Product of Array Except Self Without Division

Question

The candidate is asked to implement a function that returns an array where each element is the product of all the elements of the input array except for the element at that index, without using division.

Codemia · Accepted Answer

To solve the problem of calculating the product of an array except self, we can utilize two passes through the array. The first pass will calculate the products of elements to the left of each index, and the second pass will calculate the products of elements to the right. This allows us to combine the results without using division.

Here is a step-by-step breakdown of the algorithm:

1. Initialize an output array of the same length as the input array, filled with ones.
2. Iterate through the input array from left to right, maintaining a running product of the elements seen so far, and store this in the output array.
3. Iterate through the input array from right to left, again maintaining a running product and multiplying it with the corresponding index in the output array.

This approach ensures that each index contains the product of all other elements in O(n) time complexity.

```python
def product_except_self(nums):
    length = len(nums)
    output = [1] * length

# Calculate products to the left of each index
    left_product = 1
    for i in range(length):
        output[i] = left_product
        left_product *= nums[i]

# Calculate products to the right of each index
    right_product = 1
    for i in range(length - 1, -1, -1):
        output[i] *= right_product
        right_product *= nums[i]

return output
```

The time complexity of this solution is O(n) because we traverse the input array twice. The space complexity is O(1) if we do not count the output array, as we are using a constant amount of space for the left and right product variables.

It is important to consider edge cases such as:
- An empty array, which should return an empty array.
- An array with one element, which should return an array with one element (1). 
These cases should be handled gracefully in the implementation.

Interviewers are looking for clarity in your thought process, the ability to articulate your approach, and how you handle edge cases. They also want to see if you can optimize your solution and consider the implications of time and space complexity.

Product of Array Except Self Without Division

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