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Sign of the Product of an Array

Difficulty: Easy

Problem Description

Implement a function signFunc(x) that returns:

  • 1 if x is positive.
  • -1 if x is negative.
  • 0 if x is equal to 0.

You are given an integer array nums. Let product be the product of all values in the array nums. Return signFunc(product).

Key Insights

  • The product of the array can be determined by the count of negative numbers and the presence of zero.
  • If the array contains a zero, the product will be zero, and thus the return value will be 0.
  • The sign of the product is determined by the number of negative numbers:
    • An even number of negative numbers results in a positive product.
    • An odd number of negative numbers results in a negative product.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we will iterate through the array while maintaining a count of negative numbers and checking for the presence of zero. At the end of the iteration, we can determine the sign of the product based on these counts.

Code Solutions

def signFunc(x):
    if x > 0:
        return 1
    elif x < 0:
        return -1
    else:
        return 0

def arraySign(nums):
    negative_count = 0
    for num in nums:
        if num == 0:
            return 0  # If any number is zero, product is zero
        elif num < 0:
            negative_count += 1
    return signFunc(-1 if negative_count % 2 else 1)  # Determine sign based on negative count
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