Product of Array Except Self

Introduction

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

We need to go through array in backward and forward direction by multiplying numbers one by one. We can reuse output array. Need to make sure that current number is not participating in multiplication.

func productExceptSelf(nums []int) []int {
    n := len(nums)
    if n == 0 {
        return nil
    }
    out := make([]int, n + 1)
    out[n] = 1
    for j := n - 1; j >= 0; j-- {
        out[j] =  out[j+1] * nums[j]
    }
    p := 1
    for i := 0; i < n; i++ {
        out[i] = p * out[i+1]
        p *= nums[i]
    }
    return out[:n]
}