max_flow_dinic.py

# from CP4
# Dinic's algorithm, to be run only once
from collections import deque; INF = float('inf')

def BFS(s, t):
    d[s] = 0; q = deque([s])
    while q:
        u = q.popleft()
        if u == t: break
        for idx in AL[u]:
            v, cap, flow = EL[idx]
            if cap > flow and d[v] == -1: d[v] = d[u]+1; q.append(v)
    return d[t] != -1

def DFS(u, t, f=INF):
    if u == t or f == 0: return f
    for i in range(last[u], len(AL[u])):
        last[u] = i; v, cap, flow = EL[AL[u][i]]
        if d[v] != d[u]+1: continue
        pushed = DFS(v, t, min(f, cap-flow))
        if pushed: EL[AL[u][i]][2] += pushed; EL[AL[u][i]^1][2] -= pushed; return pushed
    return 0

def add(u, v, c):
    AL[u].append(len(EL)); EL.append([v, c, 0]); AL[v].append(len(EL)); EL.append([u, 0, 0])

V = 4; source, sink = V-2, V-1; EL, AL = [], [[] for _ in range(V)]; mf = 0; d = [-1]*V
while BFS(source, sink):
    last = [0]*V; f = DFS(source, sink)
    while f: mf += f; f = DFS(source, sink)
    d = [-1]*V
print(mf)