結果

問題 No.3201 Corporate Synergy
コンテスト
ユーザー dp_ijk
提出日時 2025-07-11 22:35:47
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 89 ms / 2,000 ms
コード長 5,439 bytes
コンパイル時間 486 ms
コンパイル使用メモリ 81,604 KB
実行使用メモリ 76,772 KB
最終ジャッジ日時 2025-07-11 22:35:50
合計ジャッジ時間 3,047 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 20
権限があれば一括ダウンロードができます

ソースコード

diff # 

from __future__ import annotations


class Dinic:
   def __init__(self, N):
      self.N = N
      self.G = [[] for i in range(N)]
      self.A = []
      self.C = []

   def add_edge(self, frm, to, cap, rcap=0):
      assert cap >= 0 and rcap >= 0
      id = len(self.A)
      assert id%2 == 0
      self.G[frm].append(id)
      self.G[to].append(id|1)
      self.A.append(to)
      self.A.append(frm)
      self.C.append(cap)
      self.C.append(rcap)

   def _dual(self, s, t):
      G = self.G
      A = self.A
      C = self.C
      from collections import deque
      assert s != t
      NIL = -1
      depth = [NIL] * self.N
      Q = deque([s])
      depth[s] = 0
      while Q:
         v = Q.popleft()
         for id in G[v]:
            a = A[id]
            cap = C[id]
            if cap > 0 and depth[a] == NIL:
               depth[a] = depth[v] + 1
               Q.append(a)
      if depth[t] == NIL:
         return []
      return depth

   def _primal(self, s, t, depth, it):
      G = self.G
      A = self.A
      C = self.C

      Q = [s]
      pi_edge = []
      found = False
      while Q:
         v = Q[-1]
         Gv = G[v]
         while it[v] < len(Gv):
            id = Gv[it[v]]
            a = A[id]
            cap = C[id]
            if cap > 0 and depth[v] + 1 == depth[a]:
               Q.append(a)
               pi_edge.append(id)
               if a == t:
                  found = True
                  Q.clear()
               break
            else:
               it[v] += 1
         else:
            v = Q.pop()
            if pi_edge:
               pi_edge.pop()
            if Q:
               it[Q[-1]] += 1

      if not found: return 0

      w = min(C[id] for id in pi_edge)
      assert w > 0
      cur = t
      while cur != s:
         id = pi_edge.pop()
         C[id] -= w
         C[id^1] += w
         cur = A[id^1]
      return w

   def flow(self, s, t):
      assert s != t
      F = 0
      while depth := self._dual(s, t):
         it = [0]*self.N
         while dF := self._primal(s, t, depth, it):
            F += dF
      return F

   def __repr__(self, map: dict[str, int]|None = None):   # type: ignore
      inv = {}
      if map is not None:
         for k, v in map.items():
            inv[v] = k

      def repr_id(v: int) -> str:
         if map is None:
            return str(v)
         else:
            return inv[v]

      res = []
      for v in range(self.N):
         for id in self.G[v]:
            a = self.A[id]
            cap = self.C[id]
            rcap = self.C[id^1]
            if rcap != 0 and id&1 == 0:
               res.append(f"{repr_id(v)} -> {repr_id(a)}: {rcap}/{rcap + cap}")
      return "\n".join(res)



class PSP:

   INF = 10**18

   def __init__(self, N: int):
      self.N = N
      self.V = N
      self.types = ["R"]*N
      self.baseline = 0
      self.const = [[0, 0] for _ in range(self.V)]
      self.rel = []

   def _add_vertex(self, type: str) -> int:
      assert type in ["S", "T", "I"]
      self.const.append([0, 0])
      self.types.append(type)
      self.V += 1
      return self.V - 1

   def set_const(self, x, a):
      assert 0 <= x < self.N
      self.baseline += a

   def set_1(self, x, a):
      if self.types[x] == "R": assert 0 <= x < self.N
      else: assert 0 <= x < self.V
      self.const[x][1] += a

   def set_01(self, x, y, a):
      assert 0 <= x < self.N
      assert 0 <= y < self.N
      if x == y:
         return
      assert a <= 0
      self.rel.append((x, y, abs(a)))

   def set_10(self, x, y, a):
      return self.set_01(y, x, a)

   def set_matrix(self, x, y, M: list[list[int]]):
      assert 0 <= x < self.N
      assert 0 <= y < self.N
      assert len(M) == 2
      assert len(M[0]) == 2
      a, b = M[0]
      c, d = M[1]
      assert a+d >= b+c
      self.set_const(x, a)
      self.set_1(x, c-a)
      self.set_1(y, d-c)
      self.set_01(x, y, (b+c) - (a+d))

   def max(self):

      S = self._add_vertex("S")
      T = self._add_vertex("T")

      mf = Dinic(self.V)

      for v in range(self.V):
         if 0 <= v < self.N:
            assert self.types[v] == "R"

         if self.types[v] in ["S", "T"]:
            continue

         mf.add_edge(S, v, 0)
         mf.add_edge(v, T, 0)

         if self.const[v][0] > 0:
            self.baseline += self.const[v][0]
            mf.add_edge(S, v, self.const[v][0])
         elif self.const[v][0] < 0:
            mf.add_edge(v, T, -self.const[v][0])

         if self.const[v][1] > 0:
            self.baseline += self.const[v][1]
            mf.add_edge(v, T, self.const[v][1])
         elif self.const[v][1] < 0:
            mf.add_edge(S, v, -self.const[v][1])

      for x, y, c in self.rel:
         mf.add_edge(x, y, c)

      mincut = mf.flow(S, T)

      return self.baseline - mincut


def solve(N, P, M, E, K, ABS):
   INF = 10**18
   psp = PSP(N)
   for i, p in enumerate(P):
      psp.set_1(i, p)
   for u, v in E:
      psp.set_01(u, v, -INF)
   for a, b, s in ABS:
      psp.set_matrix(a, b, [[0, 0], [0, s]])
   ans = psp.max()
   return ans


N = int(input())
P = list(map(int, input().split()))
M = int(input())
E = [tuple(map(lambda x: int(x) - 1, input().split())) for _ in range(M)]
K = int(input())
ABS = []


class Read:
   for _ in range(K):
      a, b, s = map(int, input().split())
      a -= 1
      b -= 1
      ABS.append((a, b, s))


ans = solve(N, P, M, E, K, ABS)
print(ans)
0