python 贪婪算法

贪婪算法

覆盖问题，有个节目想要将自己的节目通过电台发布到几个州，这些电台可能互相有所覆盖，即覆盖了相同的州，现在如何能找到几个电台，最优的覆盖这些州。

# 想要电台覆盖的州
states_needed = set(["mt", "wa", "or", "id", "nv", "ut", "ca", "az"])

# 每个电台覆盖的范围
stations = {}
stations["kone"] = set(["id", "nv", "ut"])
stations["ktwo"] = set(["wa", "id", "mt"])
stations["kthree"] = set(["or", "nv", "ca"])
stations["kfour"] = set(["nv", "ut"])
stations["kfive"] = set(["ca", "az"])

final_stations = set()

while states_needed:
  best_station = None
  states_covered = set()
  for station, states_for_station in stations.items():
    covered = states_needed & states_for_station  # 两个集合的交集，也就是当前电台能覆盖几个我们想要覆盖的州
    if len(covered) > len(states_covered):  # 找出覆盖范围最大的那个电台，贪婪算法，每步都找最优解
      best_station = station
      states_covered = covered

  states_needed -= states_covered  # 找到一个电台，就将这个电台覆盖的州剔除掉
  final_stations.add(best_station)

print(final_stations)