MediumNo. 2939
Maximum Xor Product — LeetCode 2939 Python Solution
- Pattern
- Bit Manipulation
- Topics
- Greedy, Bit Manipulation, Math
- Reading time
- 3 min
- Source
- leetcode.com
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 % modComplexity
- Time
- O(n)where n is the integer given in the problem
- Space · auxiliary
- O(1)
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.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 0670 | Maximum Swap | Medium |
| 0738 | Monotone Increasing Digits | Medium |
| 0861 | Score After Flipping Matrix | Medium |
| 0910 | Smallest Range II | Medium |
| 0976 | Largest Perimeter Triangle | Easy |
| 0991 | Broken Calculator | Medium |
Frequently asked questions
- How hard is LeetCode 2939. Maximum Xor Product?
LeetCode 2939. Maximum Xor Product is rated Medium on LeetCode.
- What is the time complexity of LeetCode 2939. Maximum Xor Product?
The Python solution on this page runs in O(n), where n is the integer given in the problem.
- What is the space complexity of LeetCode 2939. Maximum Xor Product?
The Python solution on this page uses O(1) auxiliary space.
- What topics does LeetCode 2939. Maximum Xor Product cover?
LeetCode 2939. Maximum Xor Product is tagged Greedy, Bit Manipulation and Math on LeetCode.