Construct lexicographically smallest Binary array of size N with A 0s and X inversion count

Given three numbers N, A, and X, the task is to construct the lexicographically smallest binary array of size N, containing A 0s and having an inversion count of X.

Examples:

Input: N=5, A=2, X=1
Output: 0 1 0 1 1
Explanation: 
The number of inversions in this array is 1(2nd and 3rd index).

Input: N=5, A=2, X=3
Output: 0 1 1 1 0

Approach: The given problem can be solved using two pointer technique based on the following observations: 

1. The array with A 0s having 0 inversion is the array with all 0s to the beginning and then the all the 1s.
2. If an element 0 at index i and an element 1 at index j is swapped, then inversion count increases by count of 1s in the range [i, j].
3. The maximum possible inversion count is A*(N-A).

Follow the steps below to solve the problem:

• If X is greater than A*(N-A), print -1 and then return.
• Initialize an array say arr[] of size N and fill the first A Indices with 0s and the remaining with 1s.
• Initialize two variables curr as A-1 and prev as N-1 to iterate over the array.
• Iterate until X is greater than 0 and curr, is not less than 0, and perform the following steps:
  • If X is greater than or equal prev-cur, then do the following:
    • Swap the two elements at arr[prev], and arr[curr].
    • Subtract prev-cur from X.
    • Decrement prev and curr by 1.
  • Otherwise, do the following:
    • Swap the two elements arr[curr] and arr[cur+1].
    • Increment curr by 1 and decrement X by 1.
• Print the array arr.

Below is the implementation of the above approach:

0 1 0 1 1 

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