Sum the XOR of Every Cross-Array Pair
Company: IBM
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Online Assessment
# Sum the XOR of Every Cross-Array Pair
You are given two integer arrays, `a` and `b`. For every ordered cross-array pair `(a[i], b[j])`, compute `a[i] XOR b[j]` and return the sum of all those results.
Implement `sumPairwiseXor(a, b)`.
## Input and Output
- `a` and `b` are arrays of non-negative integers.
- Return one integer equal to
$\sum_{i=0}^{|a|-1}\sum_{j=0}^{|b|-1}(a[i]\mathbin{\mathrm{XOR}}b[j])$.
- Pair positions are counted separately, so repeated values still contribute once for every index pair.
## Constraints
- `1 <= a.length, b.length <= 50,000`
- `0 <= a[i], b[j] <= 1,000,000,000`
- The result fits in a signed 64-bit integer.
- An approach that enumerates every pair will not finish within the intended limits.
## Example 1
```text
Input: a = [1, 2], b = [3, 4]
Output: 14
```
The four XOR values are `2`, `5`, `1`, and `6`.
## Example 2
```text
Input: a = [0, 7], b = [1, 7, 8]
Output: 37
```
The six XOR values are `1`, `7`, `8`, `6`, `0`, and `15`.
Quick Answer: Compute the sum of XOR values across every pair drawn from two integer arrays without enumerating the full Cartesian product. The problem tests bit-frequency reasoning, duplicate handling, and overflow-safe accumulation under large input limits.