Maximum Xor Product — LeetCode 2939 Python Solution

The problem

Given three integers a, b, and n, return the maximum value of (a XOR x) * (b XOR x) where 0 <= x < 2n. Since the answer may be too large, return it modulo 109 + 7.

Example

Input

a = 12, b = 5, n = 4

Output

98

Explanation

For x = 2, (a XOR x) = 14 and (b XOR x) = 7. Hence, (a XOR x) * (b XOR x) = 98.

Python solution

class Solution:
    def maximumXorProduct(self, a: int, b: int, n: int) -> int:
        mod = 10**9 + 7
        ax, bx = (a >> n) << n, (b >> n) << n
        for i in range(n - 1, -1, -1):
            x = a >> i & 1
            y = b >> i & 1
            if x == y:
                ax |= 1 << i
                bx |= 1 << i
            elif ax > bx:
                bx |= 1 << i
            else:
                ax |= 1 << i
        return ax * bx % mod

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 2939. Maximum Xor Product is filed here because LeetCode tags it Bit Manipulation, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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