Approach (time taken ~10 hours):
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Use basic Django framework to create the desired layout with some dummy data - https://www.djangoproject.com/
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Use Twython for twitter sign up and pull tweets and feed actual data to above - https://github.com/ryanmcgrath/twython
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I also tried Authomatic, but found Twython to be little better - http://peterhudec.github.io/authomatic/
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Use Twitter Bootstrap for styling - http://getbootstrap.com/.
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Design is influenced by - http://www.sentiment140.com/
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Studied this paper for sentiment analysis - http://arxiv.org/pdf/1305.6143v2.pdf
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Used their open source implementation to plug this into my webapp - https://github.com/vivekn/sentiment
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Host on to Heroku using Gunicorn as middle layer to handle the requests.
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Post to Github.
Links: