sorting,lisp,common-lisp,polynomials , Sorting a list of lists based on nth element, then n+1th element, etc


Sorting a list of lists based on nth element, then n+1th element, etc

Question:

Tag: sorting,lisp,common-lisp,polynomials

My basic problem is that I have a list of lists that represent polynominals functions and I want to sort them based on the variable and then the exponent.

So for example variable 'x' before variable 'y' and variable 'x^n' before variable 'x^n-1'.

I have a function 'merge' which with the following input:

(merge '((5 x 2)(3 x 2)(10 x 2)(15 x 2)(20 x 2)))

Will result in this output

(53 X 2)

53 is the coefficient, x is the variable and 2 is the exponent. I can sort by the variable to get first all of the a's and then b's and then c's etc. but I don't know how to switch around the exponents afterwards.


Answer:

If you have two criteria to sort by, you can first sort by the secondary, then stable-sort by the primary criterion:

(stable-sort (sort polynomial #'< :key #'third)
             #'string<
             :key #'second)

(You can compare symbols with string< because symbols are string designators.)

If you have a more complicated function that defines the order, define that separately, for example:

(sort polynomial #'term<)

(defun term< (term0 term1)
  (if (string= (second term0) (second term1))
      (< (third term0) (third term1))
      (string< (second term0) (second term1))))

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