I optimized XOR maximization algorithm reduces complexity from O(log r) to O(log l) by iterating only over the smaller number L. It uses bitwise comparison to maximize the XOR value, flipping bits of l or r as needed while respecting the range [L,R] . The final XOR result is calculated using a fast power function, ensuring minimal operations and efficiency. This method ensures the maximum XOR value is computed while preserving the range constraints.

code with more detalied explain: https://github.com/MohamedHussienMansour/Maximum-XOR-problem-with-O-log-L-