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Sign of the Product of an Array

Easy

Asked by:

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Topics:

Arrays

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).

Example 1:

Input: nums = [-1,-2,-3,-4,3,2,1]
Output: 1
Explanation: The product of all values in the array is 144, and signFunc(144) = 1

Example 2:

Input: nums = [1,5,0,2,-3]
Output: 0
Explanation: The product of all values in the array is 0, and signFunc(0) = 0

Example 3:

Input: nums = [-1,1,-1,1,-1]
Output: -1
Explanation: The product of all values in the array is -1, and signFunc(-1) = -1

Constraints:

1 <= nums.length <= 1000
-100 <= nums[i] <= 100

Try coding it in LeetCode

Sign of the Product of an Array

Easy

Asked by:

25 views

Topics:

Arrays

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).

Example 1:

Input: nums = [-1,-2,-3,-4,3,2,1]
Output: 1
Explanation: The product of all values in the array is 144, and signFunc(144) = 1

Example 2:

Input: nums = [1,5,0,2,-3]
Output: 0
Explanation: The product of all values in the array is 0, and signFunc(0) = 0

Example 3:

Input: nums = [-1,1,-1,1,-1]
Output: -1
Explanation: The product of all values in the array is -1, and signFunc(-1) = -1

Constraints:

1 <= nums.length <= 1000
-100 <= nums[i] <= 100

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the expected data type of the numbers in the array, and what is the range of possible values?
Can the input array be empty or null? If so, what should the return value be?
Does the array contain only integers, or can there be floating-point numbers as well?
If the product is positive, negative, or zero, what specific integer value should I return (e.g., 1, -1, or 0)?
How large can the input array be?

Brute Force Solution

Approach

To figure out if multiplying all the numbers together results in a positive, negative, or zero answer, we can simply go through each number one by one. We keep track of whether we've seen an odd or even number of negative numbers.

Here's how the algorithm would work step-by-step:

Start by assuming the product is positive.
Look at each number in the collection, one at a time.
If the number is positive, don't change anything.
If the number is negative, flip our assumption about whether the product is positive or negative.
If the number is zero, we immediately know the product is zero, so we can stop.
After checking all the numbers, if we flipped our assumption an even number of times, the product is positive. If we flipped it an odd number of times, the product is negative.

Code Implementation

def sign_of_the_product(numbers):
    product_is_positive = True
    
    for number in numbers:
        if number == 0:
            # If a zero is found, product is zero
            return 0

        if number < 0:
            # Flip the product sign if negative
            product_is_positive = not product_is_positive

    if product_is_positive:
        # Even number of negatives means positive
        return 1
    else:
        # Odd number of negatives means negative
        return -1

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through each element of the input array nums of size n exactly once. Inside the loop, there are only constant-time operations: checking if a number is positive, negative, or zero, and potentially flipping the sign based on whether the number is negative. Since the number of operations is directly proportional to the number of elements in the array, the time complexity is O(n).

Space Complexity

O(1) – The algorithm uses a single variable to keep track of whether the product is positive or negative and a counter to track the number of negative numbers seen. These variables take up constant space regardless of the size of the input array. Therefore, the auxiliary space complexity is O(1).

Optimal Solution

Approach

The key to efficiently finding the sign of the product is recognizing that we only care about negative numbers. We can completely ignore the positive numbers and just focus on counting the negatives because they change the sign. A zero immediately makes the product zero, so we can stop there.

Here's how the algorithm would work step-by-step:

Start by checking if there is a zero. If you find one, you already know the product is zero and can stop.
If there is no zero, count how many negative numbers there are.
If the count of negative numbers is even, the product is positive.
If the count of negative numbers is odd, the product is negative.

Code Implementation

def array_sign(numbers):
    negative_count = 0
    for number in numbers:
        if number == 0:
            # Zero immediately makes the product zero
            return 0
        elif number < 0:

            negative_count += 1

    # Even negative count means product is positive
    if negative_count % 2 == 0:
        return 1
    # Odd negative count means product is negative
    else:

        return -1

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the input array nums of size n at most once to check for a zero. If no zero is found, it iterates through the array again to count the number of negative numbers. In the worst case, the algorithm iterates through the array twice. Therefore, the number of operations is proportional to n, resulting in a time complexity of O(n).

Space Complexity

O(1) – The algorithm only uses a counter for negative numbers. This counter requires a fixed amount of memory regardless of the input array's size, N. No additional data structures such as arrays or hash maps are created that scale with the input size. Therefore, the auxiliary space complexity is constant.

Edge Cases

Case	How to Handle
Empty input array	Return 1 as the product of no numbers is often defined as 1.
Null input array	Throw an IllegalArgumentException to signal invalid input.
Array contains zero	Return 0 immediately, as any product involving 0 is 0.
Array contains only positive numbers	Return 1, as the product of positive numbers is positive.
Array contains only negative numbers with an even length	Return 1, as an even number of negative numbers results in a positive product.
Array contains only negative numbers with an odd length	Return -1, as an odd number of negative numbers results in a negative product.
Integer overflow during multiplication for very large arrays	Continuously check for overflow in each multiplication, returning 0 when detected or using a long type.
Array with extreme boundary values (Integer.MAX_VALUE, Integer.MIN_VALUE) and negative numbers	Be cautious of potential overflow if multiplying Integer.MIN_VALUE with -1, and handle accordingly by pre-checking or using long type.

Empty input array

How to Handle:

Return 1 as the product of no numbers is often defined as 1.

Null input array

How to Handle:

Throw an IllegalArgumentException to signal invalid input.

Array contains zero

How to Handle:

Return 0 immediately, as any product involving 0 is 0.

Array contains only positive numbers

How to Handle:

Return 1, as the product of positive numbers is positive.

Array contains only negative numbers with an even length

How to Handle:

Return 1, as an even number of negative numbers results in a positive product.

Array contains only negative numbers with an odd length

How to Handle:

Return -1, as an odd number of negative numbers results in a negative product.

Integer overflow during multiplication for very large arrays

How to Handle:

Continuously check for overflow in each multiplication, returning 0 when detected or using a long type.

Array with extreme boundary values (Integer.MAX_VALUE, Integer.MIN_VALUE) and negative numbers

How to Handle:

Be cautious of potential overflow if multiplying Integer.MIN_VALUE with -1, and handle accordingly by pre-checking or using long type.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the expected data type of the numbers in the array, and what is the range of possible values?
Can the input array be empty or null? If so, what should the return value be?
Does the array contain only integers, or can there be floating-point numbers as well?
If the product is positive, negative, or zero, what specific integer value should I return (e.g., 1, -1, or 0)?
How large can the input array be?

Brute Force Solution

Approach

Here's how the algorithm would work step-by-step:

Start by assuming the product is positive.
Look at each number in the collection, one at a time.
If the number is positive, don't change anything.
If the number is negative, flip our assumption about whether the product is positive or negative.
If the number is zero, we immediately know the product is zero, so we can stop.
After checking all the numbers, if we flipped our assumption an even number of times, the product is positive. If we flipped it an odd number of times, the product is negative.

Code Implementation

def sign_of_the_product(numbers):
    product_is_positive = True
    
    for number in numbers:
        if number == 0:
            # If a zero is found, product is zero
            return 0

        if number < 0:
            # Flip the product sign if negative
            product_is_positive = not product_is_positive

    if product_is_positive:
        # Even number of negatives means positive
        return 1
    else:
        # Odd number of negatives means negative
        return -1

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

Start by checking if there is a zero. If you find one, you already know the product is zero and can stop.
If there is no zero, count how many negative numbers there are.
If the count of negative numbers is even, the product is positive.
If the count of negative numbers is odd, the product is negative.

Code Implementation

def array_sign(numbers):
    negative_count = 0
    for number in numbers:
        if number == 0:
            # Zero immediately makes the product zero
            return 0
        elif number < 0:

            negative_count += 1

    # Even negative count means product is positive
    if negative_count % 2 == 0:
        return 1
    # Odd negative count means product is negative
    else:

        return -1

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Empty input array	Return 1 as the product of no numbers is often defined as 1.
Null input array	Throw an IllegalArgumentException to signal invalid input.
Array contains zero	Return 0 immediately, as any product involving 0 is 0.
Array contains only positive numbers	Return 1, as the product of positive numbers is positive.
Array contains only negative numbers with an even length	Return 1, as an even number of negative numbers results in a positive product.
Array contains only negative numbers with an odd length	Return -1, as an odd number of negative numbers results in a negative product.
Integer overflow during multiplication for very large arrays	Continuously check for overflow in each multiplication, returning 0 when detected or using a long type.
Array with extreme boundary values (Integer.MAX_VALUE, Integer.MIN_VALUE) and negative numbers	Be cautious of potential overflow if multiplying Integer.MIN_VALUE with -1, and handle accordingly by pre-checking or using long type.

Empty input array

How to Handle:

Return 1 as the product of no numbers is often defined as 1.

Null input array

How to Handle:

Throw an IllegalArgumentException to signal invalid input.

Array contains zero

How to Handle:

Return 0 immediately, as any product involving 0 is 0.

Array contains only positive numbers

How to Handle:

Return 1, as the product of positive numbers is positive.

Array contains only negative numbers with an even length

How to Handle:

Return 1, as an even number of negative numbers results in a positive product.

Array contains only negative numbers with an odd length

How to Handle:

Return -1, as an odd number of negative numbers results in a negative product.

Integer overflow during multiplication for very large arrays

How to Handle:

Continuously check for overflow in each multiplication, returning 0 when detected or using a long type.

Array with extreme boundary values (Integer.MAX_VALUE, Integer.MIN_VALUE) and negative numbers

How to Handle:

Be cautious of potential overflow if multiplying Integer.MIN_VALUE with -1, and handle accordingly by pre-checking or using long type.