File: sign-of-the-product-of-an-array/solution.py

Date: 2026-06-06

Time: 19:06

Purpose

This file solves LeetCode 1822 — Sign of the Product of an Array. It determines whether the product of all elements in an integer array is positive, negative, or zero — without actually computing the product. This avoids overflow concerns and reduces the problem to pure sign tracking.

Key Components

signFunc(nums: list[int]) -> int

The sole public function. Contract:

| Input | Output |

|-------|--------|

| Product is positive | 1 |

| Product is negative | -1 |

| Product is zero | 0 |

The function counts negative numbers and short-circuits on zero. It never computes the actual product.

Patterns

Parity counting. Instead of multiplying values and checking the result's sign, the solution counts negatives. An even count means the negatives cancel; odd means one survives. This is the canonical approach for sign-of-product problems — it sidesteps overflow entirely and runs in O(n) time with O(1) space.

Early exit. The return 0 inside the loop is a short-circuit: if any element is zero, the entire product is zero regardless of remaining elements. This is both a correctness guarantee and a minor performance optimization.

Dependencies

Imports: None. The solution is self-contained with no standard library or third-party dependencies.

Imported by: The test_solution.py in the same directory imports this function. The massive "Imported By" list in the prompt is misleading — those are unrelated test files that happen to share a common test harness pattern (likely via sys.path manipulation or a shared conftest), not actual consumers of signFunc.

Flow

1. Initialize neg_count = 0.

2. Iterate through nums:

• If element is 0 → return 0 immediately.
• If element is negative → increment neg_count.
• Positive elements are implicitly skipped (they don't affect sign).

3. After the loop, return -1 if neg_count is odd, else 1.

Invariants

• Zero dominance: A single zero in the array forces a 0 return, regardless of all other values.
• Sign parity: The sign of a product depends only on the count of negative factors mod 2.
• No mutation: The input list is never modified.
• Total function: Every possible list[int] input produces one of {-1, 0, 1}. The function assumes nums is non-empty (per the LeetCode constraint 1 <= nums.length).

Error Handling

None. The function assumes valid input per the problem constraints. An empty list would fall through to the final return and produce 1 (since neg_count would be 0) — arguably wrong, but the problem guarantees non-empty input.

Topics to Explore

• [file] sign-of-the-product-of-an-array/test_solution.py — See what edge cases the tests cover (all-positive, all-negative, contains zero, single element)
• [file] sign-of-the-product-of-an-array/review.md — Read the code review for any noted trade-offs or alternative approaches
• [function] subtract-the-product-and-sum-of-digits-of-an-integer/solution.py:subtractProductAndSum — A related problem that does compute the actual product, showing the contrast in approach
• [general] parity-counting-pattern — Other solutions in this repo that use odd/even counting instead of computing a value directly (e.g., bit-counting problems)

Beliefs

• sign-func-returns-ternary — signFunc returns exactly one of {-1, 0, 1} for any non-empty integer list
• sign-func-never-computes-product — The function determines sign via negative-count parity, never multiplying elements together
• sign-func-zero-short-circuit — If any element is zero, the function returns 0 immediately without examining remaining elements
• sign-func-o1-space — The function uses constant extra space (a single integer counter) regardless of input size