A game on an undirected graph is played by two players, Mouse and Cat, who alternate turns.
The graph is given as follows: graph[a]
is a list of all nodes b
such that ab
is an edge of the graph.
Mouse starts at node 1 and goes first, Cat starts at node 2 and goes second, and there is a Hole at node 0.
During each player's turn, they must travel along one edge of the graph that meets where they are. For example, if the Mouse is at node 1
, it must travel to any node in graph[1]
.
Additionally, it is not allowed for the Cat to travel to the Hole (node 0.)
Then, the game can end in 3 ways:
- If ever the Cat occupies the same node as the Mouse, the Cat wins.
- If ever the Mouse reaches the Hole, the Mouse wins.
- If ever a position is repeated (ie. the players are in the same position as a previous turn, and it is the same player's turn to move), the game is a draw.
Given a graph
, and assuming both players play optimally, return 1
if the game is won by Mouse, 2
if the game is won by Cat, and 0
if the game is a draw.
Example 1:
Input: [[2,5],[3],[0,4,5],[1,4,5],[2,3],[0,2,3]]
Output: 0
Explanation:
4---3---1
| |
2---5
\ /
0
Note:
3 <= graph.length <= 50
- It is guaranteed that
graph[1]
is non-empty.
- It is guaranteed that
graph[2]
contains a non-zero element.