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| ##include "bits/stdc++.h"
using namespace std;
typedef long long ll;
##define INF 0x3f3f3f3f
const int N = 105, M = 1005;
int n, m, s, t, x;
int maxflow;
int deep[N], cur[N];
struct Edge {
int v, next;
int cap;
} e[M << 1];
int head[M << 1], cnt;
inline void init() {
mem(head, -1);
cnt = maxflow = 0;
}
inline void add(int u, int v, int cap) {
e[cnt].v = v;
e[cnt].cap = cap;
e[cnt].next = head[u];
head[u] = cnt++;
e[cnt].v = u;
e[cnt].cap = 0;
e[cnt].next = head[v];
head[v] = cnt++;
}
bool bfs() {
for (int i = 0; i <= t; i++) {
deep[i] = -1;
cur[i] = head[i];
}
queue<int> q;
q.push(s);
deep[s] = 0;
while (!q.empty()) {
int u = q.front();
q.pop();
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].v;
if (deep[v] == -1 && e[i].cap) {
deep[v] = deep[u] + 1;
q.push(v);
}
}
}
if (deep[t] >= 0) return true;
else return false;
}
int dfs(int u, int mx) {
int a;
if (u == t) return mx;
for (int i = cur[u]; ~i; i = e[i].next) {
cur[u] = i;
int v = e[i].v;
if (e[i].cap && deep[v] == deep[u] + 1 && (a = dfs(v, min(mx, e[i].cap)))) {
e[i].cap -= a;
e[i ^ 1].cap += a;
return a;
}
}
return 0;
}
void dinic() {
int res;
while (bfs()) {
while (1) {
res = dfs(s, INF);
if (!res) break;
maxflow += res;
}
}
}
int u[M << 1], v[M << 1];
int cap[M << 1];
bool judge(double w) {
init();
for (int i = 1; i <= m; i++) {
add(u[i], v[i], (int)min(1.0 * x, cap[i] / w));
}
dinic();
if (maxflow >= x) return true;
else return false;
}
void solve() {
cin >> n >> m >> x;
s = 1; t = n;
for (int i = 1; i <= m; i++) {
cin >> u[i] >> v[i] >> cap[i];
}
double l = 0, r = 1e18;
double ans = 0;
for (int i = 0; i <= 100; i++) {
double mid = (l + r) / 2;
if (judge(mid)) {
ans = mid;
l = mid;
} else {
r = mid;
}
}
cout << fixed << setprecision(10) << ans * x << endl;
}
signed main() {
solve();
}
|