How do you solve Find XOR Sum of All Pairs Bitwise AND on LeetCode?

Find XOR Sum of All Pairs Bitwise AND (LeetCode #1835) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding bitwise operations can lead to significant optimizations.

What is the brute force solution for Find XOR Sum of All Pairs Bitwise AND?

The brute force approach for Find XOR Sum of All Pairs Bitwise AND is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves calculating the AND for every possible pair of elements from both arrays and then finding the XOR of all these results. This is straightforward but inefficient for large inputs. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find XOR Sum of All Pairs Bitwise AND?

Find XOR Sum of All Pairs Bitwise AND uses the following concepts: Array, Math, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, XOR Properties.

What are the interview tips for Find XOR Sum of All Pairs Bitwise AND?

Always start with a brute-force solution to understand the problem better. Look for patterns in the problem that can lead to optimizations. Explain your thought process clearly during the interview, especially when transitioning from brute-force to optimal solutions.

What are common mistakes when solving Find XOR Sum of All Pairs Bitwise AND?

Overlooking the properties of XOR and AND, leading to unnecessary computations. Failing to optimize the solution when a pattern is evident.

#1835

Find XOR Sum of All Pairs Bitwise AND

Hard

ArrayMathBit ManipulationBit ManipulationXOR Properties

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

Instead of calculating the AND for every pair, we can leverage the properties of XOR and AND operations. By recognizing that the XOR of AND results can be simplified, we can reduce the time complexity significantly.

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Algorithm

5 steps

1Step 1: Initialize a variable to hold the XOR sum of all elements in arr2.
2Step 2: Calculate the XOR of all elements in arr2 and store it in a variable, say xor_arr2.
3Step 3: Initialize a variable to hold the final result as 0.
4Step 4: Iterate through each element in arr1, and for each element, compute the AND with xor_arr2, then XOR this result into the final result.
5Step 5: Return the final result.

solution.py10 lines

1# Full working Python code
2arr1 = [1, 2, 3]
3arr2 = [6, 5]
4xor_arr2 = 0
5for b in arr2:
6    xor_arr2 ^= b
7result = 0
8for a in arr1:
9    result ^= (a & xor_arr2)
10print(result)

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Complexity note: The time complexity is O(n) because we only make a single pass through arr2 to compute the XOR and then another pass through arr1. The space complexity is O(1) as we only use a few extra variables.

1Understanding bitwise operations can lead to significant optimizations.
2Recognizing patterns in how XOR and AND interact can simplify complex problems.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.