Report Where a Value Appears

Problem Statement

You are given an array of integers nums with an even length n, and an integer target.

You need to determine the presence of target in four specific regions/categories of the array:

1. Even Index: Does target appear at any even index (i % 2 == 0)?
2. Odd Index: Does target appear at any odd index (i % 2 == 1)?
3. First Half: Does target appear in the first half of the array (i = n // 2)?

A single occurrence of target at index i can simultaneously satisfy multiple conditions (e.g., index 0 satisfies both Even Index and First Half).

Return a list of four booleans [has_even, has_odd, has_first_half, has_second_half] corresponding to the four conditions.

To optimize runtime, scan the array from left to right and terminate early if all four conditions become True.

Function Signature

def report_target_positions(nums: list[int], target: int) -> list[bool]:
    pass

Examples

Example 1

Input: nums = [4, 2, 4, 7, 1, 4], target = 4
Output: [True, True, True, True]

Explanation:

• n = 6, so the first half is indices 0, 1, 2 and the second half is indices 3, 4, 5.
• target = 4 appears at indices 0 (even, first half), 2 (even, first half), and 5 (odd, second half).
• Since all 4 categories are covered, the result is [True, True, True, True].

Example 2

Input: nums = [1, 3, 5, 7], target = 3
Output: [False, True, True, False]

Explanation:

• target = 3 appears only at index 1.
• Index 1 is odd and belongs to the first half (1 < 2).
• It does not appear at any even index or in the second half.

Constraints

• 2 <= len(nums) <= 10^5
• len(nums) % 2 == 0
• -10^9 <= nums[i], target <= 10^9