HDU 5754Life Winner Bo

Life Winner Bo

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 1019    Accepted Submission(s): 373

Problem Description

Bo is a "Life Winner".He likes playing chessboard games with his girlfriend G.

The size of the chessboard is N×M.The top left corner is numbered(1,1) and the lower right corner is numberd (N,M).

For each game,Bo and G take turns moving a chesspiece(Bo first).At first,the chesspiece is located at (1,1).And the winner is the person who first moves the chesspiece to (N,M).At one point,if the chess can't be moved and it isn't located at (N,M),they end in a draw.

In general,the chesspiece can only be moved right or down.Formally,suppose it is located at (x,y),it can be moved to the next point (x′,y′) only if x′≥x and y′≥y.Also it can't be moved to the outside of chessboard.

Besides,There are four kinds of chess(They have movement rules respectively).

1.king.

2.rook(castle).

3.knight.

4.queen.

(The movement rule is as same as the chess.)

For each type of chess,you should find out that who will win the game if they both play in an optimal strategy.

Print the winner's name("B" or "G") or "D" if nobody wins the game.

 

 

Input

In the first line,there is a number T as a case number.

In the next T lines,there are three numbers type,N and M.

"type" means the kind of the chess.

T≤1000,2≤N,M≤1000,1≤type≤4

 

 

Output

For each question,print the answer.

 

 

Sample Input

4 1 5 5 2 5 5 3 5 5 4 5 5

 

 

Sample Output

G G D B

 

/* ***********************************************
Author        :guanjun
Created Time  :2016/7/27 13:04:59
File Name     :hdu5754.cpp
************************************************ */
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <stdio.h>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <iomanip>
#include <list>
#include <deque>
#include <stack>
#define ull unsigned long long
#define ll long long
#define mod 90001
#define INF 0x3f3f3f3f
#define maxn 100010
#define cle(a) memset(a,0,sizeof(a))
const ull inf = 1LL << 61;
const double eps=1e-5;
const double Gsr=(1+sqrt(5.))/2.; 
using namespace std;
priority_queue<int,vector<int>,greater<int> >pq;
struct Node{
    int x,y;
};
struct cmp{
    bool operator()(Node a,Node b){
        if(a.x==b.x) return a.y> b.y;
        return a.x>b.x;
    }
};

bool cmp(int a,int b){
    return a>b;
}
int a,n,m;
 
int main()
{
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    #endif
    //freopen("out.txt","w",stdout);
    int t;
    cin>>t;
    while(t--){
        cin>>a>>n>>m;
        if(a==1){
            if((n&1)&&(m&1))puts("G");
            else puts("B");
        }
        if(a==2){
            if(n==m){//后手赢
                puts("G");
            }
            else{
                puts("B");
            }
        }
        if(a==3){
            if(n<m)swap(n,m);
            if((n==m)&&(n%3==1))puts("G");
            else if((n%3==0)&&(m==n-1))puts("B");
            else puts("D");
        }
        if(a==4){//威佐夫博弈
            n--,m--;
            if(n>m)swap(n,m);
            if(n==(int)(Gsr*(m-n))){
                puts("G");
            }
            else puts("B");
        }
    }
    return 0;
}

找规律。皇后的时候转换成博弈

“有两堆石子，每次可以在一堆里取任意（非空）颗（相当于是车的走法），或者在两堆里取相同（非空）颗（相当于是象的走法），取到最后一颗石子的人获胜，问先后手谁有必胜策略。”