238. Product of Array Except Self #

Problem #

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 <= 10^5
• -30 <= nums[i] <= 30
• The input is generated such that answer[i] 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.)

Code #

package leetcode

// Solution 1: Prefix product * suffix product. Does not use division; time complexity O(n), space complexity O(1) excluding the output array.
func productExceptSelf(nums []int) []int {
	n := len(nums)
	res := make([]int, n)
	// res[i] first stores the product of all elements to the left of nums[i]
	res[0] = 1
	for i := 1; i < n; i++ {
		res[i] = res[i-1] * nums[i-1]
	}
	// Then multiply from right to left by the product of all elements to the right of nums[i]; right accumulates the suffix product
	right := 1
	for i := n - 1; i >= 0; i-- {
		res[i] *= right
		right *= nums[i]
	}
	return res
}