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The Quicksort Algorithm

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(n log(n)) steps. By convention, n is the number of elements to be compared and big O is a function of those elements. Quicksort is a recursive algorithm which first partitions an array according to several rules:

Pick an element, called a pivot, from the array.

Reorder the array so that all elements with values less than the pivot come before the pivot, while all elements with values greater than the pivot come after it (equal values can go either way). After this partitioning, the pivot is in its final position. This is called the partition operation.

Recursively apply the above steps to the sub-array of elements with smaller values and separately to the sub-array of elements with greater values.

Quicksort was invented by Tony Hoare and has undergone extensive analysis and scrutiny, and is known to be about twice as fast as the next fastest sorting algorithm. In the worst case, however, quicksort is a slow n² algorithm (and for quicksort, “worst case” corresponds to already sorted). (Click this link for an example of the Quicksort Algorithm written in C)

Credit: Wolfram Alpha/Wikipedia

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The Paradoxical Commandments

The Paradoxical Commandments were written in 1968 by Dr. Kent M. Keith. Mother Theresa reffered to them often. People are illogical, unreasonable, and self-centered. Love them anyway.   If you do good, people will accuse you of selfish ulterior motives. Do good anyway.   If you are successful, you will win false friends and true enemies. Succeed anyway.   The good you do today will be forgotten tomorrow. Do good anyway.   Honesty and frankness make you vulnerable. Be honest and frank anyway.   The biggest men and women with the biggest ideas can be shot down by the smallest men and women with the smallest minds. Think big anyway.   People favor underdogs but follow only top dogs. Fight for a few underdogs anyway.   What you spend years building may be destroyed overnight. Build anyway.   People really need help but may attack you if you do help them. Help people anyway.   Give the world the best you have and you'll get kicked in the teeth. Give the world the best you have anyway. © Copyright Kent M. Keith 1968, renewed 2001

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Sorting algorithms are of great interest because of their obvious applications in computer programs, but also because of their mathematical properties. One question in particular: what is the minimum number of comparisons necessary to sort a list of values? For lists of

The Cosmic Web: Large structures in the universe on the scale of billions of light years

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