All Tracks Data Structures Advanced Data Structures Fenwick (Binary Indexed) Trees Problem

Vanya and Array
Tag(s):

Ad-Hoc, BIT, Data Structures, Easy-Medium, Sorting

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Let's define 2 functions a function \(F(i)\) and \(Val(i,j)\) for an Array A of size N as follows:

\(F(i) =\) \( \sum_{j=i+1}^{N} Val(i,j) \)

\( Val(i,j) =\) 1 ,if \(A[i] < A[j]\), else, \(Val(i,j) =\) 0.

Now, Vanya has been given one such array A of size N and an integer K. She needs to find the number of Distinct Unordered Pairs of elements \((a,b)\) in array A such that \(F(a) +F(b) \ge K\).

Input Format:

The first line contains 2 space separated integers N and K denoting the size of array A and the integer k from the description given above. The next line contains N space separated integers denoting the elements of array A .

Output Format:

You need to print the required answer on a single line.

Constraints:

Subtask 1: (Worth 40% of the total points):

\( 1 \le N \le 5000 \)

\( 1 \le A[i] \le 10^5 \)

\( 0 \le K \le 10^4 \)

Subtask 2: (Worth 60% of the total points) :

\( 1 \le N \le 10^6 \)

\( 1 \le A[i] \le 10^9 \)

\( 0 \le K \le 10^9 \)

SAMPLE INPUT
8 10
1 3 2 4 5 6 8 7
SAMPLE OUTPUT
5
Explanation

Here the values of Function \(F(x)\) for all the elements of Array A from 1 to N are:

\( [7,5,5,4,3,2,0,0]\)

So, the following 5 unordered pairs are considered:

\( (1,2) \)

\( (1,3) \)

\( (1,4) \)

\( (1, 5) \)

\( (2,3) \)

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Visual Basic

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This Problem was Asked in

Moonfrog Labs

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Moonfrog Labs Backend Hiring Challenge

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