#1912. 变异大老鼠（arrest）

https://sjzezoj.com/submission/69226

S2OJ/1912/1912.cpp

@@ -0,0 +1,116 @@
+#include <iostream>
+#include <algorithm>
+#include <functional>
+#include <iomanip>
+#include <iterator>
+#include <queue>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 305,
+          M = 3e4 + 5;
+const int INF = 0x3f3f3f3f;
+
+int n, m, k, x[M], y[M], z[M];
+double p[N][N], f[N][N];
+std::vector<std::pair<int, int>> g[N];
+int dist[N];
+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 = e.first,
+                w = e.second;
+
+            if (dist[v] > dist[u] + w) {
+                dist[v] = dist[u] + w;
+
+                q.emplace(dist[v], v);
+            }
+        }
+
+        vis[u] = true;
+    }
+}
+
+void dfs(int u) {
+    if (g[u].empty()) {
+        std::copy(std::begin(p[u]), std::end(p[u]), std::begin(f[u]));
+
+        return;
+    }
+
+    for (auto e : g[u]) {
+        int v = e.first;
+
+        dfs(v);
+
+        for (int i = k; i; i--) {
+            for (int j = 1; j <= i; j++) {
+                f[u][i] = std::max(f[u][i], f[u][i - j] + f[v][j] / g[u].size());
+            }
+        }
+    }
+
+    for (int i = k; i; i--) {
+        for (int j = 1; j <= i; j++) {
+            f[u][i] = std::max(f[u][i], p[u][j] + f[u][i - j] * (1.0 - p[u][j]));
+        }
+    }
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m >> k;
+
+    for (int i = 1; i <= m; i++) {
+        cin >> x[i] >> y[i] >> z[i];
+
+        g[x[i]].emplace_back(y[i], z[i]);
+        g[y[i]].emplace_back(x[i], z[i]);
+    }
+
+    for (int i = 1; i <= n; i++) {
+        for (int j = 1; j <= k; j++) {
+            cin >> p[i][j];
+        }
+    }
+
+    dijkstra(1);
+    std::fill(std::begin(g), std::end(g), std::vector<std::pair<int, int>>());
+
+    for (int i = 1; i <= m; i++) {
+        if (dist[x[i]] + z[i] == dist[y[i]]) {
+            g[x[i]].emplace_back(y[i], 0);
+        }
+
+        if (dist[y[i]] + z[i] == dist[x[i]]) {
+            g[y[i]].emplace_back(x[i], 0);
+        }
+    }
+
+    dfs(1);
+
+    cout << std::fixed << std::setprecision(6) << f[1][k] << endl;
+
+    return 0;
+}