Summary
In his paper “A Synthesis of Several Sorting Algorithms,” John Darlington presents syntheses for six different sorting algorithms, together with a family tree of sorting algorithms, and mentions a symmetry between Quick Sort, Selection Sort, Merge Sort, and Insertion Sort. In our own attempts to codify programming knowledge, we have developed a slightly different family tree which shows similar symmetries, and which also shows that Bubble Sort and Sinking Sort can be viewed as in-place versions of Selection Sort and Insertion Sort, thus adding another symmetry to those noted by Darlington.
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References
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Barstow, D.R. Remarks on “A Synthesis of Several Sorting Algorithms” by John Darlington. Acta Informatica 13, 225–227 (1980). https://doi.org/10.1007/BF00288643
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DOI: https://doi.org/10.1007/BF00288643