Google New Grad Software Engineer Interview Experience — Water-Flow Paths and Good Numbers at Onsite

Software Engineer II, Early Career - United States

03/31: Applied
04/01: OA
05/14: Virtual interview R1 — behavioral questions + coding (I don't remember the question)
06/08: Got an email about next steps and scheduled a recruiter meeting
06/15: Talked with the recruiter, got the onsite details
07/14: Onsite interview R2 — coding + coding

The R2 onsite questions were:

Question 1: Longest Water-Flow Path
Given an m×n height matrix, you start from any cell and can move to an adjacent cell (up, down, left, right). The rule for moving to the next cell: either the next cell's height is less than or equal to the current cell's height (flowing downhill), or the next cell is higher, but the height two steps back is greater than or equal to the next cell's height (using momentum borrowed from the previous step to push up). Find the length of the longest path.

Question 2: Good Number
A positive integer is "good" if it satisfies all of the following: it contains no digit 0; each digit appears at most once; and no digit is smaller than both of its left and right neighbors.
Follow-up: given m, how many good numbers are there from 1 to m?