min(sum[孩子], dmax/min孩子)）
+*/