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Hoare’s name burst into the computer science scene with the publication of a sorting algorithm used today in millions of programs, aptly named Quicksort [3] [4]. Quick because it can sort an array of n elements– that is to say, reorganize them in order of increasing values – in time proportional in most cases to n log n. That means “almost linear” time (where “linear” means proportional to the size n) since the “log” function grows so slowly. To appreciate the importance of this result, one should note that the need to sort lists arises in many, probably most programs, and that the size n can be very large. The simple ideas with which anyone can come up when faced with the task – for example, sweep through the array, swapping along the way any adjacent elements that are in the wrong order, and repeat the sweep until there is nothing left to swap – are “quadratic”, meaning that they take time proportional to the square of n. The difference between linear (or “almost” linear) and quadratic is enormous for large n, even with powerful computers; it can make the difference between an array that we can sort in the blink of an eye and one we could not sort in any reasonable time.
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