題目：
In computer science, a binary tree is a rooted tree in which each node has at most two children. In this problem, let’s denote n as the number of nodes, l as the number of leaf nodes and h as the height of the tree (a tree consisting of only a root node has a height of 0).
Alice and Bob are playing a game with a binary tree. In this game, Alice and Bob have a binary tree, in which node 1 is the root. They take turns to perform operations on the tree, and Alice always takes the first turn. In each operation, the player taking the turn must choose a node p (any node including the root can be chosen), and remove the subtree rooted at p from the tree. Obviously, the remaining graph, if not empty, is still a binary tree. Then they continue to play with the resulting tree. To make the game more interesting, there is a restriction on which nodes can be chosen as p: the subtree rooted at p (the subtree to be removed) must be a perfect full binary tree. Note that a perfect full binary tree is a binary tree in which all interior (non-leaf) nodes have two children and all leaf nodes have the same depth. It can be easily shown that in a perfect full binary tree, the equation l=2h holds, so does the equation n=2h+1−1. In particular, a tree consisting of only a root node is also a perfect full binary tree. When a player is unable to perform a legal operation, the game ends and that player loses, which means the other player wins.
Three examples of perfect full binary trees.
Alice and Bob are both very smart and always play optimally. Can you determine who would win the game?
Input
The input contains multiple cases. The first line of the input contains a single positive integer T, the number of cases.
For each case, the first line of the input contains a single integer n (1≤n≤5000), the number of nodes in the binary tree. The following n−1 lines each contains two integers x,y (1≤x≤n,1≤y≤n), which denotes an edge between node x and y. It is guaranteed that the input graph is a binary tree rooted at node 1.
It’s guaranteed that the sum of n over all cases does not exceed 50000.
Output
For each case, print the string “Alice” in a single line if Alice would win the game, otherwise print the string “Bob”.
Example
inputCopy
1
5
1 2
1 3
3 4
3 5
outputCopy
Alice
Note
In the sample case, Alice removes the subtree rooted at node 3 in the first turn. Then Bob can only choose p=2, which leaves Alice with only the root node 1. Because a tree consisting of only a root node is a perfect full binary tree, Alice can remove the only remaining node and win the game.
題意就是給出一顆二叉樹，然後兩個人輪流移除完美二叉樹，直到某一方拿走最後的點。
思路就是：每次拿走的完美二叉樹，你會發現，點的數量是奇數，也就是兩人輪流拿去一個奇數，這樣的博弈，從奇偶性上面來直接判斷誰勝誰負。
完整代碼：
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <climits>
#include <queue>
#include <stack>
#include <map>
//鬼畜頭文件
using namespace std;
const int INF = 0x3f3f3f3f;
//1.06e9大小
const int mod = 1e9+7;
typedef unsigned long long ULL;
typedef long long LL;
//鬼畜define
int main()
{
int t;
scanf("%d",&t);
int n;
while(t--)
{
scanf("%d",&n);
int from,to;
for(int time=0;time<n-1;time++){scanf("%d %d",&from,&to);}
if(n%2==0)printf("Bob\n");
else printf("Alice\n");
}
}