Danzev's blog

By Danzev, history, 6 weeks ago, In English,

Given an array $$$a_1,a_2,\dots,a_n$$$, $$$a_i=i$$$ and a permutation of this array $$$p_1,p_2,\dots,p_n$$$. We sort this permutation to get initial array using bubble sort.

Question: how to calculate a number of swaps in $$$O(n)$$$ instead $$$O(n^2)$$$?

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6 weeks ago, # |
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Count the inversions

6 weeks ago, # |
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In case you still haven't gotten your answer, the following takes $$$O(n \log n)$$$: perhaps the easiest way is to use a segment tree. First, initialize cnt=0. Process the array in order from left to right. When we get to a new element with value x, do the operation update(x,1) (add 1 to location x in the tree). Then, query for the sum from one more than that element's value to the maximum value in the array, and add that to a running inversion count: cnt += query(x+1, N) (where N is the maximum possible value in the array). The answer is cnt after you've processed the entire array.