The rules are local involving just two cells: current cell and the cell to its left or to its right. Moves can happen in three directions: down, left, and right. For an entry column, we start with row = -1, so first down move is valid. In the beginning of each iteration we maintain the invariant: going down is valid. Within an iteration we consider the other two directions: left or right. If we hit borders or we hit “V”, we are stuck and try next entry column.
Time: 
class Solution:
def findBall(self, grid: List[List[int]]) -> List[int]:
m, n = len(grid), len(grid[0])
exits = [-1] * n
for entry in range(n):
r, c = -1, entry
while r < m:
# Invariant: Going down is valid
r += 1
if r == m:
exits[ entry ] = c
break
# next cell exist?
curr_dir = grid[r][c]
next_c = (c+1) if curr_dir == 1 else (c-1)
if (next_c < 0) or (next_c >= n):
break
# stuck?
next_dir = grid[r][next_c]
if next_dir != curr_dir:
break
# Go to next cell
c = next_c
return exits
unreasonably effective 
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