From d512177fcba8a5d2c8ab695c11b2e359881f966e Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Thu, 5 Jan 2023 20:48:26 +0800
Subject: [PATCH] P6822 [PA2012]Tax

https://www.luogu.com.cn/record/98773803
---
 Luogu/P6822/P6822.cpp | 108 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 108 insertions(+)
 create mode 100644 Luogu/P6822/P6822.cpp

diff --git a/Luogu/P6822/P6822.cpp b/Luogu/P6822/P6822.cpp
new file mode 100644
index 00000000..280c634f
--- /dev/null
+++ b/Luogu/P6822/P6822.cpp
@@ -0,0 +1,108 @@
+#include <iostream>
+#include <algorithm>
+#include <functional>
+#include <queue>
+#include <tuple>
+#include <utility>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5,
+          M = 2e5 + 5;
+const long long INF = 0x3f3f3f3f'3f3f3f3f;
+
+int n, m, s, t;
+std::vector<std::tuple<int, int, int>> g[N];
+std::vector<std::pair<int, int>> g2[M << 1];
+long long dist[M << 1];
+bool vis[M << 1];
+
+void dijkstra() {
+    std::fill(std::begin(dist), std::end(dist), INF);
+    std::fill(std::begin(vis), std::end(vis), false);
+
+    std::priority_queue<std::pair<long long, int>, std::vector<std::pair<long long, int>>, std::greater<>> q;
+
+    q.emplace(0, s);
+    dist[s] = 0;
+
+    while (!q.empty()) {
+        long long l;
+        int u;
+
+        std::tie(l, u) = q.top();
+
+        q.pop();
+
+        if (vis[u]) continue;
+
+        for (auto e : g2[u]) {
+            int v = e.first,
+                w = e.second;
+
+            if (dist[v] > l + w) {
+                dist[v] = l + w;
+
+                q.emplace(dist[v], v);
+            }
+        }
+
+        vis[u] = true;
+    }
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    for (int i = 1, u, v, w; i <= m; i++) {
+        cin >> u >> v >> w;
+
+        g[u].emplace_back(v, w, i << 1);
+        g[v].emplace_back(u, w, i << 1 | 1);
+    }
+
+    s = 0, t = 2 * m + 2;
+
+    for (int i = 1; i <= n; i++) {
+        std::sort(g[i].begin(), g[i].end(), [](const std::tuple<int, int, int> &lhs, const std::tuple<int, int, int> &rhs) {
+            return std::get<1>(lhs) < std::get<1>(rhs);
+        });
+
+        for (int j = 0; j < g[i].size(); j++) {
+            int v, w, id;
+
+            std::tie(v, w, id) = g[i][j];
+
+            g2[id ^ 1].emplace_back(id, w);
+
+            if (i == 1) {
+                g2[s].emplace_back(id, w);
+            }
+
+            if (v == n) {
+                g2[id].emplace_back(t, w);
+            }
+
+            if (j != 0) {
+                int w2, id2;
+
+                std::tie(std::ignore, w2, id2) = g[i][j - 1];
+
+                g2[id2].emplace_back(id, w - w2);
+                g2[id].emplace_back(id2, 0);
+            }
+        }
+    }
+
+    dijkstra();
+
+    cout << dist[t] << endl;
+
+    return 0;
+}