算法1

二分+最大流分层见图，好题

C++ 代码

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;

const int N = 60 * 110, M = (1 + 110 + N + 2450 * 110) * 2, INF = 0x3f3f3f3f;
int n, m, C, S, T;
int h[N], ne[M], e[M], f[M], idx;
int d[N], q[N], cur[N], hh, tt;
struct Edge{
    int a, b, w;
}edges[2500];

void add(int a, int b, int c)
{
    e[idx] = b, ne[idx] = h[a], f[idx] = c, h[a] = idx ++;
    e[idx] = a, ne[idx] = h[b], f[idx] = 0, h[b] = idx ++;
}

bool bfs()
{
    memset(d, -1, sizeof d);
    hh = 0, tt = 0;
    q[0] = S, d[S] = 0, cur[S] = h[S];
    while(hh <= tt)
    {
        int t = q[hh ++ ];
        for(int i = h[t]; ~i; i = ne[i])
        {
            int j = e[i];
            if(d[j] == -1 && f[i])
            {
                d[j] = d[t] + 1;
                cur[j] = h[j];
                if(j == T) return true;
                q[ ++ tt ] = j;
            }
        }
    }
    return false;
}

int find(int u, int limit)
{
    if(u == T) return limit;
    int flow = 0;
    for(int i = cur[u]; ~i && flow < limit; i = ne[i])
    {
        int v = e[i];
        cur[u] = i;
        if(f[i] && d[v] == d[u] + 1)
        {
            int r = find(v, min(f[i], limit - flow));
            if(!r) d[v] = -1;
            flow += r, f[i] -= r, f[i ^ 1] += r;
        }
    }
    return flow;
}

int dinic()
{
    int res = 0;
    while(bfs()) res += find(S, INF);
    return res;
}

bool check(int mid)
{
    memset(h, -1, sizeof h);
    idx = 0;
    S = 0, T = (mid + 1) * n + 1;
    add(S, 1, C);
    for(int i = 0; i <= mid; ++ i)
        add((i + 1) * n, T, INF);
    for(int i = 0; i < mid; ++ i)
        for(int j = 1; j <= n; ++ j)
            add(i * n + j, (i + 1) * n + j, INF);
    for(int i = 0; i < mid; ++ i)
        for(int j = 0; j < m; ++ j)
        {
            int a = edges[j].a, b = edges[j].b, w = edges[j].w;
            add(n * i + a, n * (i + 1) + b, w);
        }
    return dinic() >= C;
}

int main()
{
    scanf("%d %d %d", &n, &m, &C);
    int l = 1, r = n + C;    
    for(int i = 0; i < m; ++ i)
    {
        int a, b, c;
        scanf("%d %d %d", &a, &b, &c);
        edges[i] = {a, b, c};
    }
    while(l < r)
    {
        int mid = (l + r) / 2;
        if(check(mid)) r = mid;
        else l = mid + 1;
    }
    printf("%d", r);
}