LeetCode 238. Product of Array Except Self

Description

https://leetcode.com/problems/product-of-array-except-self/

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.

Follow up: Can you solve the problem in O(1) extra space complexity? (The output array does not count as extra space for space complexity analysis.)

Explanation

We can use two passes to get the final result. One pass is to get products before each number, another pass is to get products after each number.

Python Solution

class Solution:
    def productExceptSelf(self, nums: List[int]) -> List[int]:
        
        before_product = [1 for i in range(len(nums))]
        
        after_product = [1 for i in range(len(nums))]
        
        
        for i in range(1, len(nums)):
            before_product[i] = before_product[i - 1] * nums[i - 1]
        
        
        for i in range(len(nums) - 2, -1, -1):
            after_product[i] = after_product[i + 1] * nums[i + 1]

            
        results = []
        
        for p1, p2 in zip(before_product, after_product):
            results.append(p1 * p2)
            
        return results    
        
  • Time complexity: O(N).
  • Space complexity: O(N).

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