class MaxFlow: def __init__(self, n=0): self._n = n self.g = [[] for _ in range(n)] self.pos = [] def add_edge(self, frm, to, cap): m = len(self.pos) e1 = MaxFlow._edge(to, cap) e2 = MaxFlow._edge(frm, 0) e1.rev = e2 e2.rev = e1 self.pos.append(e1) self.g[frm].append(e1) self.g[to].append(e2) return m class edge: def __init__(self, frm, to, cap, flow): self.frm = frm self.to = to self.cap = cap self.flow = flow def __iter__(self): yield self.frm yield self.to yield self.cap yield self.flow def get_edge(self, i): """ i 番目に追加された辺について (from, to, 初期の cap, 現在の流量(始めは 0)) """ e1 = self.pos[i] e2 = e1.rev return MaxFlow.edge(e2.to, e1.to, e1.cap + e2.cap, e2.cap) def edges(self): """ get_edge の返り値をリストで並べたもの """ return [self.get_edge(i) for i in range(len(self.pos))] def change_edge(self, i, new_cap, new_flow): e = self.pos[i] e.cap = new_cap - new_flow e.rev.cap = new_flow def flow(self, s, t, flow_limit=0XFFFFFFFFFFFFFFF): g = self.g flow = 0 while flow < flow_limit: level = [-1] * self._n level[s] = 0 que = [None] * self._n ql = 0 qr = 1 que[0] = s unreached = True while unreached and ql < qr: v = que[ql] ql += 1 for e in g[v]: to = e.to if e.cap and level[to] < 0: level[to] = level[v] + 1 if to == t: unreached = False break que[qr] = to qr += 1 if unreached: return flow ptr = [len(es) for es in g] stack = [] v = t up = flow_limit - flow res = 0 while True: if v == s or not ptr[v]: if v == s: res = up while stack: tmp = res e, up, res = stack.pop() e.cap -= tmp e.rev.cap += tmp res += tmp if res < up: v = e.to break else: flow += res break i = ptr[v] while i: i -= 1 e = g[v][i] if level[e.to] == level[v] - 1 and e.rev.cap: ptr[v] = i stack.append((e.rev, up, res)) v = e.to up = min(up, e.rev.cap) res = 0 break else: ptr[v] = i return flow def min_cut(self, s): """ 残余グラフから到達可能な頂点集合を返す。 流量の最大値を十分大きくとった場合、この頂点集合はmin_cutとなる。 """ visited = [False] * self._n que = [None] * self._n ql = 0 qr = 1 que[0] = s visited[s] = True while ql < qr: p = que[ql] ql += 1 for e in self.g[p]: if e.cap and not visited[e.to]: visited[e.to] = True que[qr] = e.to qr += 1 return visited def draw(self): """ :return: グラフを可視化 """ import matplotlib.pyplot as plt import networkx as nx G = nx.DiGraph() for frm, to, cap, cap_now in self.edges(): G.add_edge(frm, to, label="{}/{}".format(cap_now,cap)) edge_labels = {(i, j): w['label'] for i, j, w in G.edges(data=True)} pos = nx.spring_layout(G) nx.draw_networkx(G, pos, with_labels=True, connectionstyle='arc3, rad = 0.1') nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels) plt.axis("off") plt.show() class _edge: def __init__(self, to, cap): self.to = to self.cap = cap def __iter__(self): yield self.to yield self.cap def example(): global input example = iter( """ 7 6 0 1 4 1 3 1 1 4 1 2 5 1 3 6 1 4 6 1 """ .strip().split("\n")) input = lambda: next(example) ##################################################################################### import sys input = sys.stdin.readline # example() N=int(input()) mf = MaxFlow(2*N) for i in range(1,N): a,b=map(int, input().split()) for j in range(1,N): if i==j:continue mf.add_edge(i,N+j,a) mf.add_edge(0,i,a) mf.add_edge(N+i,N,b) f=mf.flow(0,N) print(f+1)