在《演算法圖解》裡面有一個蠻有意思的小案例，背景是一個廣播節目，要讓全美的50個周的聽眾都能夠聽到，但是每個電臺可能覆蓋多個州，每在一個電臺播出就需要一筆費用，所以就是從成本的角度來看，怎麼儘可能在所有的州都播出，這是一個典型的集合覆蓋的問題，而且在我們的生活中算是比較典型。
比如我們先縮小範圍，指定5個州，那麼50個州也是同樣的演算法。
states_need = set(["mt", "wa", "or", "id", "nv", "ut", "ca", "az"]) # 傳入一個陣列， 它被轉換為集合
有的同學可能對這些州沒概念，這個簡稱就跟京代表北京，魯代表山東，甘代表甘肅一樣，細細一看，都是西部的一些州。
如何使用貪心演算法呢，就是選擇覆蓋儘可能多的州的電臺，然後逐步縮小範圍。那麼覆蓋面廣的州所對應的電臺就優先被選中，依次類推。
程式的實現是指定了一個集合states_need，裡面包含所有的州，每個電臺對應的州是透過初始化的陣列元素來實現的，按照一二三四五的順序來命名，當然實際上這種元素的排列set不是按照陣列名的順序，在這個場景裡是kfive,ktwo,kthree,kone,kfour
然後逐步縮小範圍來收斂，裡面比較特別的一點就是集合的運算，使用了 & ,得到的是交集，如果是並集是 |，差集是 -，
程式程式碼如下：
#!/usr/bin/env
python# coding:utf-8states_need = set(["mt", "wa", "or", "id", "nv",
"ut", "ca", "az"]) # 傳入一個陣列， 它被轉換為集合# 可供選擇的廣播臺清單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(stations)# 最終選擇的廣播臺集合final_stations = set()while
states_need:best_station = Nonestates_covered = set()for station,
states_for_station in stations.items():covered = states_need &
states_for_station #
求交集print("states_need:",states_need,"states_for_station:",states_for_station,"covered:",covered)if
len(covered) > len(states_covered):best_station =
stationstates_covered = coveredstates_need -=
states_coveredfinal_stations.add(best_station)print("states_needed:",states_need,"best_station:",best_station,"final_stations:",final_stations)print("---")print("Final_stations:",final_stations)
為了方便除錯和得到一個迭代的結果，我加了幾處輸出日誌，工參考。
{'kfive':
set(['ca', 'az']), 'ktwo': set(['mt', 'id', 'wa']), 'kthree':
set(['ca', 'or', 'nv']), 'kone': set(['ut', 'id', 'nv']), 'kfour':
set(['ut', 'nv'])}('states_need:', set(['wa', 'ut', 'ca', 'id', 'mt',
'az', 'or', 'nv']), 'states_for_station:', set(['ca', 'az']),
'covered:', set(['ca', 'az']))('states_needed:', set(['wa', 'ut', 'id',
'mt', 'or', 'nv']), 'best_station:', 'kfive', 'final_stations:',
set(['kfive']))---('states_need:', set(['wa', 'ut', 'id', 'mt', 'or',
'nv']), 'states_for_station:', set(['mt', 'id', 'wa']), 'covered:',
set(['mt', 'id', 'wa']))('states_needed:', set(['ut', 'or', 'nv']),
'best_station:', 'ktwo', 'final_stations:', set(['ktwo',
'kfive']))---('states_need:', set(['ut', 'or', 'nv']),
'states_for_station:', set(['ca', 'or', 'nv']), 'covered:', set(['or',
'nv']))('states_needed:', set(['ut', 'or', 'nv']), 'best_station:',
'ktwo', 'final_stations:', set(['ktwo', 'kfive']))---('states_need:',
set(['ut', 'or', 'nv']), 'states_for_station:', set(['ut', 'id', 'nv']),
'covered:', set(['ut', 'nv']))('states_needed:', set(['ut', 'or',
'nv']), 'best_station:', 'ktwo', 'final_stations:', set(['ktwo',
'kfive']))---('states_need:', set(['ut', 'or', 'nv']),
'states_for_station:', set(['ut', 'nv']), 'covered:', set(['ut',
'nv']))('states_needed:', set(['ut', 'or', 'nv']), 'best_station:',
'ktwo', 'final_stations:', set(['ktwo', 'kfive']))---('states_need:',
set(['ut', 'or', 'nv']), 'states_for_station:', set(['ca', 'az']),
'covered:', set([]))('states_needed:', set(['ut', 'or', 'nv']),
'best_station:', None, 'final_stations:', set(['ktwo', None,
'kfive']))---('states_need:', set(['ut', 'or', 'nv']),
'states_for_station:', set(['mt', 'id', 'wa']), 'covered:',
set([]))('states_needed:', set(['ut', 'or', 'nv']), 'best_station:',
None, 'final_stations:', set(['ktwo', None,
'kfive']))---('states_need:', set(['ut', 'or', 'nv']),
'states_for_station:', set(['ca', 'or', 'nv']), 'covered:', set(['or',
'nv']))('states_needed:', set(['ut']), 'best_station:', 'kthree',
'final_stations:', set(['ktwo', 'kthree', None,
'kfive']))---('states_need:', set(['ut']), 'states_for_station:',
set(['ut', 'id', 'nv']), 'covered:', set(['ut']))('states_needed:',
set(['ut']), 'best_station:', 'kthree', 'final_stations:', set(['ktwo',
'kthree', None, 'kfive']))---('states_need:', set(['ut']),
'states_for_station:', set(['ut', 'nv']), 'covered:',
set(['ut']))('states_needed:', set(['ut']), 'best_station:', 'kthree',
'final_stations:', set(['ktwo', 'kthree', None,
'kfive']))---('states_need:', set(['ut']), 'states_for_station:',
set(['ca', 'az']), 'covered:', set([]))('states_needed:', set(['ut']),
'best_station:', None, 'final_stations:', set(['ktwo', 'kthree', None,
'kfive']))---('states_need:', set(['ut']), 'states_for_station:',
set(['mt', 'id', 'wa']), 'covered:', set([]))('states_needed:',
set(['ut']), 'best_station:', None, 'final_stations:', set(['ktwo',
'kthree', None, 'kfive']))---('states_need:', set(['ut']),
'states_for_station:', set(['ca', 'or', 'nv']), 'covered:',
set([]))('states_needed:', set(['ut']), 'best_station:', None,
'final_stations:', set(['ktwo', 'kthree', None,
'kfive']))---('states_need:', set(['ut']), 'states_for_station:',
set(['ut', 'id', 'nv']), 'covered:', set(['ut']))('states_needed:',
set([]), 'best_station:', 'kone', 'final_stations:', set(['ktwo',
'kthree', None, 'kfive', 'kone']))---('states_need:', set([]),
'states_for_station:', set(['ut', 'nv']), 'covered:',
set([]))('states_needed:', set([]), 'best_station:', 'kone',
'final_stations:', set(['ktwo', 'kthree', None, 'kfive',
'kone']))---('Final_stations:', set(['ktwo', 'kthree', None, 'kfive',
'kone']))
最後的結果是：ktwo,kthree,kfive,kone這四個電臺。
當然貪心演算法得到的不是精確的結果，即可能不是最優解，算是一種近似演算法，能夠基本得到的最優解，而且效率很高。