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OI-codes/S2OJ/1912/1912.cpp

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#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;
}