1319. 移棋子游戏

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1319. 移棋子游戏

• 题意

  给定一个有 N个节点的有向无环图，图中某些节点上有棋子，两名玩家交替移动棋子。
  玩家每一步可将任意一颗棋子沿一条有向边移动到另一个点，无法移动者输掉游戏。
  对于给定的图和棋子初始位置，双方都会采取最优的行动，询问先手必胜还是先手必败。

• 思路

  类似于集合-NIM游戏，只不过有向图游戏，换成了连边的有向图

• 代码

  '''
  Author: NEFU AB-IN
  Date: 2023-03-23 20:36:19
  FilePath: \Acwing\1319\1319.py
  LastEditTime: 2023-03-23 20:46:55
  '''
  read = lambda: map(int, input().split())
  from collections import Counter, deque
  from heapq import heappop, heappush
  from itertools import permutations
  
  N = int(2e3 + 10)
  INF = int(2e9)
  f = [-1] * N
  
  
  def sg(u): # 依然记忆化搜索
      if f[u] != -1:
          return f[u]
  
      d = Counter()
      for v in g[u]:
          d[sg(v)] = 1
  
      for i in range(INF):
          if d[i] == 0:
              f[u] = i
              return i
  
  
  g = [[] for _ in range(N)]
  n, m, k = read()
  
  for i in range(m):
      x, y = read()
      g[x].append(y)
  
  res = 0
  lst = list(read())
  for i in lst:
      res ^= sg(i)
  
  print("win" if res != 0 else "lose")