[Solution] Inversion Graph solution codeforces

Inversion Graph solution codeforces – You are given a permutation 𝑝1,𝑝2,,𝑝𝑛p1,p2,…,pn. Then, an undirected graph is constructed in the following way: add an edge between vertices 𝑖i𝑗j such that 𝑖<𝑗i<j if and only if 𝑝𝑖>𝑝𝑗pi>pj. Your task is to count the number of connected components in this graph.

Two vertices 𝑢u and 𝑣v belong to the same connected component if and only if there is at least one path along edges connecting 𝑢u and 𝑣v.

A permutation is an array consisting of 𝑛n distinct integers from 11 to 𝑛n in arbitrary order. For example, [2,3,1,5,4][2,3,1,5,4] is a permutation, but [1,2,2][1,2,2] is not a permutation (22 appears twice in the array) and [1,3,4][1,3,4] is also not a permutation (𝑛=3n=3 but there is 44 in the array).

Inversion Graph solution codeforces

Each test contains multiple test cases. The first line contains a single integer 𝑡t (1𝑡1051≤t≤105) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer 𝑛n (1𝑛1051≤n≤105) — the length of the permutation.

The second line of each test case contains 𝑛n integers 𝑝1,𝑝2,,𝑝𝑛p1,p2,…,pn (1𝑝𝑖𝑛1≤pi≤n) — the elements of the permutation.

It is guaranteed that the sum of 𝑛n over all test cases does not exceed 21052⋅105.

Output

For each test case, print one integer 𝑘k — the number of connected components.

Inversion Graph solution codeforces

6
3
1 2 3
5
2 1 4 3 5
6
6 1 4 2 5 3
1
1
6
3 2 1 6 5 4
5
3 1 5 2 4

output

Copy
3
3
1
1
2
1


Inversion Graph solution codeforces

Each separate test case is depicted in the image below. The colored squares represent the elements of the permutation. For one permutation, each color represents some connected component. The number of distinct colors is the answer.