From 165b8e0dd1c2613b8330ddfe70c3ef4b941af408 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Tue, 14 Feb 2023 19:04:41 +0800
Subject: [PATCH] P6413 [COCI2008-2009#3] NAJKRACI

https://www.luogu.com.cn/record/102143043
---
 Luogu/P6413/P6413.cpp | 157 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 157 insertions(+)
 create mode 100644 Luogu/P6413/P6413.cpp

diff --git a/Luogu/P6413/P6413.cpp b/Luogu/P6413/P6413.cpp
new file mode 100644
index 00000000..7e48b73a
--- /dev/null
+++ b/Luogu/P6413/P6413.cpp
@@ -0,0 +1,157 @@
+#include <iostream>
+#include <algorithm>
+#include <iterator>
+#include <queue>
+#include <tuple>
+#include <utility>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1505,
+          M = 5005;
+const int INF = 0x3f3f3f3f;
+const int mod = 1e9 + 7;
+
+int n, m, dist[N], deg[N], cnt_in[N], cnt_out[N], ans[M];
+std::vector<std::tuple<int, int, int>> g[N];
+std::tuple<int, int, int, bool> edges[M];
+bool vis[N];
+
+void dijkstra(int s) {
+    std::fill(std::begin(dist), std::end(dist), INF);
+    std::fill(std::begin(vis), std::end(vis), false);
+
+    std::priority_queue<
+        std::pair<int, int>,
+        std::vector<std::pair<int, int>>,
+        std::greater<>>
+        q;
+
+    q.emplace(0, s);
+    dist[s] = 0;
+
+    while (!q.empty()) {
+        int u = q.top().second;
+        q.pop();
+
+        if (vis[u]) continue;
+
+        for (auto e : g[u]) {
+            int v, w;
+
+            std::tie(v, w, std::ignore) = e;
+
+            if (dist[v] > dist[u] + w) {
+                dist[v] = dist[u] + w;
+
+                q.emplace(dist[v], v);
+            }
+        }
+
+        vis[u] = true;
+    }
+}
+
+void topo(int s) {
+    std::fill(std::begin(deg), std::end(deg), 0);
+    std::fill(std::begin(cnt_in), std::end(cnt_in), 0);
+    std::fill(std::begin(cnt_out), std::end(cnt_out), 0);
+
+    for (int i = 1; i <= m; i++) {
+        if (std::get<3>(edges[i])) {
+            deg[std::get<1>(edges[i])]++;
+        }
+    }
+
+    std::queue<int> q;
+    std::vector<int> v;
+
+    cnt_in[s] = 1;
+    q.emplace(s);
+
+    while (!q.empty()) {
+        int u = q.front();
+
+        v.emplace_back(u);
+        q.pop();
+
+        for (auto e : g[u]) {
+            int v, w, id;
+
+            std::tie(v, w, id) = e;
+
+            if (std::get<3>(edges[id])) {
+                cnt_in[v] = (static_cast<long long>(cnt_in[v]) + cnt_in[u]) % mod;
+
+                if (--deg[v] == 0) {
+                    q.emplace(v);
+                }
+            }
+        }
+    }
+
+    std::for_each(v.rbegin(), v.rend(), [&](int u) {
+        for (auto e : g[u]) {
+            int v, w, id;
+
+            std::tie(v, w, id) = e;
+
+            if (std::get<3>(edges[id])) {
+                cnt_out[u] = (static_cast<long long>(cnt_out[u]) + cnt_out[v]) % mod;
+            }
+        }
+
+        cnt_out[u] = (cnt_out[u] + 1) % mod;
+    });
+}
+
+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);
+        edges[i] = {u, v, w, false};
+    }
+
+    for (int i = 1; i <= n; i++) {
+        dijkstra(i);
+
+        std::for_each(
+            std::begin(edges) + 1,
+            std::begin(edges) + m + 1,
+            [&](auto &e) {
+                int u = std::get<0>(e),
+                    v = std::get<1>(e),
+                    w = std::get<2>(e);
+
+                std::get<3>(e) = dist[u] + w == dist[v];
+            });
+
+        topo(i);
+
+        for (int j = 1; j <= m; j++) {
+            int u, v;
+            bool is_short;
+
+            std::tie(u, v, std::ignore, is_short) = edges[j];
+
+            if (is_short) {
+                ans[j] = (static_cast<long long>(ans[j])
+                          + static_cast<long long>(cnt_in[u]) * cnt_out[v] % mod)
+                       % mod;
+            }
+        }
+    }
+
+    std::copy_n(std::begin(ans) + 1, m, std::ostream_iterator<int>(cout, "\n"));
+
+    return 0;
+}