A tree game
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 314 Accepted Submission(s): 146
Problem Description
Alice and Bob want to play an interesting game on a tree.
Given is a tree on N vertices, The vertices are numbered from 1 to N. vertex 1 represents the root. There are N-1 edges. Players alternate in making moves, Alice moves first. A move consists of two steps. In the first step the player selects an edge and removes it from the tree. In the second step he/she removes all the edges that are no longer connected to the root. The player who has no edge to remove loses.
You may assume that both Alice and Bob play optimally.
Input
The first line of the input file contains an integer T (T<=100) specifying the number of test cases.
Each test case begins with a line containing an integer N (1<=N<=10^5), the number of vertices,The following N-1 lines each contain two integers I , J, which means I is connected with J. You can assume that there are no loops in the tree.
Output
For each case, output a single line containing the name of the player who will win the game.
Sample Input
3
3
1 2
2 3
3
1 2
1 3
10
6 2
4 3
8 4
9 5
8 6
2 7
5 8
1 9
6 10
Sample Output
Alice
Bob
Alice
Source
2009 Multi-University Training Contest 18 - Host by ECNU
Recommend
lcy
題意：每次選擇一條邊刪去，並把不和根連的邊移去。
據說是賈志豪神牛的論文。
結論：葉子節點的sg值為0，中間節點的SG值為它的所有子節點的SG值加1 後的異或和。
[cpp]
#include<iostream>
#include<cstdlib>
#include<stdio.h>
#include<memory.h>
#include<vector>
using namespace std;
vector<int>v[100005];
int dfs(int x,int pre)
{
int ans=0;
for(int i=0;i<v[x].size();i++)
{
//printf("%d %d %d \n",x,i,v[x][i]);
if(v[x][i]!=pre)
{
ans^=(1+dfs(v[x][i],x));
}
}
return ans;
}
int main()
{
int t,a,b,n;
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
for(int i=1;i<=n;i++)
v[i].clear();
n--;
while(n--)
{
scanf("%d%d",&a,&b);
v[a].push_back(b);
v[b].push_back(a);
}
//printf("%d\n",v[1][2]);
if(dfs(1,-1)) puts("Alice");
else puts("Bob");
}
}
