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

-spec product_except_self(Nums :: [integer()]) -> [integer()].
product_except_self(Nums) ->
    Forwards = product(Nums, [], 1),
    Backwards = lists:reverse(product(lists:reverse(Nums), [], 1)),
    except_self([1|Forwards], Backwards ++ [1], []).

product([], Res, _) -> lists:reverse(Res);
product([H|T], Res, Acc) ->
    P = H * Acc,
    product(T, [P|Res], P).

except_self([_], [_], Res) -> lists:reverse(Res);
except_self([F|T1], [_, B|T2], Res) ->
    except_self(T1, [B|T2], [F * B|Res]).

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