Dinic's Algorithm

Dinic.py

class Dinic:
    class Edge:
        def __init__(self, to, cap, rev):
            self.to = to
            self.cap = cap
            self.rev = rev
        
        def __repr__(self):
            return "(to: {0} cap: {1} rev: {2})".format(self.to, self.cap, self. rev)

    def __init__(self,V):
        self.V = V
        self.size = [0 for i in range(V)]
        self.G = [[] for i in range(V)]

    def add_edge(self, _from, to, cap):
        self.G[_from].append(self.Edge(to, cap, self.size[to]))
        self.G[to].append(self.Edge(_from, 0, self.size[_from]))
        self.size[_from] += 1
        self.size[to] += 1

    def bfs(self,s):
        level = [-1 for i in range(self.V)]
        level[s] = 0
        q = []
        q.append(s)
        while q != []:
            v = q.pop(0)
            for u in self.G[v]:
                if u.cap > 0 and level[u.to] < 0:
                    level[u.to] = level[v] + 1
                    q.append(u.to)
        return level

    def dfs(self, v, t, f):
        if v == t: return f
        for i in range(self.iterator[v],self.size[v]):
            self.iterator[v] = i
            edge = self.G[v][i]
            if edge.cap > 0 and self.level[v] < self.level[edge.to]:
                d = self.dfs(edge.to, t, f if f < edge.cap else edge.cap)
                if d > 0:
                    self.G[v][i].cap -= d
                    self.G[edge.to][edge.rev].cap += d
                    return d
        return 0

    def max_flow(self, s, t):
        flow = 0
        while True:
            self.level = self.bfs(s)
            if self.level[t] < 0:
                return flow
            self.iterator = [0 for i in range(self.V)]
            while True:
                f = self.dfs(s, t, float('inf'))
                if f == 0:
                    break
                flow += f