X DAYS

:

HOUR

:

MINS

:

SEC

Copied to Clipboard
Bit Difference
Hard Accuracy: 46.07% Submissions: 11772 Points: 8

We define f (X, Y) as number of different corresponding bits in binary representation of X and Y. For example, f (2, 7) = 2, since binary representation of 2 and 7 are 010 and 111, respectively. The first and the third bit differ, so f (2, 7) = 2.

You are given an array A of N integers, A1, A2 ,…, AN. Find sum of f(Ai, Aj) for all ordered pairs (i, j) such that 1 ≤ i, j ≤ N. Return the answer modulo 109+7.

Example 1:

Input: N = 2
A = {2, 4}
Output: 4
Explaintion: We return
f(2, 2) + f(2, 4) +
f(4, 2) + f(4, 4) =
0 + 2 +
2 + 0 = 4.

Example 2:

Input: N = 3
A = {1, 3, 5}
Output: 8
Explaination: We return
f(1, 1) + f(1, 3) + f(1, 5) +
f(3, 1) + f(3, 3) + f(3, 5) +
f(5, 1) + f(5, 3) + f(5, 5) =
0 + 1 + 1 +
1 + 0 + 2 +
1 + 2 + 0 = 8.

You do not need to read input or print anything. Your task is to complete the function countBits() which takes the value N and the array A as input parameters and returns the desired count modulo 109+7.

Expected Time Complexity: O(N * log2(Max(Ai)))
Expected Auxiliary Space: O(1)

Constraints:
1 ≤ N ≤ 105
20 ≤ A[i] < 231

We are replacing the old Disqus forum with the new Discussions section given below.

Editorial

We strongly recommend solving this problem on your own before viewing its editorial. Do you still want to view the editorial?

My Submissions:  