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product-of-array-except-itself

Problem

Problem Description

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]
Constraint: It's guaranteed that the product of the elements of any prefix or suffix of the array (including the whole array) fits in a 32 bit integer.
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.)

Solution

Intuitive solution is to product the whole array, result is to divide itself. Notice from problem, without division and solve it in O(n).
Idea is to product from left to right, then right to left:
  1. 1.
    Init res[len], res[0] = 1, left = 1;
  2. 2.
    Scan array from left to right, skip the last number, from
    index = 1, left = left * nums[index -1], res[index] = left;
  3. 3.
    init right = nums[len - 1], from second right most element, from
    index = len - 2, res[index] = res[index] * right, right = nums[index] * right
  4. 4.
    return res.
For example:
Product of Array Except Itself

Complexity Analysis

Time Complexity: O(N)
Space Complexity: O(N)
  • N - the length of array nums

Code

class Solution {
public int[] productExceptSelf(int[] nums) {
int len = nums.length;
int[] res = new int[len];
res[0] = 1;
// from left to right
for (int i = 1; i < len; i++) {
res[i] = res[i - 1] * nums[i - 1];
}
// from right to left
int right = nums[len - 1];
for (int i = len - 2; i >= 0; i--) {
res[i] *= right;
right *= nums[i];
}
return res;
}
}