LeetCode-in-All

238. Product of Array Except Self

Medium

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.)

Solution

(define/contract (product-except-self nums)
  (-> (listof exact-integer?) (listof exact-integer?))
  (let* ((first-pass (foldl mult-w-track-zero '(1 0) nums))
	 (prod (car first-pass))
	 (zero-count (second first-pass)))
    (map (lambda (x)
	   (cond
	    [(zero? zero-count)
	     (/ prod x)]
	    [(= 1 zero-count)
	     (if (zero? x) prod 0)]
	    [else 0])) nums)))

(define (mult-w-track-zero x acc)
  (let* ((prod (car acc))
	(zero-count (second acc))
	(new-count (if (zero? x) (add1 zero-count) zero-count)))
    (list (if (= 0 x) prod (* prod x))
	  new-count)))

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