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Problem

Submissions

Reverse Pairs

Contributed by

Vishal Modani

Hard

0/120

Avg time to solve 50 mins

Success Rate 90 %

57 upvotes

Problem Statement

You are given an array/list say ‘ARR’ of size ‘N’. We call pair (i, j) a Reverse Pair when i < j and 'ARR[i]' > 2 * 'ARR[j]'.

Your task is to find the number of Reverse Pairs present in given 'ARR'.

For example :

For the array [50, 21, 9], if we follow 1-based indexing, the Reverse Pairs are (1, 2), (1, 3) and (2, 3). Thus, the total count i.e. the answer becomes 3.

Note :

A single index of the pair (i, j) can be used multiple times.

Detailed explanation ( Input/output format, Notes, Constraints, Images )

Input Format :

The first line of input contains an integer ‘T’ denoting the number of test cases.

The first line of every test case contains an integer ‘N’ denoting the size of the array/list. 

The second line of every test case contains ‘N’ space-separated integers denoting the elements of array/list 'ARR'.

Output Format :

For each test case, print the number of distinct pairs.

The output of each test case will be printed in a separate line.

Note :

You don’t have to print anything, it has already been taken care of. Just implement the function.

Constraints :

1 <= T <= 5    
2 <= N <= 3000
1 <= ARR[i] <= 10^5

Where 'ARR[i]' denotes the i-th elements in the array/list. 

Time Limit: 1 sec

Sample Input 1 :

1
6
1 2 3 2 3 1

Sample Output 1 :

Explanation Of Sample Input 1 :

Test case 1: 
Given that we follow 1-based indexing, for the array {1, 2, 3, 2, 1}, the pairs satisfying the conditions of Reverse Pairs are 
For i = 3, arr[i] = 3 and for j = 6, arr[j] = 1.
For i = 5, arr[i] = 3 and for j = 6, arr[j] = 1.
Hence there are two possible pairs.

Sample Input 2 :

2
6
6 4 8 2 1 3
5
2 4 3 5 1

Sample Output 2 :

6
3

Explanation Of Sample Input 2 :

Test case 1: 
Given that we follow 1-based indexing,The possible pairs satisfying the conditions of Reverse Pairs are (1, 4), (1, 5), (2, 5), (3, 4), (3, 5), (3, 6). Thus, the answer is 6.

Test case 2: 
Given that we follow 1-based indexing, The possible pair of indices satisfying the above condition are (2, 5), (3, 5), (4, 5). Thus, the answer is 3.

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