319. Bulb Switcher

package LeetCode_319

/**
 * 319. Bulb Switcher
 * https://leetcode.com/problems/bulb-switcher/
 *
 * There are n bulbs that are initially off. You first turn on all the bulbs. Then, you turn off every second bulb.
 * On the third round, you toggle every third bulb (turning on if it's off or turning off if it's on).
 * For the i-th round, you toggle every i bulb. For the n-th round, you only toggle the last bulb.
 * Find how many bulbs are on after n rounds.
 *
Example:
Input: 3
Output: 1
Explanation:
At first, the three bulbs are [off, off, off].
After first round, the three bulbs are [on, on, on].
After second round, the three bulbs are [on, off, on].
After third round, the three bulbs are [on, off, off].
So you should return 1, because there is only one bulb is on.
 * */
class Solution {
    /*
    * solution: Math, Time complexity:O(sqrt(n)), Space complexity:O(1)
    * init：    X    X    X    X    X
      first：      √    √    √    √    √
      second：      √     X    √    X    √
      third：      √     X    X    X    √
      fourth：      √     X    X    √    √
      fifth：      √     X    X    √    X
       all squared bulbs will be lit
    * */
    fun bulbSwitch(n: Int): Int {
        var result = 1
        while (result * result <= n) {
            result++
        }
        return result - 1
    }
}