Composition

From the viewpoint of composition the story includes introduction, exposition, development of the events, climax and denuouement. A conclusion the author left on the reader.=)
In the introduction O' Henry prepares the reader to the intrigue and makes him think about the events which may happen.

In the exposition we get acquainted with  the main character, Trysdale, and the setting ( the action takes place in the Trysdale's house). 

The goes the development of the evnts, which mostly is an author's description of the Trysdale' s flight of ideas, concerning his foolishnes and egoism. Here the character tries to find the answers. And he does it, but that fact upsets him a lot. 

The climax of the story, I suppose, is when Captain Carruthers asks about the cactus which stands by a table in the bachelor appartament. 
And the denouement. All answers to the questions were given, when the Captain translates the name of the green plant, which in English means: "Come and take me".
To sum up, I’d like to say that the plot of the story is logically built, though it goes without author's conclusion. Unexpected endings are typical of O'Henty's writings. The story is rather intriguing and the interest is maintained till the very end. It demonstrates that love demands truth and openness of heart. Vanity and pride are killers of love.