Product of Array Except Self

Description

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.)

Code

$O(n)$ Time, $O(n)$ Space

class Solution {
public:
    vector<int> productExceptSelf(vector<int>& nums) {
        vector<int> prefixSum(nums);
        vector<int> postfixSum(nums);
        for(int i = 1; i < prefixSum.size(); i++) {
            prefixSum[i] *= prefixSum[i - 1];
        }
        for(int j = postfixSum.size() - 2; j >= 0; j--) {
            postfixSum[j] *= postfixSum[j + 1];
        }
        int n = nums.size();
        vector<int> answer(n);
        for(int i = 0; i < n; i++) {
            int pre = i - 1 >= 0 ? prefixSum[i - 1] : 1;
            int post = i + 1 < n ? postfixSum[i + 1] : 1;
            answer[i] = pre * post;
        }   
        return answer;
    }
};

$O(n)$ Time, $O(1)$ Space

思路和 $O(n)$ Space 的解法相同，都是要計算由右至左，以及由左至右的 prefix product，只是 do it inplace。

class Solution {
public:
    vector<int> productExceptSelf(vector<int>& nums) {
        int n = nums.size();
        vector<int> res(n, 0); 
        res[0] = 1;
        for(int i = 1; i < n; i++) {
            res[i] = res[i - 1] * nums[i - 1];
        }
 
        int r = 1;
        for(int i = n - 1; i >= 0; i--) {
            res[i] *= r;
            r *= nums[i];
        }
        return res;
        
    }
};

Source

• Product of Array Except Self - LeetCode