Nine-chapter algorithm surface test 40 do not use Division to calculate the product

Nine chapters count judges Net-original website

http://www.jiuzhang.com/problem/40/

Topic

Given an array of A[1..N], find array B[1..N], make b[i] = a[1] * a[2]. * A[i-1] * a[i+1].. * A[n]. It is required not to use division and to complete in O (n), using an extra space of O (1) (which does not contain space occupied by the B array).

Answer

Calculate prefix product Prefix[i] = a[1] * a[2]. A[i], compute suffix product suffix[i] = a[i] * a[i+1]. A[n], easy to know, b[i] = prefix[i-1] * suffix[i + 1]. In fact, there is no need to actually construct the prefix and suffix arrays, use the B array to iterate from left to right once to get prefix[i], and then iterate from right to left to calculate the required B array.

Interviewer Angle

This method (Foward-backward-traverse), which is traversed from the front to the back and then traversed from the back to the front, is used for reference in many topics. such as the nine-chapter algorithm surface Question 31 sub-array of the maximum difference.

Nine-chapter algorithm surface test 40 do not use Division to calculate the product