319. Bulb Switcher

题目:

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 ith round, you toggle every i bulb. For the nth round, you only toggle the last bulb. Find how many bulbs are on after n rounds.

Example:

Given n = 3. 

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.

链接:  https://leetcode.com/problems/bulb-switcher/

题解:

类似智力题。划一下5个灯泡的流程图就会发现最后亮的是1号和4号灯泡。最后结果就是求在n里包含多少个完全平方数。 在Discuss里Stefan Pochmann写得很好，放在reference里。

Time Complexity - O(1)，  Space Complexity - O(1)。

public class Solution {
    public int bulbSwitch(int n) {
        if (n < 1) {
            return 0;
        }
        return (int)Math.sqrt(n);
    }
}

 

Reference:

https://leetcode.com/discuss/75014/math-solution