Day 15 of 30 days Leetcode Challenge - Product of Array Except Self

Product of Array Except Self

Given an array nums of n integers where n > 1, return an array output such that output[i] is equal to the product of all the elements of nums except nums[i].

Example:

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

Constraint: It's guaranteed that the product of the elements of any prefix or suffix of the array (including the whole array) fits in a 32 bit integer.

Note: Please solve it without division and in O(n).

Follow up:
Could you solve it with constant space complexity? (The output array does not count as extra space for the purpose of space complexity analysis.)

Solution

if we can use division, it's simple
Apply same technique as prefix sum, we calculate both prefix product and suffix product, product at i is prefix[i - 1] * suffix[i + 1]

class Solution {
    func productExceptSelf(_ nums: [Int]) -> [Int] {
        
        var prefix = Array(repeating: 1, count: nums.count)
        var suffix = Array(repeating: 1, count: nums.count)
        
        let lastIndex = nums.count - 1
        
        prefix[0] = nums[0]
        suffix[lastIndex] = nums[lastIndex]
        
        for i in 1...lastIndex {
            prefix[i] = prefix[i - 1] * nums[i]
            suffix[lastIndex - i] = suffix[lastIndex - i + 1] * nums[lastIndex - i]
        }
        
        var res = [Int]()
        res.append(suffix[1])
        
        for i in 1..<nums.count-1 {
            res.append(prefix[i-1] * suffix[i+1])
        }
        
        res.append(prefix[nums.count - 2])
        
        return res
    }
}

Constant space solution: updating...