（周日赛）Non-square Equation

题意：给n 求最小的x

题解：二元一次方程求解，x*x+x*b-n=0 遍历b

 

Description
Let's consider equation:

x^2 + s(x)·x - n = 0, 
where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.

You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.

Input
A single line contains integer n(1 ≤ n ≤ 1018) — the equation parameter.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

Output
Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x(x > 0), that the equation given in the statement holds.

Sample Input
Input
2
Output
1

Input
110
Output
10

Input
4
Output
-1

Hint
In the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.

In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.

In the third test case the equation has no roots.

 

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

__int64 find(__int64 x)
{
    __int64 b=0;
    while(x)
    {
        b+=x%10;
        x=x/10;
    }
    return b;
}

int main()
{
    __int64 n,i,d,x;
    while(~scanf("%I64d",&n))
    {
        __int64 ans=-1;
        for(i=1;i<=100;i++)
        {
            d=sqrt((double)(i*i+4*n));
            x=d-i;
            if(x%2==0&&find(x/2)==i)
            {
                ans=x/2;
                break;
            }
        }
        printf("%I64d\n",ans);
    }
        
    return 0;
}