1822. Sign of An Array - Explanation

Problem Link

1. Count Negative Numbers

Intuition

The sign of a product depends on two things: whether any factor is zero, and whether the count of negative factors is odd or even. If any number is zero, the product is 0. Otherwise, an even count of negatives gives a positive product (negatives cancel out), and an odd count gives a negative product. We do not need to compute the actual product; just counting negatives is enough.

Algorithm

1. Initialize a counter neg = 0 for negative numbers.
2. Iterate through each number in the array:
   • If the number is 0, return 0 immediately.
   • If the number is negative, increment neg.
3. After the loop, if neg is even, return 1; otherwise, return -1.

class Solution:
    def arraySign(self, nums: list[int]) -> int:
        neg = 0
        for num in nums:
            if num == 0:
                return 0
            neg += (1 if num < 0 else 0)
        return -1 if neg % 2 else 1

Time & Space Complexity

• Time complexity: $O(n)$
• Space complexity: $O(1)$

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2. Track the Sign of the Product

Intuition

Instead of counting negatives and checking parity at the end, we can track the running sign directly. Start with a sign of 1 (positive). Each time we encounter a negative number, we flip the sign by multiplying by -1. If we encounter zero, the product is immediately 0. This approach mirrors the actual multiplication process but only tracks the sign.

Algorithm

1. Initialize sign = 1.
2. Iterate through each number in the array:
   • If the number is 0, return 0 immediately.
   • If the number is negative, flip the sign: sign *= -1.
3. Return sign.

class Solution:
    def arraySign(self, nums: list[int]) -> int:
        sign = 1
        for num in nums:
            if num == 0:
                return 0
            if num < 0:
                sign *= -1
        return sign

Time & Space Complexity

• Time complexity: $O(n)$
• Space complexity: $O(1)$

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Common Pitfalls

Not Handling Zero as a Special Case

If any element in the array is zero, the entire product is zero, and the function should immediately return 0. A common mistake is forgetting to check for zeros and only focusing on counting or tracking negative numbers, which leads to returning 1 or -1 when the answer should be 0.

Computing the Actual Product

Attempting to calculate the actual product of all elements is unnecessary and dangerous. For large arrays or large values, the product can overflow even 64-bit integers, causing undefined behavior or incorrect results. The problem only asks for the sign, so you should track sign changes without computing the full product.