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Luogu

解题思路

分层图加网络流,有点像这题

可以证明最多不超过100天，所以才可以分层，不然图的规模会很大。

首先连源点汇点： \((s,1,INF), (n, t, INF)\)

以时间分层，每次把原图中的边 \((u, v, w)\) 改为一条 \((u_{day1}, v_{day2}, w)\) 的弧。

对于 \(u < n\)，连一条弧 \((u_{day1}, u_{day2}, INF)\)，以及一条 \((n_{day2}, n_{day1}, INF)\)。

然后每次在残量网络上加边增广直至最大流大于等于 \(T\)。

细节注意事项

• 每次增广时都要把流量累加

参考代码

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <cctype>
#include <cmath>
#include <ctime>
#include <queue>
#define rg register
using namespace std;
template < typename T > inline void read(T& s) {
    s = 0; int f = 0; char c = getchar();
    while (!isdigit(c)) f |= (c == '-'), c = getchar();
    while (isdigit(c)) s = s * 10 + (c ^ 48), c = getchar();
    s = f ? -s : s;
}

const int _ = 5010;
const int __ = 250010;
const int INF = 2147483647;

int tot = 1, head[_], nxt[__ << 1], ver[__ << 1], cap[__ << 1];
inline void Add_edge(int u, int v, int d)
{ nxt[++tot] = head[u], head[u] = tot, ver[tot] = v, cap[tot] = d; }
inline void link(int u, int v, int d) { Add_edge(u, v, d), Add_edge(v, u, 0); }

int n, m, k, s, t, dep[_], cur[_];
struct node { int u, v, d; } x[2452];

inline int id(int u, int d) { return u + (d - 1) * n; }

inline int bfs() {
    static queue < int > Q;
    memset(dep, 0, sizeof dep);
    dep[s] = 1, Q.push(s);
    while (!Q.empty()) {
        int u = Q.front(); Q.pop();
        for (rg int i = head[u]; i; i = nxt[i]) {
            int v = ver[i];
            if (dep[v] == 0 && cap[i] > 0)
                dep[v] = dep[u] + 1, Q.push(v);
        }
    }
    return dep[t] > 0;
}

inline int dfs(int u, int flow) {
    if (u == t) return flow;
    for (rg int& i = cur[u]; i; i = nxt[i]) {
        int v = ver[i];
        if (dep[v] == dep[u] + 1 && cap[i] > 0) {
            int res = dfs(v, min(flow, cap[i]));
            if (res) { cap[i] -= res, cap[i ^ 1] += res; return res; }
        }
    }
    return 0;
}

inline int Dinic(int day) {
    int res = 0;
    while (bfs()) {
        cur[s] = head[s], cur[t] = head[t];
        for (rg int x = 1; x <= day; ++x)
            for (rg int i = 1; i <= n; ++i)
                cur[id(i, x)] = head[id(i, x)];
        while (int d = dfs(s, INF)) res += d;
    }
    return res;
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("in.in", "r", stdin);
#endif
    read(n), read(m), read(k);
    for (rg int i = 1; i <= m; ++i)
        read(x[i].u), read(x[i].v), read(x[i].d);
    s = _ - 1, t = _ - 2;
    link(s, id(1, 1), INF);
    link(id(n, 1), t, INF);
    int res = 0;
    for (rg int d = 2; ; ++d) {
        for (rg int i = 1; i <= m; ++i)
            link(id(x[i].u, d - 1), id(x[i].v, d), x[i].d);
        for (rg int i = 1; i < n; ++i)
            link(id(i, d - 1), id(i, d), INF);
        link(id(n, d), id(n, d - 1), INF);
        res += Dinic(d);
        if (res >= k) { printf("%d\n", d - 1); return 0; }
    }
    return 0;
}

完结撒花 \(qwq\)