Is Count Triplets with Even XOR Set Bits I easy or hard?

Count Triplets with Even XOR Set Bits I is categorized as an Easy problem with a high acceptance rate. The main trick is recognizing the XOR parity property, which turns a brute-force O(n * m * k) search into a linear counting solution.

Count Triplets with Even XOR Set Bits I Python/Java solution

The implementation typically uses a popcount operation such as bin(x).count('1') in Python or Integer.bitCount(x) in Java to determine parity. After counting even and odd occurrences in each array, multiply the valid combinations to compute the total number of triplets.

How to solve Count Triplets with Even XOR Set Bits I in O(n)?

Compute the parity (even or odd number of set bits) for each value using a popcount operation. Count how many elements in each array have even parity and how many have odd parity. Valid triplets occur when pa ^ pb ^ pc equals 0, so combine the counts accordingly. This avoids iterating through all triplets.

What is the best approach for Count Triplets with Even XOR Set Bits I?

The best approach uses bit parity counting. Instead of checking every triplet, compute whether each number has an even or odd number of set bits. Because parity(popcount(a ^ b ^ c)) equals pa ^ pb ^ pc, you only need to count combinations where this XOR equals 0. This reduces the complexity to O(n + m + k).

Is Count Triplets with Even XOR Set Bits I asked at Google/Amazon/Meta?

Problems based on XOR parity and bit manipulation appear frequently in interviews at companies like Google, Amazon, and Meta. While this exact question may vary, the underlying concept of using XOR properties and popcount parity to reduce complexity is a common interview pattern.

What data structure is used in Count Triplets with Even XOR Set Bits I?

The solution mainly relies on simple counters and bit manipulation operations. No complex data structure is required; you only track counts of numbers with even and odd set-bit parity in each array.

What is the time complexity of Count Triplets with Even XOR Set Bits I?

The optimal solution runs in O(n + m + k) time, where n, m, and k are the sizes of the three arrays. Each number is processed once to compute the parity of its set bits, and the final answer is derived using simple count combinations. Space complexity is O(1).

Description Hints 1 Solution Video 2:19

3199. Count Triplets with Even XOR Set Bits I

Easy83.3% acceptance1 companyPremium elsewhere, free here

Given three integer arrays a, b, and c, return the number of triplets (a[i], b[j], c[k]), such that the bitwise XOR of the elements of each triplet has an even number of set bits.

Example 1:

Input: a = [1], b = [2], c = [3]

Output: 1

Explanation:

The only triplet is (a[0], b[0], c[0]) and their XOR is: 1 XOR 2 XOR 3 = 00₂.

Example 2:

Input: a = [1,1], b = [2,3], c = [1,5]

Output: 4

Explanation:

Consider these four triplets:

(a[0], b[1], c[0]): 1 XOR 3 XOR 1 = 011₂
(a[1], b[1], c[0]): 1 XOR 3 XOR 1 = 011₂
(a[0], b[0], c[1]): 1 XOR 2 XOR 5 = 110₂
(a[1], b[0], c[1]): 1 XOR 2 XOR 5 = 110₂

Constraints:

1 <= a.length, b.length, c.length <= 100
0 <= a[i], b[i], c[i] <= 100

Asked at 1 company

Amazon

Topics

Array Bit Manipulation

Hints open one at a time

Hint 1

Iterate over all possible triplets and calculate its XOR.

2:19

Still stuck?Read the written solution, or watch a walkthrough.

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1class Solution:
  def solve(self):
      pass


Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[1]
[2]
[3]

Input

[1,1]
[2,3]
[1,5]

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