I don't understand the 2nd sample test.
Is a player go on the path from where the othe player reach?
Or are the players move on different path?

Each player starts from the point that the other player selects.
Here's an explanation for the 2nd test

       1
      / \
     2   3
    / \ / \
    4 5 6 7
    - + + 0

If the first player chooses the 2 node, the second player will choose the 4th and win.
If the first player chooses the 3 node, the second player will choose the 7th node (he prefers to draw than to loose)

So, the player will choose the 3rd node, as he prefers drawing rather than loosing.

Edited by author 22.06.2012 16:52