Added implementation of Dinic's

[Chillee]

Comes in at 42 lines and 800 non-whitespace characters, compared to 36 lines and 592 non-whitespace characters for Edmonds-Karp, and 46 lines and 761 non-whitespace characters for Hopcroft-Karp. Note that about 4 of these lines and 100 of the characters are due to addEdge (whereas you need to add edges yourself for Edmonds-Karp).

Unluckily, it seems to run at 0.45 seconds on SPOJ MATCHING compared to 0.15 from Hopcroft-Karp... In addition, it doesn't return the matches themselves like Hopcroft-Karp it does.

For now I haven't included it in the document - I think that's another discussion. See #75 .

[simonlindholm]

Looks good. Golfed to 40 lines and 678 characters. (Counted by tr -d '[:space:]' | wc -c; Edmonds-Karp gets 556 by the same measure.) Then ungolfed to 42 lines and 704 chars because you need to do a full blocking flow to get the right time complexity. Double-check me and I'll merge.

[Chillee]

Looks good to me! I think the issue with the full blocking flow is actually important, nice catch. It seems to make a large difference on the LOJ flow problem. (whups, misremembered the previous results). BTW, it is possible to get substantially better worst case complexity (VE log U, where U is the maximum edge capacity) with the following alteration to calc.

        for (int lim = (1 << 30); lim > 0; lim >>= 1) {
            do {
                lvl = ptr = vi(sz(q));
                int qi = 0, qe = lvl[s] = 1;
                while (qi < qe && !lvl[t]) {
                    int v = q[qi++];
                    trav(e, adj[v]) 
                        if (!lvl[e.to] && e.f < e.c && e.c - e.f >= lim) 
                            q[qe++] = e.to, lvl[e.to] = lvl[v] + 1;
                }
                while (ll p = dfs(s, t, LLONG_MAX))
                    flow += p;
            } while (lvl[t]);
        }

We could just put this in by default and note that if lim=1 instead of 1<<30, it's the same as regular Dinic's.

[Chillee]

As with our discussion, the original version is already doing a full blocking flow.

[simonlindholm]

Right, I misparsed how the ptr stuff worked. ... also, right, perhaps merged too early, given the scaling thing. Let's do that in another PR if we decide to, I guess.

[simonlindholm]

Added scaling in b552ece.