NISHIO Hirokazu[English][日本語]

number of events (e.g. accidents, crimes, meetings, housing starts, hits on a web page)

An inversion of a sequence in computer science and discrete mathematics is a pair of terms in that sequence such that the components of those terms are out of their natural order. $\mathrm{inv}(A)=#{(A_{i},A_{j})\mid i<j{,,\mathrm{ and },,}A_{i}>A_{j}}$

The number of overturns in the combined column x+y is obtained from the respective number of overturns f and the frequency table c ACLPC L PAST4K.

  • $f(x + y) = f(x) + f(y) + \sum_i\sum_j c(x, i)c(y, j)[i > j]$

  • Fennic tree and obtained by O(NlogN) python

init(N)
inv = 0
for a in seqs[i]:
    bit_add(a, 1)
    inv += bit_sum(N) - bit_sum(a)

This page is auto-translated from /nishio/転倒数 using DeepL. If you looks something interesting but the auto-translated English is not good enough to understand it, feel free to let me know at @nishio_en. I'm very happy to spread my thought to non-Japanese readers.


(C)NISHIO Hirokazu / Converted from Markdown (en)
Source: [GitHub] / [Scrapbox]