I am currently preparing for IOI. I have a strong math background ( I almost made it to IMO last year and can solve many of the ISL C 4+). I have my IOI TSTs in about $$$1 \frac{1}{2}$$$ months. Since I have so less time, how should I prepare? How should I practice for IOI? Also, since very little time is left, I would want to not waste time in things out of syllabus. From where should I practice different algorithms and data structures? ( I often have problems implementing data structures.)
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Having strong math background help you to learn faster and more efficient, since it amends your thinking ability and intuition. I have glanced your submission history, although I don't want to frustrate you but I'd say that, at your level, training to reach IOI TSTs in about 1,5 months is something near to impossible. I think it would be good if you had about 6 months to 1 year for preparation.
Read IOI syllabus and learn everything it asks. Solve many problems from previous IOI and your national OI.