Swift's latest hit "We Are Never Ever Getting Back Together" was presumed to be about Gyllenhaal while "I Knew You Were Trouble" is said to be about Mayer.
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Swift, who notably refuses to reveal details of her personal life, didn't name any names herself in the interview, but said "since 2010 I have dated exactly two people," referring to Kennedy and Styles.
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The relationship ended after Styles was photographed kissing another woman, but he "pursued her for the better part of a year until she finally took him back," the source said.
Swift, who became a teenage darling within the country-pop scene for her raw, honest and catchy songs, has seen her music slowly becoming overshadowed by the spotlight cast on her private life.
"I'm dealing with a little bit of a chaotic media circus right now ... But there's also a lesson in all this ... In knowing that you can live your life in a way that you're proud of and people are still gonna take shots," Swift said.
The full interview will appear in Vanity Fair's April issue, out in New York and Los Angles on Thursday and nationally on March 12.