「模版」最大流 + 费用流

最大流模板【Luogu3376】（dinic）

#include <cstring>
#include <queue>
using namespace std;
typedef long long ll;
const int maxn = 10005;
const int maxm = 200005;
const ll inf = 0x3f3f3f3f3f3f3f3f;
int n, m, src, snk, dis[maxn];
int tot, ter[maxm], nxt[maxm], lnk[maxn];
ll wei[maxm];
void adde(int u, int v, int w) {
    ter[tot] = v;
    wei[tot] = w;
    nxt[tot] = lnk[u];
    lnk[u] = tot++;
}
bool bfs(int s, int t) {
    queue<int> que;
    que.push(s);
    memset(dis, -1, sizeof(dis));
    dis[s] = 0;
    ll w;
    for (int u, v; !que.empty(); ) {
        u = que.front();
        que.pop();
        for (int i = lnk[u]; ~i; i = nxt[i]) {
            v = ter[i], w = wei[i];
            if (w && dis[v] == -1) {
                dis[v] = dis[u] + 1;
                que.push(v);
            }
        }
    }
    return ~dis[t];
}
ll find(int u, ll lft) {
    if (u == snk) {
        return lft;
    }
    ll w, tmp, res = 0;
    for (int v, i = lnk[u]; ~i && res < lft; i = nxt[i]) {
        v = ter[i], w = wei[i];
        if (w && dis[u] + 1 == dis[v]) {
            tmp = find(v, min(w, lft - res));
            if (tmp) {
                wei[i] -= tmp;
                wei[i ^ 1] += tmp;
                res += tmp;
            }
        }
    }
    if (res < lft) {
        dis[u] = -1;
    }
    return res;
}
ll dinic() {
    ll tmp, res = 0;
    while (bfs(src, snk)) {
        tmp = find(src, inf);
        while (tmp) {
            res += tmp;
            tmp = find(src, inf);
        }
    }
    return res;
}
int main() {
    memset(lnk, -1, sizeof(lnk));
    scanf("%d %d %d %d", &n, &m, &src, &snk);
    ll w;
    for (int u, v, i = 1; i <= m; i++) {
        scanf("%d %d %lld", &u, &v, &w);
        adde(u, v, w), adde(v, u, 0);
    }
    printf("%lld\n", dinic());
    return 0;
}

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费用流模版【Luogu3381】（多路增广）

#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;
typedef long long ll;
const int maxn = 5005;
const int maxm = 100005;
const ll inf = 0x3f3f3f3f3f3f3f3f;
bool vis[maxn];
int n, m, src, snk;
int tot, ter[maxm], nxt[maxm], lnk[maxn];
ll ans, len[maxm], wei[maxm], dis[maxn];
void adde(int u, int v, int w0, int w1) {
    ter[tot] = v;
    len[tot] = w0;
    wei[tot] = w1;
    nxt[tot] = lnk[u];
    lnk[u] = tot++;
}
bool spfa(int s, int t) {
    queue<int> que;
    que.push(s);
    memset(dis, 0x3f, sizeof(dis));
    dis[s] = 0, vis[s] = 1;
    ll w0, w1;
    for (int u, v; !que.empty(); ) {
        u = que.front();
        que.pop();
        vis[u] = 0;
        for (int i = lnk[u]; ~i; i = nxt[i]) {
            v = ter[i], w0 = len[i], w1 = wei[i];
            if (w0 && dis[v] > dis[u] + w1) {
                dis[v] = dis[u] + w1;
                if (!vis[v]) {
                    vis[v] = 1;
                    que.push(v);
                }
            }
        }
    }
    return dis[t] < inf;
}
ll find(int u, ll lft) {
    if (u == snk) {
        return lft;
    }
    vis[u] = 1;
    ll w0, w1, tmp, res = 0;
    for (int v, i = lnk[u]; ~i && res < lft; i = nxt[i]) {
        v = ter[i], w0 = len[i], w1 = wei[i];
        if (w0 && !vis[v] && dis[u] + w1 == dis[v]) {
            tmp = find(v, min(lft - res, w0));
            if (tmp) {
                ans += tmp * w1;
                len[i] -= tmp;
                len[i ^ 1] += tmp;
                res += tmp;
            }
        }
    }
    vis[u] = 0;
    return res;
}
ll mcmf() {
    ll tmp, res = 0;
    while (spfa(src, snk)) {
        tmp = find(src, inf);
        while (tmp) {
            res += tmp;
            tmp = find(src, inf);
        }
    }
    return res;
}
int main() {
    memset(lnk, -1, sizeof(lnk));
    scanf("%d %d %d %d", &n, &m, &src, &snk);
    ll w0, w1;
    for (int u, v, i = 1; i <= m; i++) {
        scanf("%d %d %lld %lld", &u, &v, &w0, &w1);
        adde(u, v, w0, w1), adde(v, u, 0, -w1);
    }
    printf("%lld ", mcmf());
    printf("%lld\n", ans);
    return 0;
}