UVA10025 - The ? 1 ? 2 ? ... ? n = k problem

算法需要自己猜，参考了题解。

题目：

 

 The ? 1 ? 2 ? ... ? n = k problem 

 

The problem

Given the following formula, one can set operators '+' or '-' instead of each '?', in order to obtain a given k
? 1 ? 2 ? ... ? n = k

For example: to obtain k = 12 , the expression to be used will be:
- 1 + 2 + 3 + 4 + 5 + 6 - 7 = 12
with n = 7

 

The Input

The first line is the number of test cases, followed by a blank line.

Each test case of the input contains integer k (0<=|k|<=1000000000).

Each test case will be separated by a single line.

The Output

For each test case, your program should print the minimal possible n (1<=n) to obtain k with the above formula.

Print a blank line between the outputs for two consecutive test cases.

Sample Input

 

2

12

-3646397

 

Sample Output

 

7

2701

---

Alex Gevak
September 15, 2000 (Revised 4-10-00, Antonio Sanchez)

解答：

#include<stdio.h>
int main()
{
    int i,j,t;
    scanf("%d",&t);
    while(t--)
    {
        int k;
        scanf("%d",&k);
        if(k<0)
            k=-k;
        for(i=1;;i++)
        {
            if((1+i)*i/2>=k)
            {
                int flag=1,res=(1+i)*i/2;
                for(j=i;flag;)
                {
                    if((res-k)%2==0)
                        flag=0;
                    else
                    {
                        j++;
                        res+=j;
                    }
                }
                if(flag==0)
                    break;
            }
        }
        printf("%d\n",j);
        if(t)
            printf("\n");
    }
    return 0;
}