A Neighborhood of Infinity google_ad_section_start(name=default) Saturday, May 17, 2014 Types, and two approaches to problem solving Introduction There are two broad approaches to problem solving that I see frequently in mathematics and computing. One is attacking a problem via subproblems, and another is attacking a problem via quotient problems. The former is well known though I’ll give some examples to make things clear. The latter can be harder to recognise but there is one example that just about everyone has known since infancy. Subproblems Consider sorting algorithms. A large class of sorting algorithms, including quicksort , break a sequence of values into two pieces. The two pieces are smaller so they are easier to sort. We sort those pieces and then combine them, using some kind of merge operation, to give an ordered version of the origina...