[LeetCode 解题报告]238. Product of Array Except Self

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]

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.)

Method 1.

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

Method 2.

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