Max Flow (Dinic's, HLPP)

dinic.cpp

template <int MAXV, class T = int> struct Dinic {
    const static bool SCALING = false; // non-scaling = V^2E, Scaling=VElog(U) with higher constant
    int lim = 1;
    const T INF = numeric_limits<T>::max();
    struct edge {
        int to, rev;
        T cap, flow;
    };
    int s = MAXV - 2, t = MAXV - 1;

    int level[MAXV], ptr[MAXV];
    vector<edge> adj[MAXV];
    void addEdge(int a, int b, T cap, bool isDirected = true) {
        adj[a].push_back({b, adj[b].size(), cap, 0});
        adj[b].push_back({a, adj[a].size() - 1, isDirected ? 0 : cap, 0});
    }
    bool bfs() {
        queue<int> q({s});
        fill(all(level), -1);
        level[s] = 0;
        while (!q.empty() && level[t] == -1) {
            int v = q.front();
            q.pop();
            for (auto e : adj[v]) {
                if (level[e.to] == -1 && e.flow < e.cap && (!SCALING || e.cap - e.flow >= lim)) {
                    q.push(e.to);
                    level[e.to] = level[v] + 1;
                }
            }
        }
        return level[t] != -1;
    }
    T dfs(int v, T flow) {
        if (v == t || !flow)
            return flow;
        for (; ptr[v] < adj[v].size(); ptr[v]++) {
            edge &e = adj[v][ptr[v]];
            if (level[e.to] != level[v] + 1)
                continue;
            if (T pushed = dfs(e.to, min(flow, e.cap - e.flow))) {
                e.flow += pushed;
                adj[e.to][e.rev].flow -= pushed;
                return pushed;
            }
        }
        return 0;
    }
    long long calc() {
        long long flow = 0;
        for (lim = SCALING ? (1 << 30) : 1; lim > 0; lim >>= 1) {
            while (bfs()) {
                fill(all(ptr), 0);
                while (T pushed = dfs(s, INF))
                    flow += pushed;
            }
        }
        return flow;
    }
};

hlpp.cpp

template <int MAXN, class T = int> struct HLPP {
    const T INF = numeric_limits<T>::max();
    struct edge {
        int to, rev;
        T f;
    };
    int s = MAXN - 1, t = MAXN - 2;
    vector<edge> adj[MAXN];
    vector<int> lst[MAXN], gap[MAXN];
    T excess[MAXN];
    int highest, height[MAXN], cnt[MAXN], work;
    void addEdge(int from, int to, int f, bool isDirected = true) {
        adj[from].push_back({to, adj[to].size(), f});
        adj[to].push_back({from, adj[from].size() - 1, isDirected ? 0 : f});
    }
    void updHeight(int v, int nh) {
        work++;
        if (height[v] != MAXN)
            cnt[height[v]]--;
        height[v] = nh;
        if (nh == MAXN)
            return;
        cnt[nh]++, highest = nh;
        gap[nh].push_back(v);
        if (excess[v] > 0)
            lst[nh].push_back(v);
    }
    void globalRelabel() {
        work = 0;
        fill(all(height), MAXN);
        fill(all(cnt), 0);
        for (int i = 0; i < highest; i++)
            lst[i].clear(), gap[i].clear();
        height[t] = 0;
        queue<int> q({t});
        while (!q.empty()) {
            int v = q.front();
            q.pop();
            for (auto &e : adj[v])
                if (height[e.to] == MAXN && adj[e.to][e.rev].f > 0)
                    q.push(e.to), updHeight(e.to, height[v] + 1);
            highest = height[v];
        }
    }
    void push(int v, edge &e) {
        if (excess[e.to] == 0)
            lst[height[e.to]].push_back(e.to);
        T df = min(excess[v], e.f);
        e.f -= df, adj[e.to][e.rev].f += df;
        excess[v] -= df, excess[e.to] += df;
    }
    void discharge(int v) {
        int nh = MAXN;
        for (auto &e : adj[v]) {
            if (e.f > 0) {
                if (height[v] == height[e.to] + 1) {
                    push(v, e);
                    if (excess[v] <= 0)
                        return;
                } else
                    nh = min(nh, height[e.to] + 1);
            }
        }
        if (cnt[height[v]] > 1)
            updHeight(v, nh);
        else {
            for (int i = height[v]; i <= highest; i++) {
                for (auto j : gap[i])
                    updHeight(j, MAXN);
                gap[i].clear();
            }
        }
    }
    T calc(int heur_n = MAXN) {
        fill(all(excess), 0);
        excess[s] = INF, excess[t] = -INF;
        globalRelabel();
        for (auto &e : adj[s])
            push(s, e);
        for (; highest >= 0; highest--) {
            while (!lst[highest].empty()) {
                int v = lst[highest].back();
                lst[highest].pop_back();
                discharge(v);
                if (work > 4 * heur_n)
                    globalRelabel();
            }
        }
        return excess[t] + INF;
    }
};

Both of these implementations are very fast, although the HLPP one is faster. On all of these problems, this HLPP implementation is the fastest submission/tied for the fastest.

Dinic's:
SPOJ FASTFLOW (ran without scaling): 0.04
SPOJ FASTFLOW (ran with scaling): 0.27
VNSPOJ FASTFLOW (ran with scaling): 0.00 (1st!)
VNSPOJ FASTFLOW (ran without scaling): TLE
Weird Chinese Flow Problem that's trying to force you to use HLPP (https://loj.ac/problem/127): 88 points with scaling, 44 without

HLPP:
SPOJ FASTFLOW: 0.00 (1st)
VNSPOJ FASTFLOW: 0.00 (1st)
LOJ: 100 pts, 1087 ms (1st)

One limitation of the HLPP implementation is that you can't recover the weights for the full flow - use Dinic's for this.

actually what means scaling here?

This is the only hlpp solution I can find on the web.

hlpp.cpp is buggy, as mentioned in a comment on Codeforces.

On the following max flow test case (8 nodes, 8 directed edges, source = 1, sink = 7)

8 8 1 7
1 7 1
1 2 2
2 3 1
3 4 1
4 5 1
5 6 1
6 7 1
8 3 1

hlpp.cpp outputs maxflow = 1, but the correct answer is 2.