你怎么能确定一个问题表现出“贪婪的选择属性”?

一个可能更理论的方法是证明你的问题有 Matroid 结构。如果你能证明你的问题有这样的结构,有一个贪婪的算法来解决它。

"Introduction to Algorithms"

* S is a finite nonemtpy set
* l is a nonempty family of subsets of S, such that B element of l and 
  A a subset of B than also A is element of l. l is called the independent 
  subsets of S.
* If A and B are elements of l and A is a smaller cardinality than B, then 
  there is some element x that is in B, but not in A, so that A extended 
  by x is also element of l. That is called exchange property.

通常还有一个权重函数w,它为S中的每个元素x分配一个权重。

如果可以将函数表示为加权拟阵,那么以下类似Python的伪代码可以解决您的问题:

GREEDY(M,w):
   (S,l) = M
   a = {}
   sort S into monotonically decreasing order by weight w
   for x in S:
      if A + {x} in l:
         A = A + {x}