algoadvance

Given an integer n and an integer start.

Define an array nums where nums[i] = start + 2*i (0-indexed) and n == nums.length.

Your task is to return the bitwise XOR of all elements of nums.

Example:

Clarifying Questions

  1. Constraints:
    • 1 <= n <= 1000
    • 0 <= start <= 1000
  2. Output:
    • Single integer which is the bitwise XOR of the array elements.
  3. Special Cases:
    • n = 1, here the result will be just start.
    • Consistency of the start, i.e., always non-negative integers for simplification purposes.

Strategy

  1. Initialize Result:
    • Initialize a variable to store the XOR result, say result = 0.
  2. Iterate Through the Array:
    • Loop through the range [0, n-1].
    • Calculate nums[i] = start + 2*i.
    • Perform the XOR operation on the variable result with nums[i].
  3. Return Result:
    • After the loop, the result variable will hold the desired XOR value.

Code Implementation

def xorOperation(n: int, start: int) -> int:
    result = 0
    for i in range(n):
        result ^= start + 2 * i
    return result

# Example usage
print(xorOperation(5, 0))  # Output: 8
print(xorOperation(4, 3))  # Output: 8
print(xorOperation(1, 7))  # Output: 7
print(xorOperation(10, 5)) # Output: 2

Time Complexity

The time complexity of this algorithm is O(n) because we are iterating through the array only once, performing constant-time operations for each element.

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