During much of the last century people would use a publication known as a phone book to look up a person's phone number. Entries appears in order, sorted by a key that identifies it (the person's name) n both cases). A brute-force solution would be to start at the beginning, examine each entry one at a time, and continue until you find the name. No one uses that method: instead, you open the book to some interior page and look for the name on that page. If it is there, you are done; otherwise, you eliminate either the part of the book before the current page or the part of the book after the current page from consideration and repeat.