Dot grid game winner

Two players play a dots-and-boxes style game on a 9 x 9 grid of dots. The grid has 8 x 8 = 64 unit squares ("boxes"). Rows and columns are numbered 0 to 8.

You are given moves, a list of the sticks placed in order. moves[i] = [r1, c1, r2, c2] places a stick between dot (r1, c1) and dot (r2, c2). The two dots are always horizontally or vertically adjacent, and they may appear in either order.

Players strictly alternate. Player 1 makes moves 1, 3, 5, ... and player 2 makes moves 2, 4, 6, ..., whether or not a move closes a box. Whoever places the fourth side of a box scores that box. A single stick can close two boxes at once, and both count for its player.

Implement find_winner(moves: list[list[int]]) -> int. Return 1 or 2 for the player who owns more boxes after all moves, or 0 for a tie.

Constraints

• 0 <= len(moves) <= 144 (the total number of sticks on a 9 x 9 dot grid)
• 0 <= r1, c1, r2, c2 <= 8
• No stick is placed twice. (A natural follow-up asks you to validate this yourself.)

Example 1

moves = [[0,0,0,1], [0,0,1,0], [1,0,1,1], [0,1,1,1]]
output: 2

The first four sticks are the four sides of the top-left box. The 4th move is player 2's, so player 2 scores 1 and player 1 scores 0.

Example 2

moves = [[0,1,0,0], [5,5,5,6], [1,0,0,0], [6,6,6,7], [1,1,1,0], [7,7,7,8], [1,1,0,1]]
output: 1

Player 1's sticks (moves 1, 3, 5, 7) are the four sides of the top-left box, written with the endpoints reversed. Player 1 places the last side on move 7. Player 2's sticks close nothing.

Expected: O(1) work per move.

Reconstructed from the reported question; details may differ from what interviewers ask.