洛谷-P3381 【模板】最小费用最大流

【模板】最小费用最大流

EK 改 SPFA

#include <iostream>
#include <queue>
#include <algorithm>
using namespace std;
typedef long long ll;
const int maxn = 1e5 + 10;
const ll inf = 1e17 + 10;
int tp = 1, nex[maxn], head[maxn], to[maxn], vis[maxn], last[maxn];
ll cost[maxn], dis[maxn], val[maxn], flow[maxn];
int n, m, s, t;

void add(int u, int v, ll f, ll c)
{
    tp++;
    nex[tp] = head[u];
    head[u] = tp;
    to[tp] = v;
    cost[tp] = c;
    val[tp] = f;
}

ll SPFA()
{
    for(int i=0; i<=n; i++) flow[i] = last[i] = 0;
    for(int i=0; i<=n; i++) dis[i] = inf;
    dis[s] = 0;
    queue<int>q;
    q.push(s);
    flow[s] = inf;
    while(!q.empty())
    {
        int now = q.front();
        q.pop();
        vis[now] = 0;
        for(int i=head[now]; i; i=nex[i])
        {
            int v = to[i];
            if(val[i] > 0 && dis[now] + cost[i] < dis[v])
            {
                dis[v] = dis[now] + cost[i];
                flow[v] = min(flow[now], val[i]);
                last[v] = i ^ 1;
                if(vis[v] == 0)
                {
                    vis[v] = 1;
                    q.push(v);
                }
            }
        }
    }
    return flow[t];
}

ll ans = 0, cur = 0;
void EK()
{
    ans = cur = 0;
    while(SPFA())
    {
        ans += flow[t];
        for(int i=last[t]; i; i=last[to[i]])
        {
            cur += cost[i ^ 1] * flow[t];
            val[i] += flow[t];
            val[i ^ 1] -= flow[t];
        }
    }
}

int main()
{
    cin >> n >> m >> s >> t;
    while(m--)
    {
        int u, v;
        ll f, c;
        cin >> u >> v >> f >> c;
        add(u, v, f, c);
        add(v, u, 0, -c);
    }
    EK();
    cout << ans << " " << cur << endl;
    return 0;
}

Dinic 里的 bfs 分层改成 SPFA 分层

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long ll;
const int maxn = 1e5 + 10;
const ll inf = 1e17 + 10;
int n, m, s, t, tp = 1;
int head[maxn], nex[maxn], to[maxn], cur[maxn], vis[maxn];
ll val[maxn], cost[maxn], dis[maxn];

void add(int u, int v, ll f, ll c)
{
    tp++;
    nex[tp] = head[u];
    head[u] = tp;
    to[tp] = v;
    cost[tp] = c;
    val[tp] = f;
}

bool spfa()
{
    for(int i=0; i<=n; i++) cur[i] = head[i];
    for(int i=0; i<=n; i++) dis[i] = inf;
    dis[s] = 0;
    queue<int>q;
    q.push(s);
    while(q.size())
    {
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for(int i=head[u]; i; i=nex[i])
        {
            int v = to[i];
            if(val[i] > 0 && dis[u] + cost[i] < dis[v])
            {
                dis[v] = dis[u] + cost[i];
                if(vis[v] == 0)
                {
                    vis[v] = 1;
                    q.push(v);
                }
            }
        }
    }
    return dis[t] != inf;
}

ll c_ans = 0;
ll dfs(int now, ll flow)
{
    if(now == t) return flow;
    vis[now] = 1;
    ll ans = 0;
    for(int i=cur[now]; i && ans < flow; i=nex[i])
    {
        cur[now] = i;
        int v = to[i];
        if(vis[v] == 0 && val[i] > 0 && dis[v] == dis[now] + cost[i])
        {
            ll x = dfs(v, min(val[i], flow - ans));
            c_ans += x * cost[i];
            val[i] -= x;
            val[i ^ 1] += x;
            ans += x;
        }
    }
    vis[now] = 0;
    return ans;
}

ll mcmf()
{
    ll ans = 0;
    while(spfa())
    {
        ll x = dfs(s, inf);
        ans += x;
    }
    return ans;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cin >> n >> m >> s >> t;
    while(m--)
    {
        int u, v;
        ll f, c;
        cin >> u >> v >> f >> c;
        add(u, v, f, c);
        add(v, u, 0, -c);
    }
    ll ans = mcmf();
    cout << ans << " " << c_ans << endl;
    return 0;
}