Gdtyjr

I am typing up solutions to a variety of problems in a textbook, and I want to use the proof environment for proofs but a similar environment for solutions. The link here

Duplicating the amsthm proof environment

shows how I can make my own solution environment, but I want the indication for the end of a solution to be slightly different than that of a proof. I'd like solutions to end with the QED as blackbox whereas I want the proof environment to stay as it is (white box to indicate QED). Is there an easy way to make this happen?

You also can do that very simply with ntheorem. Its advantage is an automatic placement of endmarks even if the environment ends in a display math environment:

documentclass[leqno]article
usepackage[utf8]inputenc
usepackage[T1]fontenc
usepackagefourier
usepackageheuristica

 usepackageamsmath
usepackage[thmmarks, amsmath, thref]ntheorem

theoremstylenonumberplain
theoremheaderfontitshape
theorembodyfontupshape
theoremseparator.
theoremsymbolensuremathsquare
newtheoremproofProof
theoremsymbolensuremathblacksquare
newtheoremsolutionSolution
theoremseparator. ---
theoremsymbolmboxtexttt;o)
newtheoremvarsolSolution (variant)

begindocument

 beginproofSince something is true, we have
 [ A = B. ]
 endproof


 beginsolution[of some exercise]
 This is a very intricate solution.
 beginalign*
 a & = b \ c & = d.
 endalign*
 endsolution

 beginvarsol
 This solution is so very simple that it’s not even worth writing it. Just pure thought:
 beginequationlabelvoid
 endequation
 endvarsol
enddocument 

Gonzalo's answer can be easily modified to do this. Just add renewcommandqedsymbol$blacksquare$ to the definition

documentclassarticle
usepackageamsthm,amssymb

newenvironmentsolution
 renewcommandqedsymbol$blacksquare$beginproof[Solution]
 endproof

begindocument

beginproof
test.
endproof

beginsolution
test.
endsolution

beginproof
test.
endproof

enddocument

please can anybody help with the brute force knn algorithm in latex