Given an integer array of N integers, find sum of bit differences in all pairs that can be formed from array elements. Bit difference of a pair (x, y) is count of different bits at same positions in binary representations of x and y.
For example, bit difference for 2 and 7 is 2. Binary representation of 2 is 010 and 7 is 111 (first and last bits differ in two numbers).
Note: (x, y) and (y, x) are considered two separate pairs.
Example 1:
Input:
N = 2
arr[] = {1, 2}
Output: 4
Explanation: All pairs in array are (1, 1)
(1, 2), 2, 1), (2, 2)
Sum of bit differences = 0 + 2 + 2 + 0
= 4
Example 2:
Input:
N = 3
arr[] = {1, 3, 5}
Output: 8
Explanation:
All pairs in array are (1, 1), (1, 3),
(1, 5), (3, 1), (3, 3) (3, 5),(5, 1),
(5, 3), (5, 5)
Sum of bit differences = 0 + 1 + 1 +
1 + 0 + 2 +
1 + 2 + 0
= 8
Your Task:
You don't need to read input or print anything. Your task is to complete the function sumBitDifferences() which takes the array arr[] and n as inputs and returns an integer denoting the answer.
Expected Time Complexity: O(N)
Expected Auxiliary Space: O(1)
Constraints:
1 <= N <= 10^{5}
1 <= arr[i] <= 10^{5}

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