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AnswersTree Game

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class TreeNode {

TreeNode parent; //parent node

TreeNode left; //left child

TreeNode right; //right child

}

Two people in a game, player scores by claiming nodes in binary tree, tree node class as shown above.

The player who eventually owns more nodes wins the game.

Player A and B each claims a node at first.

After the first round, a player will only be able to claim a node adjacent to any node owned by himself.

A tree node is adjacent to its parent, left right and right child.

A node owned cannot be re-claimed.

End game when all nodes are owned.

If player A gets the first claim at node N, find whether it is possible for player B to win.

If yes, find out which node player B should claim at his first move.

Follow up: if player B takes the first hand instead, which node should he pick?| Report Duplicate | Flag | PURGE

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Solution

```
class TreeNode {
int id;
TreeNode left;
TreeNode right;
TreeNode parent;
TreeNode(int id) {
this.id = id;
}
}
/*
The opponent's first move on Node N divides the tree into 3 components - left subtree, right subtree and parent branch of N.
Your best move is to claim a node adjacent to Node N at the biggest component.
Function countNodes() counts the sizes of 3 components. Function win() finds the largest component, whose size is your score.
*/
public static boolean win(TreeNode root, TreeNode n) { //N is the first move by opponent
int sizeParent = countNodes(n.parent, n); //size of parent component
int sizeLeft = countNodes(n.left, n); //size of left subtree component
int sizeRight = countNodes(n.right, n); //size of right subtree component
int myScore = Math.max(Math.max(sizeParent, sizeLeft), sizeRight); //I take the biggest component
int treeSize = 1 + sizeParent + sizeLeft + sizeRight;
int opponentScore = treeSize - myScore; //opponent takes remaining nodes
System.out.print("my best score is " + myScore + "/" + treeSize + ". ");
if(myScore > opponentScore) {
TreeNode bestmove = myScore == sizeParent ? n.parent: myScore == sizeLeft ? n.left : n.right;
System.out.println("my first move on " + bestmove.id);
}
return myScore > opponentScore;
}
private static int countNodes(TreeNode node, TreeNode ignore) {
if(node == null) return 0;
int count = 1;
if(node.parent != ignore) {
count += countNodes(node.parent, node);
}
if(node.left != ignore) {
count += countNodes(node.left, node);
}
if(node.right != ignore) {
count += countNodes(node.right, node);
}
return count;
}
```

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