Set covering problem with the greedy algorithm

Thought the greedy algorithm: each step select local optimal solution is to finally get global optimal solution.

Approximation algorithm: long time is required to obtain exact solutions can be used approximation algorithm.

Analyzing approximation algorithm criteria:

The addition of fast speed;

Approximate solution obtained with the proximity of the optimal solution;

Greedy algorithm is a good choice, not only simple, but typically runs very quickly.

Set operations:

Their union: setA | setB

Intersection operator: setA & setB

Set difference operation: setA - setB

Collection does not contain duplicate elements;

Most coverage area with a minimum of a broadcasting station, a different broadcasting station coverage areas may overlap problem:

DEF Greedy (states_needed): 
    # stores the final selection of the broadcasting station 
    final_stations = the SET () 

    the while states_needed: 
        # storage covers most of the uncovered state broadcasting station 
        best_station = None 
        # include all states not covered by the radio station covered, for loop iteration each broadcast station, and determine whether it is the best radio station 
        states_covered = the SET () 
        # iterate through all of the broadcast stations 
        for station, States in stations.items (): 
            # seek to be covered with a collection of stations broadcasting station covering the intersection of state collections 
            covered's = states_needed States & 
            # each time to find a radio station covering most of the state 
            IF len (covered's)> len (states_covered): 
                # save the current radio station 
                best_station = station 
                # save the current set of states covered 
                = covered's states_covered 
        # update the set of states to be covered
        states_needed -= states_covered
        # 将找出的广播台添加到最终集合
        final_stations.add(best_station)

    # print(final_stations)
    return final_stations


if __name__ == '__main__':

    states_needed = set(["mt", "wa", "or", "id", "nv", "ut", "ca", "az"])
    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"])
    print(greedy(states_needed))