Example of search space reduction using poker cards
Consider a stack of 52 poker cards. You ask your friend to randomly pick a card from this stack. How fast can you to find out which card that your friend took?
In the 1st scenario, let's assume that your stack of cards are totally disorganized. You will have to go through every card and do some book-keeping to find it out. Because there are 52 possibilities, you will need a maximal of 52 steps to find the missing card.
In the 2nd scenario, let's assume that your stack of cards are organized by suites: diamonds, hearts, spades, and clubs. You can first see which suit is short of 13 cards and then look for the missing card in that suite. In this case, you will have a maximal of 4+13 steps to find the missing card.
Hence, with a properly arranged data structure and search strategy, we have reduced the maximal steps to a third.