How LGM like tourist, Um_Nik, Petr, dotorya, ACRUSH , rng58 etc. are able to come up with such complex ideas which are required to solve div 1 e or atcoder grand contest last 2 problems which are almost unsolvable. From where they learn these hard tricks,methods and maths(imo level). Like tourist submits first 3 problems of div1 within 10 minutes.
Moreover, if you see problems from google code jam finals, distributed code jam they required very deep observation and intution, How they reach the correct observation and solution everytime.
They have mastered almost every concepts and tricks from maths to algos. And as ICHIGO said, its practice. Only practice make you grow. Earlier I find dp hard skip dp problems now able to solve them upto 2200/2300 rating as I practiced almost 100+ on dp.
Consider other case, I stuck in graph problems even of ratings 1800/1900 as I don't have too much practice on them. Barely solved 20 on them.
Third, seg tree: one month back skips all problems of seg tree now attempts most of them, as i practiced nearly 20 problems from spoj on seg tree. similarly my just 20 — 50 — 100 problems are enough to take me to make me comfortable with 2000+, they have solved more than 5000+ may be much more, have very exaustive trainings, background of maths too strong from beginning etc.
so just solve problems bit above your level.
I am not LGM, but to become red ( Grandmaster or International Grandmaster ), I think that my blog: A way to Practice Competitive Programming : From Rating 1000 to 2400+ may be useful.