Sign of the Product of an Array - Practice Coding Problems

Sign of the Product of an Array - Problem

Array Math Easy

Given an integer array nums, you need to determine the sign of the product of all elements in the array without actually calculating the product itself.

The challenge is to implement a function that returns:

1 if the product is positive
-1 if the product is negative
0 if the product is zero

Key insight: You don't need to calculate the actual product (which could overflow), just determine its sign! Think about what makes a product positive, negative, or zero.

Example: For [1, 5, 0, 2, -3], since there's a zero, the product is 0, so return 0.

Input & Output

example_1.py — Basic positive result

$ Input: nums = [-1,1,-1,1,1]

› Output: 1

💡 Note: The product is (-1) * 1 * (-1) * 1 * 1 = 1, which is positive, so return 1. Alternatively, count negatives: 2 negatives (even) = positive result.

example_2.py — Negative result

$ Input: nums = [-1,1,-1,1,-1]

› Output: -1

💡 Note: The product is (-1) * 1 * (-1) * 1 * (-1) = -1, which is negative, so return -1. Count negatives: 3 negatives (odd) = negative result.

example_3.py — Zero in array

$ Input: nums = [-1,1,0,1,-1]

› Output: 0

💡 Note: Since there's a 0 in the array, the product is 0, so return 0. Any zero makes the entire product zero.

Constraints

1 ≤ nums.length ≤ 1000
-100 ≤ nums[i] ≤ 100
No need to calculate actual product - avoid overflow issues

Visualization

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Understanding the Visualization

Check for Zero

If any element is 0, the entire product becomes 0

Count Negatives

Each negative number flips the sign of the product

Apply Sign Rule

Even count of negatives = positive, odd count = negative

Key Takeaway

🎯 Key Insight: The sign of a product depends only on the parity (even/odd) of negative numbers, not their actual values!

Asked in

G Google 23 a Amazon 18 f Meta 15 ⊞ Microsoft 12

The optimal solution avoids calculating the actual product by recognizing that the sign depends only on: (1) presence of zeros, and (2) count of negative numbers. Even negatives = positive product, odd negatives = negative product. This prevents overflow and runs in O(n) time with O(1) space.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Calculate Actual Product)	O(n)	O(1)	Calculate the actual product and return its sign
Count Negatives (Optimal)	O(n)	O(1)	Count negative numbers to determine sign without calculating product

Brute Force (Calculate Actual Product) — Algorithm Steps

Initialize product to 1
Multiply each number in the array with the product
Return 1 if product > 0, -1 if product < 0, 0 if product == 0

Visualization

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Step-by-Step Walkthrough

Initialize

Start with product = 1

Multiply

Multiply each array element with current product

Check Sign

Determine if final product is positive, negative, or zero

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int arraySign(int* nums, int numsSize) {
    long long product = 1;
    for (int i = 0; i < numsSize; i++) {
        product *= nums[i];
    }
    
    if (product > 0) {
        return 1;
    } else if (product < 0) {
        return -1;
    } else {
        return 0;
    }
}

int main() {
    int nums[1000];
    int size = 0;
    char ch;
    int num = 0;
    int sign = 1;
    int reading = 0;
    
    while ((ch = getchar()) != '\n' && ch != EOF) {
        if (ch >= '0' && ch <= '9') {
            num = num * 10 + (ch - '0');
            reading = 1;
        } else if (ch == '-') {
            sign = -1;
        } else if (ch == ',' || ch == ']') {
            if (reading) {
                nums[size++] = sign * num;
                num = 0;
                sign = 1;
                reading = 0;
            }
        }
    }
    
    printf("%d\n", arraySign(nums, size));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

We iterate through the array once, performing constant time multiplication

✓ Linear Growth

Space Complexity

O(1)

We only use a single variable to store the product

✓ Linear Space

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Medium Frequency

~8 min Avg. Time

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force (Calculate Actual Product) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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