07/16/2016 Array

## Question

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].

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.)

## Solution

Result: Accepted Time: 36 ms

Here should be some explanations.

/**
* Return an array of size *returnSize.
* Note: The returned array must be malloced, assume caller calls free().
*/
int* productExceptSelf(int* nums, int numsSize, int* returnSize) {
int *ans = malloc(sizeof(int)*numsSize + 8);
ans[0] = 1;
for(int i = 1; i < numsSize; i++)
ans[i] = ans[i-1]*nums[i-1];
int mul = 1;
for(int i = numsSize - 2 ; i >= 0 ; i--)
{
mul *= nums[i+1];
ans[i] = ans[i]*mul;
}
*returnSize = numsSize;
return ans;

}


Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$