Product of Array Except Self (Medium)

update Feb 10,2018 19:26

LeetCode

Given an array of n integers where n > 1, nums, return an array output such that output[i] is equal to the product of all the elements of nums except nums[i].

Solve it without division and in O(n).

For example:

given [1,2,3,4], return [24,12,8,6].

Follow up:
Could you solve it with constant space complexity? (Note: The output array does not count as extra space for the purpose of space complexity analysis.)

Basic Idea:

• 思路 1：Using division

  如果可以使用除法，我们可以先求出所给定数列的连乘积，那么结果就是连乘积除以每个数字的商；

• 思路 2：Without division

  如果不用division，就需要使用一些特殊的技巧。这里，我们注意到对于如下情况：

                      0  1  2  3  4
    input:    nums = [1, 2, 3, 4, 5]
  
    对于 nums[2], 它对应的解为 nums[0] 到 nums[1] 的乘积乘以 nums[3] 到 nums[4] 的乘积
  

  所以，事实上我们可以预处理input，生成两个数组，分别存储从左到右和从右到左的 prefix product，然后对于每个位置的解就是其左边部分乘积和右边部分乘积相乘。总的时间复杂度为 O(n);

  • Java Code：

        class Solution {
           public int[] productExceptSelf(int[] nums) {
               int[] left = new int[nums.length];
               int[] right = new int[nums.length];
               int[] ret = new int[nums.length];
               int t = 1;
               for (int i = 0; i < nums.length; ++i) {
                   left[i] = t * nums[i];
                   t = left[i];
               }
               t = 1;
               for (int i = nums.length - 1; i >= 0; --i) {
                   right[i] = t * nums[i];
                   t = right[i];
               }
               for (int i = 0; i < ret.length; ++i) {
                   int leftProduct = i == 0 ? 1 : left[i - 1];
                   int rightProduct = i == ret.length - 1 ? 1 : right[i + 1];
                   ret[i] = leftProduct * rightProduct;
               }
               return ret;
           }
       }