File: xor-operation-in-an-array/solution.py

Date: 2026-06-06

Time: 19:43

xor-operation-in-an-array/solution.py

Purpose

This file solves LeetCode 1486 — XOR Operation in an Array. It owns the computation of the bitwise XOR across a virtual array nums where nums[i] = start + 2*i for i in [0, n). The array is never materialized — the solution computes the XOR on the fly.

Key Components

Solution.xorOperation(self, n: int, start: int) -> int

The single method. Contract:

• Input: n (array length, 1 <= n <= 1000) and start (starting value, 0 <= start <= 1000, even per the problem constraints).
• Output: The XOR of all n elements start, start+2, start+4, ..., start+2*(n-1).
• Side effects: None.

Patterns

Accumulator pattern. result is initialized to 0 (the identity element for XOR) and each element is folded in via ^=. This is the standard reduce-over-XOR idiom — equivalent to functools.reduce(operator.xor, (start + 2*i for i in range(n))) but more explicit.

Virtual array. The problem defines nums[i] = start + 2*i, but the solution never allocates the array. Each element is computed inline inside the loop. This keeps space at O(1).

Dependencies

Imports: None. Pure computation with no library dependencies.

Imported by: The xor-operation-in-an-array/test_solution.py file imports this Solution class. The massive "Imported By" list in the prompt is an artifact of the test harness structure — those other test files don't actually import *this* solution; they share a common test runner pattern.

Flow

1. Initialize result = 0.

2. For each i in [0, n), compute the element start + 2*i and XOR it into result.

3. Return result.

Concrete trace: n=4, start=3 produces elements 3, 5, 7, 9.

• 0 ^ 3 = 3
• 3 ^ 5 = 6
• 6 ^ 7 = 1
• 1 ^ 9 = 8
• Returns 8.

Invariants

• result after iteration i equals the XOR of the first i+1 elements.
• The step size is always 2, so all elements share the same parity as start.
• XOR is commutative and associative, so ordering doesn't affect correctness — but the loop processes elements sequentially anyway.

Error Handling

None. The method assumes valid inputs per the LeetCode constraint guarantees. No bounds checking, no type validation. This is appropriate for a competitive programming solution where the caller (the judge) guarantees valid input.