Count possible permutations of given array satisfying the given conditions

Given an array, arr[] consisting of N distinct elements, the task is to count possible permutations of the given array that can be generated which satisfies the following properties: 

• The two halves must be sorted.
• arr[i] must be less than arr[N / 2 + i]

Note: N is always even and indexing starts from 0.

Examples:

Input: arr[] = {10, 20, 30, 40} 
Output: 2 
Explanation: 
Possible permutations of the given array that satisfy the given conditions are:{{10, 20, 30, 40}, {10, 30, 20, 40}}. 
Therefore, the required output is 2. 

Input: arr[] = {1, 2}
Output: 1

Approach: Follow the steps below to solve the problem: 

• Initialize a variable, say cntPerm to store the count of permutations of the given array that satisfy the given condition.
• Find the value of the binomial coefficient of ^2NC_N using the following formula:

 = [{N × (N - 1) × ............. × (N - R + 1)} / {(R × (R - 1) × ..... × 1)}]  

• Finally, calculate catalan number = ^2NC_N / (N + 1) and print it as the required answer.

Below is the implementation of the above approach: 

2

Time Complexity: O(N)
Auxiliary Space: O(1)