319 bulb switcher

Posted 2021-01-17 learning-c

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.

 

解法
求1-n中完全平方数的个数。
举例,假设n=5。

4=2x2是完全平方数。
5不是完全平方数。

对于第4个灯, 4=1x4=2x2。
n=1时，它被打开。
n=2时，它被关闭。
n=4时，它被打开。
完全平方数保证了他被操作奇数次。

对于第5个灯,5=1x5
n=1时，它被打开。
n=5时，它被关闭。

 

class Solution {
public:
  int bulbSwitch(int n) {
   return sqrt(n);
}
};