hdu4282

A very hard mathematic problem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 2680    Accepted Submission(s): 775

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

 

**=============================================**
||快速pow（多次使用时及其有效）               ||
**=============================================**
__int64 qpow(int a, int b){
    __int64 c, d; c = 1; d = a;
    while (b > 0){
        if (b & 1)
          c *= d;
        b = b >> 1;
        d = d * d;
    }
    return c;
}
**=============================================**
||快速1/sqrt(x)（牛顿迭代法）                    ||
**=============================================**
float InvSqrt (float x) {
     float xhalf = 0.5f * x;
     long i = *(long*)&x;
     i = 0x5f3759df - (i >> 1);
     x = *(float *)&i;
     x = x * (1.5f - xhalf * x * x);
     return x;
}

**=============================================**
||快速pow（多次使用时及其有效）               ||
**=============================================**
__int64 qpow(int a, int b){
    __int64 c, d; c = 1; d = a;
    while (b > 0){
        if (b & 1)
          c *= d;
        b = b >> 1;
        d = d * d;
    }
    return c;
}
**=============================================**
||快速1/sqrt(x)（牛顿迭代法）                    ||
**=============================================**
float InvSqrt (float x) {
     float xhalf = 0.5f * x;
     long i = *(long*)&x;
     i = 0x5f3759df - (i >> 1);
     x = *(float *)&i;
     x = x * (1.5f - xhalf * x * x);
     return x;
}

 

(转)

 

#include <stdio.h>
#include <math.h>

__int64 k;
//其实我也试着写了一个pow。。只不过弱爆了。。不够快。。
/*
__int64 myqpow(__int64 x, __int64 y)
{
    if (y == 1)
    {
        return x;
    }
    __int64 tmp = qpow(x, y/2);
    if (y%2 == 1)
    {
        return (tmp * tmp * x);
    }
    else
    {
        return (tmp * tmp);
    }
}
*/

__int64 qpow(int a, int b)
{
    __int64 c, d; c = 1; d = a;
    while (b > 0)
    {
        if (b & 1)
          c *= d;
        b = b >> 1;
        d = d * d;
    }
    return c;
}

__int64 solve(__int64 x, __int64 z)
{
    __int64 l = x + 1, r = 32768, y = (l + r) >> 1;//r = k - qpow(x, z)
    while (l <= r)
    {
        __int64 tmp = x * y * z + qpow(x, z) + qpow(y, z);
        if (tmp == k)
        {
            return y ;
        }
        else if (tmp > k || tmp < 0)
        {
            r = y - 1;
        }
        else
        {
            l = y + 1;
        }
        y = (l + r) >> 1;
    }
/*
    if (x * y * z + qpow(x, z) + qpow(y, z) == k)
    {
        return y ;
    }
*/
    return 0 ;
}

int main()
{
    while (scanf("%I64d", &k), k)
    {
        __int64 i, j, ans=0;
        for (i = 2; i <= 31; i++)
        {
            for (j = 1;  ; j++)
            {
                __int64 tmp1 = qpow(j, i);
                if (tmp1*2 > k || tmp1 < 0)
                {
                    break ;
                }

//                __int64 a = solve(j, i);
                if (solve(j, i))
                {
                    ans++;
//                    printf("%I64d %I64d %I64d\n", j, a, i);
                }
            }
        }
        printf("%I64d\n", ans);
    }
    return 0;
}