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iLoveIOI's blog

Construction Problem
By iLoveIOI, history, 4 years ago, In English

Given n<=1000000 and k<=n*(n-1)/2 construct a sequence of length n that has exactly k inversions. How do I solve this? Thanks!

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4 years ago, # |
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Every number $$$1 \le i \le n$$$ can add maximum $$$n - i$$$ inversions. So we can run from $$$1$$$ to $$$n$$$ and if $$$cnt_{inversion} + (n - i) \le k$$$ then place $$$i$$$ on maximum right unused position and doing $$$cnt_{inversion} += (n - i)$$$. Else place $$$i$$$ on minimal left unused position and $$$cnt_{inversion}$$$ was not changed.

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