From 73fbb2f131eef86f56ccf0fa2a509d47ceb92d98 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Fri, 6 Jan 2023 22:01:46 +0800
Subject: [PATCH] F - Imbalance Value of a Tree

https://codeforces.com/contest/915/submission/188221976
---
 Codeforces/915/F/F.cpp | 89 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 89 insertions(+)
 create mode 100644 Codeforces/915/F/F.cpp

diff --git a/Codeforces/915/F/F.cpp b/Codeforces/915/F/F.cpp
new file mode 100644
index 00000000..1ca03362
--- /dev/null
+++ b/Codeforces/915/F/F.cpp
@@ -0,0 +1,89 @@
+#include <iostream>
+#include <algorithm>
+#include <iterator>
+#include <numeric>
+#include <tuple>
+#include <utility>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e6 + 5;
+
+int n, a[N], fa_min[N], fa_max[N], siz_min[N], siz_max[N];
+long long ans;
+std::pair<int, int> e[N];
+std::tuple<int, int, int> edges_min[N], edges_max[N];
+
+int find(int *fa, int x) {
+    return fa[x] == x ? x : fa[x] = find(fa, fa[x]);
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+    }
+
+    for (int i = 1; i < n; i++) {
+        cin >> e[i].first >> e[i].second;
+    }
+
+    std::fill(std::begin(siz_min), std::end(siz_min), 1);
+    std::fill(std::begin(siz_max), std::end(siz_max), 1);
+
+    std::iota(fa_min, fa_min + N, 0);
+    std::iota(fa_max, fa_max + N, 0);
+
+    std::transform(e + 1, e + n, edges_min + 1, [&](const std::pair<int, int> &edge) -> std::tuple<int, int, int> {
+        return std::make_tuple(edge.first, edge.second, std::min(a[edge.first], a[edge.second]));
+    });
+    std::transform(e + 1, e + n, edges_max + 1, [&](const std::pair<int, int> &edge) -> std::tuple<int, int, int> {
+        return std::make_tuple(edge.first, edge.second, std::max(a[edge.first], a[edge.second]));
+    });
+
+    std::sort(edges_min + 1, edges_min + n, [&](const std::tuple<int, int, int> &a, const std::tuple<int, int, int> &b) {
+        return std::get<2>(a) > std::get<2>(b);
+    });
+    std::sort(edges_max + 1, edges_max + n, [&](const std::tuple<int, int, int> &a, const std::tuple<int, int, int> &b) {
+        return std::get<2>(a) < std::get<2>(b);
+    });
+
+    cout << std::accumulate(edges_max + 1, edges_max + n, 0ll, [&](long long acc, const std::tuple<int, int, int> &cur) -> long long {
+                int u, v, w;
+
+                std::tie(u, v, w) = cur;
+
+                u = find(fa_max, u), v = find(fa_max, v);
+
+                if (u != v) {
+                    acc += static_cast<long long>(w) * siz_max[u] * siz_max[v];
+                    fa_max[u] = v;
+                    siz_max[v] += siz_max[u];
+                }
+
+                return acc;
+            }) - std::accumulate(edges_min + 1, edges_min + n, 0ll, [&](long long acc, const std::tuple<int, int, int> &cur) -> long long {
+                int u, v, w;
+
+                std::tie(u, v, w) = cur;
+
+                u = find(fa_min, u), v = find(fa_min, v);
+
+                if (u != v) {
+                    acc += static_cast<long long>(w) * siz_min[u] * siz_min[v];
+                    fa_min[u] = v;
+                    siz_min[v] += siz_min[u];
+                }
+
+                return acc;
+            })
+         << endl;
+
+    return 0;
+}