题目链接：https://nanti.jisuanke.com/t/40397

题意：给你n(2<n<10)和z(1<z<1e5),让你求出使|x^n+y^n-z^n|最小的x,y以及该表达式的值

分析：z，n这么大，无疑是要用到大数了。具体做法就是先x取1，y取z-1,之后y一点点变小，当x和y的n次方比z大之后，再固定y，一点点加x

JAVA大数模板常用函数：

valueof()函数，用来赋值

compareTo()方法返回值为int类型，就是比较两个值，如：x.compareTo(y)。如果前者大于后者，返回1，前者等于后者则返回0，前者小于后者则返回-1。

import java.util.*;
import java.math.*;
public class Main{
    public static void main(String args[]){
       Scanner cin = new Scanner(System.in);
       BigInteger a, b;

       //以文件EOF结束
       while (cin.hasNext()){
           a = cin.nextBigInteger();
           b = cin.nextBigInteger();       

           //大整数运算
           System.out.println(a.add(b)); //大整数加法
           System.out.println(a.subtract(b)); //大整数减法
           System.out.println(a.multiply(b)); //大整数乘法
           System.out.println(a.divide(b)); //大整数除法(取整)
           System.out.println(a.remainder(b)); //大整数取模
          

           //大整数的比较
           if( a.compareTo(b) == 0 ) System.out.println("a == b"); //大整数a==b
           else if( a.compareTo(b) > 0 ) System.out.println("a > b"); //大整数a>b
           else if( a.compareTo(b) < 0 ) System.out.println("a < b"); //大整数a<b
         

           //大整数绝对值
           System.out.println(a.abs()); //大整数a的绝对值
         

           //大整数的幂
           int exponent=10;
           System.out.println(a.pow(exponent)); //大整数a的exponent次幂
          

           //返回大整数十进制的字符串表示
           System.out.println(a.toString());
          
           
           //返回大整数p进制的字符串表示
           int p=8;
           System.out.println(a.toString(p));

       }

    }

}

JAVA结构体（JAVA没有结构体，只能借助类）排序的使用方法

import java.util.*;
 
class mans
{
    long acm,money,rp;
}
class cmp implements Comparator<mans>
{
    public int compare(mans a,mans b)
    {
        if(a.acm==b.acm)
        {
            if(a.money==b.money)
            {
                return (int)(a.rp-b.rp);
            }
            return (int)(a.money-b.money);    
        }
        return (int)(a.acm-b.acm);
    }
}
public class Main
{
 
    public static void main(String[] args)
    {
        // TODO Auto-generated method stub
        Scanner scanf=new Scanner(System.in);
        mans a[]=new mans[1009];
        while(scanf.hasNext())
        {
            int n=scanf.nextInt();
            for(int i=0;i<n;i++)
            {
                a[i] = new mans();
                a[i].acm=scanf.nextLong();
                a[i].money=scanf.nextLong();
                a[i].rp=scanf.nextLong();
            }
            Arrays.sort(a,0,n,new cmp());
            for(int i=n-1;i>=0;i--)
            {
                System.out.println(a[i].acm+" "+a[i].money+" "+a[i].rp);
            }
        }
    }
}

用sort进行字典序排序

    import java.util.Arrays;  
    import java.util.Comparator;  
    import java.util.Scanner;  
    import java.util.*;    
      
    class shu ///创建类  
    {  
        String name;///比较时用String  
        int mon;  
        int hunt;  
    }  
      
    class cmp implements Comparator<shu> {  
        public int compare(shu A, shu B)   
        {  
                if(A.hunt==B.hunt)  
                {  
                    if(A.mon==B.mon)  
                    {  
                        int flag=(A.name).compareTo(B.name);///按字典序排序  
                        if(flag==0)  
                        {  
                            return 0;  
                        }  
                        else if(flag<0)  
                        {  
                            return -1;  
                        }  
                        else  
                        {  
                            return 1;  
                        }  
                    }  
                    else  
                    {  
                        if(A.mon==B.mon)  
                        {  
                            return 0;  
      
                        }  
                        else if(A.mon<B.mon)  
                        {  
                            return -1;  
                        }  
                        else  
                        {  
                            return 1;  
                        }  
                              
                    }  
                }  
                else  
                {  
      
                    if(A.hunt==B.hunt)  
                    {  
                        return 0;  
      
                    }  
                    else if(A.hunt<B.hunt)  
                    {  
                        return 1;  
                    }  
                    else  
                    {  
                        return -1;  
                    }  
                }  
      
                  
        }  
      
      
    }  
      
    public class Main {  
        public static void main(String[] args) {  
              
            Scanner in = new Scanner(System.in);  
      
            while (in.hasNext()) {  
                  
                shu num[] = new shu[100005];///创建类数组  
      
                int n;  
                n = in.nextInt();  
      
                for (int i = 0; i < n; i++) {  
                      
                    num[i]=new shu();///这个地方容易漏  
                      
                    num[i].name=in.next();  
                    num[i].hunt=in.nextInt();  
                    num[i].mon=in.nextInt();  
                }  
                  
                Arrays.sort(num, 0, n, new cmp());  
                  
                for (int i = 0; i < n; i++) {  
                    System.out.println(num[i].name);  
                }  
      
            }  
        }  
    }  

然后便是本题题解代码了

import java.io.*;
import java.util.*;
import java.math.*;


public class Exam {

    static int Ax,Ay;
    static BigInteger Adiff;

    static boolean compare(BigInteger a,BigInteger b) {
        if (b.compareTo(BigInteger.ZERO)<0)
            return true;
        
        return (a.compareTo(b)<0);
    }
    
    
    static void fast_solve(int n,int z) {
        Ax=Ay=-1;
        Adiff=BigInteger.valueOf(-1);
        boolean init=false;
        
        
        int pve_minpos=-1;
        BigInteger bzN = (BigInteger.valueOf(z)).pow(n);
        
        int min_pveY=z-1;
        
        for (int ix=1;ix<z;ix++) {
            BigInteger bx = BigInteger.valueOf(ix);
            BigInteger bxN=bx.pow(n);
            
            boolean is_neg=false;
            
            int start_y=min_pveY;
            for (int iy=start_y;iy>ix;iy--) {
                BigInteger by = BigInteger.valueOf(iy);
                BigInteger byN = by.pow(n);
                
                BigInteger diff=(bxN.add(byN)).subtract(bzN);
                
                int cmp=diff.compareTo(BigInteger.ZERO);
                if (cmp<0)
                    is_neg=true;
                
                if (cmp>0)
                    if (iy<min_pveY)
                        min_pveY=iy;
                
                diff=diff.abs();
                if (compare(diff,Adiff)==true) {
                    Ax=ix;
                    Ay=iy;
                    Adiff=diff;
                }                
                
                if (is_neg) {
                    //if (ix%1000==0)
                    //    System.out.printf("~ %d %d %s\n",ix,iy, Adiff.toString());
                    break;
                }
            }
        }
    }
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        
        int count,n,z;
        
        count=in.nextInt();
            
        for (int i=0;i<count;i++) {
            n=in.nextInt();
            z=in.nextInt();
            fast_solve(n,z);
            System.out.printf("%d %d %s\n", Ax, Ay, Adiff.toString());
        }
    }

}