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The Dutch national flag
The Dutch national flag problem[1] is a computational problem proposed by Edsger Dijkstra.[2] The flag of the Netherlands consists of three colors: red, white, and blue. Given balls of these three colors arranged randomly in a line (it does not matter how many balls there are), the task is to arrange them such that all balls of the same color are together and their collective color groups are in the correct order.
The solution to this problem is of interest for designing sorting algorithms; in particular, variants of the quicksort algorithm that must be robust to repeated elements may use a three-way partitioning function that groups items less than a given key (red), equal to the key (white) and greater than the key (blue). Several solutions exist that have varying performance characteristics, tailored to sorting arrays with either small or large numbers of repeated elements.[3]
^Cite error: The named reference monash was invoked but never defined (see the help page).
^In a chapter of his book A Discipline of Programming Prentice-Hall, 1976
^The latter case occurs in string sorting with multi-key quicksort. Kim, Eunsang; Park, Kunsoo (2009). "Improving multikey Quicksort for sorting strings with many equal elements". Information Processing Letters. 109 (9): 454–459. doi:10.1016/j.ipl.2009.01.007.
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