HDU 4282 A very hard mathematic problem 第37届ACM/ICPC长春赛区网络赛1005题 （暴力）

A very hard mathematic problem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 964    Accepted Submission(s): 279

Problem Description

　　Haoren is very good at solving mathematic problems. Today he is working a problem like this:
　　Find three positive integers X, Y and Z (X < Y, Z > 1) that holds
　　 X^Z + Y^Z + XYZ = K
　　where K is another given integer.
　　Here the operator “^” means power, e.g., 2^3 = 2 * 2 * 2.
　　Finding a solution is quite easy to Haoren. Now he wants to challenge more: What’s the total number of different solutions?
　　Surprisingly, he is unable to solve this one. It seems that it’s really a very hard mathematic problem.
　　Now, it’s your turn.

 

 

Input

　　There are multiple test cases.
　　For each case, there is only one integer K (0 < K < 2^31) in a line.
　　K = 0 implies the end of input.
　　

 

 

Output

　　Output the total number of solutions in a line for each test case.

 

 

Sample Input

9 53 6 0

 

 

Sample Output

1 1 0 　　

Hint

9 = 1^2 + 2^2 + 1 * 2 * 2 53 = 2^3 + 3^3 + 2 * 3 * 3

 

 

Source

2012 ACM/ICPC Asia Regional Tianjin Online

 

 

Recommend

liuyiding

 

 

 

 

暴力枚举z就可以了。z肯定比较小的。

当z等于2时就是平方和公式。

#include<stdio.h>

#include<math.h>

#include<string.h>

#include<algorithm>

#include<iostream>

using namespace std;



long long pow(long long a,int n)

{

    long long ret=1;

    long long temp=a;

    while(n)

    {

        if(n&1)ret*=temp;

        temp*=temp;

        n>>=1;

    }

    return ret;

}

int main()

{

    long long K;

    long long ans;

    while(scanf("%I64d",&K),K)

    {

        ans=0;

        long long temp=(long long)sqrt(K);

        if(temp*temp==K)ans+=(temp-1)/2;

        for(int z=3;z<31;z++)

        {

            for(long long x=1;;x++)

            {

                long long u=pow(x,z);

                if(u*2>=K)break;

                for(long long y=x+1;;y++)

                {

                    long long v=pow(y,z);

                    if(u+v+x*y*z>K)break;

                    if(u+v+x*y*z==K)ans++;

                }

            }

        }

        printf("%I64d\n",ans);

    }

    return 0;

}