754. Reach a Number

Problem

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

You can make some number of moves numMoves so that:

• On each move, you can either go left or right.

• During the ith move (starting from i == 1 to i == numMoves), you take i steps in the chosen direction.

Given the integer target, return **the *minimum* number of moves required (i.e., the minimum numMoves) to reach the destination**.

  Example 1:

Input: target = 2
Output: 3
Explanation:
On the 1st move, we step from 0 to 1 (1 step).
On the 2nd move, we step from 1 to -1 (2 steps).
On the 3rd move, we step from -1 to 2 (3 steps).

Example 2:

Input: target = 3
Output: 2
Explanation:
On the 1st move, we step from 0 to 1 (1 step).
On the 2nd move, we step from 1 to 3 (2 steps).

  Constraints:

• -10^9 <= target <= 10^9

• target != 0

Solution (Java)

class Solution {
    public int reachNumber(int target) {
        target = Math.abs(target);
        int val = (((int) Math.sqrt(1.0 + 8 * ((long) target))) - 1) / 2;
        int sum = (val * (val + 1)) / 2;
        while (sum < target || (sum - target) % 2 != 0) {
            val++;
            sum = sum + val;
        }
        return val;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).