I just saw it for the first time this weekend as well, and it was as good as everyone says. It doesn't deviate too much from the story, but where it does it actually furthers the plot.
Yes, it was a King short novel in Different Seasons, and its officially called "Rita Hayworth and the Shawkshank Redemption."
Also in that collection of stories is "The Body", which people might recognize as the movie
Stand By Me, and
Apt Puipl.
All 3 are great stories to read and show that he is capable of great writing that isn't horror. In case you couldn't tell, I am a big fan of his

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Oh yah, if you enjoyed that movie I think you'd enjoy The Green Mile as well, movie and book. The movie was great, and I read the book afterwards and it was even better, in my opinion.