Reach a Number

You are standing at position 0 on an infinite number line. There is a goal at position target.

On each move, you can either go left or right. During the n-th move (starting from 1), you take n steps.

Return the minimum number of steps required to reach the destination.

Example 1:

Input: target = 3
Output: 2
Explanation:
On the first move we step from 0 to 1.
On the second step we step from 1 to 3.

Example 2:

Input: target = 2
Output: 3
Explanation:
On the first move we step from 0 to 1.
On the second move we step  from 1 to -1.
On the third move we step from -1 to 2.

Note:

target will be a non-zero integer in the range [-10^9, 10^9].

/*
Step 0: Get positive target value (step to get negative target is the
        same as to get positive value due to symmetry).
Step 1: Find the smallest step that the summation from 1 to 
        step just exceeds or equals target.
Step 2: Find the difference between sum and target. 
        The goal is to get rid of the difference to reach target. 
        For ith move, if we switch the right move to the left, the change in summation will be 2*i less. 
        Now the difference between sum and target has to be an even number in order for the math to check out.
Step 2.1: If the difference value is even, we can return the current step.
Step 2.2: If the difference value is odd, 
        we need to increase the step until the difference is even (at most 2 more steps needed).
Eg:
target = 5
Step 0: target = 5.
Step 1: sum = 1 + 2 + 3 = 6 > 5, step = 3.
Step 2: Difference = 6 - 5 = 1. Since the difference is an odd value, 
        we will not reach the target by switching any right move to the left. 
        So we increase our step.
Step 2.2: We need to increase step by 2 to get an even difference 
        (i.e. 1 + 2 + 3 + 4 + 5 = 15, now step = 5, difference = 15 - 5 = 10). 
        Now that we have an even difference, 
        we can simply switch any move to the left (i.e. change + to -) as long as 
        the summation of the changed value equals to half of the difference. 
        We can switch 1 and 4 or 2 and 3 or 5.
*/
class Solution {
    public int reachNumber(int target) {
        target = Math.abs(target);
        int step = 0;
        int sum = 0;
        while (sum < target) {
            step++;
            sum += step;
        }
        while ((sum - target) % 2 != 0) {
            step++;
            sum += step;
        }
        return step;
    }
}