Can you please list some of important problem so that one can learn new data structure or algorithms ?

like e.g. FLIPCOIN problem get to know about segmented tree, WORDS1 get to know about hamiltonian cycles, etc.

also suggest some problems that you feel one must solve.

Here you can find a large collection of important algorithms and corresponding questions.

In addition this blog on Codeforces is algo very good to practice algorithm specific problems.

It will take some time but this should be sufficient for a you to know and implement algorithms effectively. Go, Get strarted

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