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Likewise in the book, Frodo shows mercy towards Saruman, and Tolkien uses the moment thus: "You have grown, halfling. Yes, you have grown very much."
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I actually read this a little differently than you. Frodo is showing mercy, yes, but Saruman’s reply is not that Frodo has grown because he has shown mercy.
I interpreted Saruman to be saying here that Frodo was punishing him far more effectively by letting him live (perhaps eternally given Saruman’s origin) without power. Also Saruman implied that those that struck him down would be cursed and that Frodo preventing that would rob him of his vengeance.
I read it as Saruman saying that Frodo’s perception of those facts were the indication that he has grown. I do not think that Saruman would see mercy as evidence of growth, after all he did not see it as Frodo showing mercy.