问题 A: Fermat‘s Optimization Problem--------------------思维(Java大数+二分)

import java.io.*;  
import java.math.*;  
import java.util.*;  
import java.text.*;  
public class Main  
{  
    public static void main(String[] args)   
    {  
        Scanner cin = new Scanner (new BufferedInputStream(System.in));  
        BigInteger [][]  p = new BigInteger[100001][11];
        for(int i=1;i<100001;i++)
        {
            p[i][0]=new BigInteger("1");
            for(int j=1;j<=10;j++) p[i][j]=p[i][j-1].multiply(BigInteger.valueOf(i)); 
        }
        BigInteger zero = new BigInteger("0");
        BigInteger one = new BigInteger("1");
        BigInteger INF=one;
        for(int i=0;i<10;i++)  INF=INF.multiply(p[10][10]);
       
        int t,z,n;
        t=cin.nextInt();
        while((t--)>0) 
        {
           n = cin.nextInt();z = cin.nextInt();
           int x=0,y=0;
           BigInteger res=INF;
           BigInteger num;
           for(int i=2;i<z;i++)
           {
               int l=1,r=i-1;
               while(l<r)
               {
                   int mid=l+r+1>>1;
                   num = p[mid][n].add(p[i][n]).subtract(p[z][n]);
                   if(num.compareTo(zero)<0) l=mid;
                   else r=mid-1;
                   
               }
               num=p[r][n].add(p[i][n]).subtract(p[z][n]);
               if(num.compareTo(zero)>=0)
               {
                   if(num.compareTo(res)<0) 
                   {
                       res=num;
                       x=r;
                       y=i;
                   }
               }
               else
               {
                   num=num.multiply(new BigInteger("-1"));
                   if(num.compareTo(res)<0) 
                   {
                       res=num;
                       x=r;
                       y=i;
                   }
                   
                   if(r<i-1)
                   {
                       r++;
                       num=p[r][n].add(p[i][n]).subtract(p[z][n]);
                       if(num.compareTo(res)<0)
                       {
                           res=num;
                           x=r;
                           y=i;
                       }
                   }
               }
        
           }
        
           	System.out.printf("%d %d ", x, y);
			System.out.println(res);
           
        }
      
    }  
}