Game of Taking Stones（java大数高精度）

最新推荐文章于 2019-10-25 19:51:03 发布

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最新推荐文章于 2019-10-25 19:51:03 发布

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分类专栏：数学

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本文探讨了一种名为威佐夫博弈的游戏策略，特别是在高精度条件下如何通过牛顿迭代法求解根号5，以确定游戏的胜负。游戏涉及两堆石头，玩家轮流取石，目标是在对方无法继续游戏时取得最后一颗石头。

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Two people face two piles of stones and make a game. They take turns to take stones. As game rules,
there are two different methods of taking stones: One scheme is that you can take any number of stones
in any one pile while the alternative is to take the same amount of stones at the same time in two piles.
In the end, the first person taking all the stones is winner.
Now, giving the initial number of two stones, can you win this game if you are the first to take
stones and both sides have taken the best strategy?
Input
Input contains multiple sets of test data.Each test data occupies one line, containing two non-negative
integers a and b, representing the number of two stones. a and b are not more than 10100
.
Output
For each test data, output answer on one line. ‘1’ means you are the winner, otherwise output ‘0’.
Sample Input
2 1
8 4
4 7
Sample Output
0
1
0

思路：

一个裸的威佐夫博奕，不过精度要求高需要用到牛顿迭代来求根号5.

代码：

import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.Scanner;

public class Main {

	/**
	 * @param args
	 */	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		Scanner cin=new Scanner(System.in);
		BigInteger a,b;
		//求解高精度根号5
		BigDecimal x=new BigDecimal("2");
		for(int i=1;i<=100;i++)
		{
			BigDecimal x1=(x.multiply(x)).subtract(new BigDecimal("5"));
			BigDecimal x2=x.multiply(new BigDecimal(2));
			BigDecimal x3=x1.divide(x2, 120, BigDecimal.ROUND_HALF_DOWN);
			x=x.subtract(x3);
		}
		
		BigDecimal xx=(x.add(new BigDecimal(1))).divide(new BigDecimal(2));
		
		while(cin.hasNext())
		{		
			a=cin.nextBigInteger();
			b=cin.nextBigInteger();
			//威佐夫博奕模板
			if(a.compareTo(b)==1)
			{
				BigInteger c;
				c=a;
				a=b;
				b=c;
			}
			String s=b.subtract(a).toString();
			BigDecimal k=new BigDecimal(s);
			BigDecimal sum1=k.multiply(xx);
			BigDecimal sum2=sum1.add(k);
			String s1=sum2.toString();
			String[] s2=s1.split("\\.");
			BigInteger t=new BigInteger(s2[0]);
			if(t.equals(b))
			{
				System.out.println(0);
			}
			else
			{
				System.out.println(1);
			}
			}
	}
}