product_of_array_except_itself.py

"""
Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].

The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

You must write an algorithm that runs in O(n) time and without using the division operation.

 

Example 1:

Input: nums = [1,2,3,4]
Output: [24,12,8,6]
Example 2:

Input: nums = [-1,1,0,-3,3]
Output: [0,0,9,0,0]
 

Constraints:

2 <= nums.length <= 105
-30 <= nums[i] <= 30
The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

"""

class Solution(object):
    def productExceptSelf(self, nums):
        """
        :type nums: List[int]
        :rtype: List[int]
        """
        n = len(nums)
        result = [1] * n
        # calculate the product of elements to the left of each element and store in result
        for i in range(1, n):
            result[i] = result[i - 1] * nums[i - 1]

        # calculate the product of elements to the right of each element and update result
        right_product = 1
        for i in range(n - 1, -1, -1):
            result[i] *= right_product
            right_product *= nums[i]

        return result