Design a comparison-based algorithm for sorting a five-element array with seven

Question

Design a comparison-based algorithm for sorting a five-element array with seven comparisons in the worst case.

Explanation / Answer

(defun small-sort (a) "Sort a vector A of length 5" (if (> (aref a 0) (aref a 1)) (rotatef (aref a 0) (aref a 1))) (if (> (aref a 2) (aref a 3)) (rotatef (aref a 2) (aref a 3))) (if (> (aref a 0) (aref a 2)) (progn (rotatef (aref a 0) (aref a 2)) (rotatef (aref a 1) (aref a 3)))) (if (> (aref a 4) (aref a 2)) (if (> (aref a 4) (aref a 3)) (progn) (rotatef (aref a 3) (aref a 4))) (if (> (aref a 4) (aref a 0)) (rotatef (aref a 2) (aref a 4) (aref a 3)) (rotatef (aref a 0) (aref a 4) (aref a 3) (aref a 2)))) (if (> (aref a 1) (aref a 3)) (if (> (aref a 1) (aref a 4)) (rotatef (aref a 1) (aref a 2) (aref a 3) (aref a 4)) (rotatef (aref a 1) (aref a 2) (aref a 3))) (if (> (aref a 1) (aref a 2)) (rotatef (aref a 1) (aref a 2)) (progn))) a) (defun check-sorted (a) (do ((i 0 (1+ i))) ((>= i (1- (array-dimension a 0)))) ;;(format t "~S ~S~%" (aref a i) (aref a (+ 1 i))) (assert (

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