UVa 10025 the? 1? 2? ... ? n = k problem: Math & Idea question & constant algorithm

10025-the? 1? 2? ... ? n = k problem

Time limit:3.000 seconds

Http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=99&page=show_problem &problem=966

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 = expression to is used would be: -1 + 2 + 3 + 4 + 5 + 6-7 =/ with n = 7

The Input

The 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 is separated by a.

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

-3646397

Sample Output

7

2701

First of all, 1~n and sum must be >=k. When the sum is >n to subtract a number, such as adding a-number to the front of number a, which is equivalent to Sum-2 * A, which means that each drop can only be even, then a sum of 2 = k 2 is required. (negative numbers in the same vein)

O (√k) code:

/*0.006s*/
  
#include <cstdio>
#include <algorithm>
using namespace std;
  
int main (void)
{
    int T, k, sum, I;
    BOOL flag = FALSE;
    scanf ("%d", &t);
    while (t--)
    {
        if (flag)
            Putchar (' \ n ');
        else
            flag = true;
        scanf ("%d", &k);
        K = ABS (k), sum = 0;
        for (i = 1;; i++)
        {
            sum = i;
            if (sum >= k && ((sum-k) & 1) = = 0)
            {
                printf ("%d\n", I);
                break;
            }
    }} return 0;
}