Hello codeforces,I'm trying to solve a problem on acmp, in this problem I only need to count the number of primes up to 10^12,do you know some algorithms to solve it?
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I have a funny solution to this problem: split the range $$$1 \ldots 10^{12}$$$ into blocks of length $$$B$$$. Locally precompute number of primes in each block (might take some time), then you can calculate $$$\pi(n)$$$ in about $$$O(B)$$$ time.
Set $$$B$$$ somewhere between $$$10^7 \ldots 10^8 $$$ to get AC. For higher $$$B$$$ you might not have enough time to process $$$O(B)$$$ numbers and for lower $$$B$$$ you might not fit into code size limit (which is $$$2^{17}$$$ bytes on acmp).